## 1. Implications of the Standard Urban Model (SUM)

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---

### Purpose and research questions
- Document similarities and differences between large agglomerations in high income and low income countries, focusing on economic and physical characteristics.
- Explain how cities with similar populations (e.g., close to 19 million) can differ markedly in GDP, satellite night lights, land area, building heights, and interior space.
- Assess whether population is a sufficient statistic to characterize urbanization and economic development within and across countries.
- Evaluate whether the standard urban model (SUM) can account for observed cross-country similarities and differences in city form and size.

### Key contributions
- Assembled a large merged data set of economic and physical characteristics for the world’s largest agglomerations, including GDP, land area, and structures.
- Decomposed population into component parts: land area, structure space per unit land, and population per unit interior space (crowding).
- Tested theoretical predictions of a modified SUM for both poor and rich countries, focusing on population, land area, structure density, and population density.
- Provided evidence that population is a sufficient statistic to characterize economic differences among cities within the same country, but not across countries with different urban technologies and income per capita.
- Documented that satellite night lights are strongly correlated with GDP when comparing cities across different countries.

### Main empirical findings and stylized facts
- The elasticity of city size with respect to income per capita across countries is zero (historical positive in the past).
- Developing countries are now as likely as developed countries to have large agglomerations when population is the measure.
- Urban giants in poor countries are not large by other measures (land area, interior square feet of space, or total value of output).
- Over time, rich country cities “built up” more (more structure/height) while poor country cities “densified” more (more crowding), causing poor-country cities to outgrow rich-country cities in population.
- Population identity: Population = land area × structure space per unit land × population per unit interior space (crowding).
- Satellite night lights are strongly correlated with GDP across cities in different countries; night lights may be a better proxy for economic size than population.

### Theoretical implications from the modified SUM
- In the basic SUM, city population increases with earnings opportunities relative to alternatives and with construction and transportation technologies.
- Housing price, land rent, structure density, and population density follow negative exponential functions depending on earnings and urban technology.
- Central model predictions:
  - City population varies directly with land area and structure density and inversely with housing consumption per capita.
  - The elasticity of city size with respect to earnings can be similar across countries, but the logarithmic relation between earnings and city size is shifted downward as country income per capita rises.
  - Population can be a sufficient statistic within a country (common urban technology) but is not a reliable indicator of other city characteristics across countries.
- These theoretical predictions are borne out by the assembled data.

### Methodology notes and limitations
- Merged multiple data sets because existing city databases lack comprehensive information on GDP, land area, or structures.
- Analysis focuses on correlations and descriptive decomposition rather than causal identification.
- The paper documents how population-based measures can diverge from economic development via crowding, land, and structure differences but does not fully explain the causes.

### Implications for research and policy use of population measures
- Using city population or urbanization rates as proxies for economic development can be misleading across countries with different incomes and urban technologies.
- Within-country comparisons using population remain useful as a first-order approximation when urban technology is similar.
- Satellite night lights provide a more reliable cross-country proxy for economic size than population.

### *Source: wpiea2019203-print-pdf - 1. Implications of the Standard Urban Model (SUM) (PDF chapter/section).*

---

### 2. Data on the World’s Largest Agglomerations

### Data sources and scope
- United Nations(2018): population of each urban agglomeration of at least 300,000 inhabitants every five years from 1950 to 2015 (N = 1,860).
- Demographia(2005,2017): population and land area (sq km) for many agglomerations (N = 360 circa 2000; N = 1,042 circa 2016).
- CTBUH(2018): online database of tall buildings; analysis restricted to 14,839 buildings above 80 meters.
- World Bank(2018) World Development Indicators: national per capita GDP (PPP and constant 2011 international $) for each country-year from 1990 to 2017.
- Oxford Economics(2019): per capita GDP (constant 2012 million $) for 775 agglomerations annually from 2000 to 2017 (treated as lower-quality for main income measures).
- NGDC(2015): radiance calibrated satellite night lights annually from 1996-2011.
- CIESIN(2017) GRUMPv1: geocoded polygons of urban extent boundaries circa 1995; used to sum night lights into agglomerations.

### Main sample and construction
- Main Sample: 1,010 agglomerations of at least 300,000 inhabitants in 2015 (UN) with land area in Demographia(2017).
- 405 of these agglomerations have tall buildings per CTBUH; other agglomerations assigned half a building (40 m) for conservative imputation.
- CTBUH-derived index used as proxy for stock of tall buildings (buildings above 80 meters).

### Auxiliary datasets and measurement notes
- Auxiliary: UN-Habitat(1993), AUE(2016), European Commission(2018), OECD(2018) used for robustness.
- Measurement caveats:
  - Demographia 2000 may omit many developing-country agglomerations.
  - CTBUH focuses on tall buildings and is concentrated on >80 m; missing smaller high-rise stock.
  - Oxford Economics city GDP estimates may involve interpolation/extrapolation.
  - Radiance calibrated night lights chosen to avoid top-coding issues.

---

### 3. Components of City Population Sizes

### 3.1. City population size and country economic development
- Top-100 agglomerations (2018): only 28 located in high income countries; 27 in low or lower-middle income countries.
- For 1,773 agglomerations > 300,000 in 2015, log population size has no relationship with log national per capita GDP (PPP) when controlling for log country population; weighted elasticity close to 0 and never significant.
- Evolution over time (full sample, controlling for total population): elasticity of log population size wrt log national per capita GDP:
  - 2015: -0.00
  - 2000: 0.10***
  - 1990: 0.21***
  - 1975: 0.33***
  - 1960: 0.50***
- Using population weights, elasticities:
  - 2015: 0.04
  - 2000: 0.20**
  - 1990: 0.31**
  - 1975: 0.40***
  - 1960: 0.42***
- Cross-dimension shares (Panel A, Row 1): developing-country cities
  - Population: 74.2%
  - Land Area: 50.3%
  - Interior Space: 34.4%
  - GDP (national PCGDP share): 42.1%
  - Night Lights: 23.7%
- Reclassification excluding upper-middle income countries (Panel B, Row 1): developing-country cities
  - Population: 29.7%
  - Land Area: 15.7%
  - Interior Space: 6.1%
  - GDP: 8.1%
  - Night Lights: 4.3%

### 3.2. City land area and country economic development
- Main sample (N = 1,010): regression of log city land area (sq km) on log national per capita GDP (PPP) yields coefficient 0.52*** (R2 = 0.19).
  - Interpretation: land area increases by 52% when per capita income doubles.
  - Agglomerations in high-income countries consume on average 6.0-6.8 times more land than cities in low-income countries.
- With population weights coefficient 0.58*** (R2 = 0.17).
- Controlling for log city population size yields elasticities 0.50***-0.54*** (R2 = 0.67-0.79).
- Robustness: similar elasticities using AUE(2016), built-up area measures, and other datasets; elasticity lower if dropping the U.S. (0.36***-0.43***).
- Evolution over time: balanced sample suggests elasticity decreased by 0.31-0.29 between 2000 and 2015; AUE and European Commission show mixed patterns depending on measure.

### 3.3. City building heights and country economic development
- Average building height (sum of tall building heights divided by land area) regressions (main sample N = 1,010):
  - Log average building height on log national per capita GDP (PPP): coefficient 0.34*** (R2 = 0.06).
  - Population-weighted coefficient: 0.71*** (R2 = 0.16).
  - Interpretation: average building heights increase by about one third when per capita income doubles; elasticity doubles when giving more weight to giants.
  - Alternatively: high-income country cities have on average 11 times taller tall buildings than low-income countries (3 times without weights).
- Robustness: results stable across imputations for cities without tall buildings, alternative height measures, sub-samples, and exclusion checks.
- Building use shares (for buildings with known function):
  - Residential: 49.9%
  - Offices: 41.8%
  - Hotels: 11.8%
  - Retail: 3.9%
- Evolution: for balanced sample (232 cities), elasticity increased by 0.19 (unweighted) and 0.25 (weighted) between 2000 and 2015.

### 3.4. City interior space, population density, and occupant density
- Interior space elasticity decomposition:
  - Unweighted: 0.52*** (land area) + 0.34*** (building heights) = 0.86***.
  - Population-weighted: 0.58*** + 0.71*** = 1.29***.
  - Direct regressions confirm interior space approximately doubles when per capita income doubles; elasticity higher when weighting larger cities.
  - Comparative: high-income country cities have on average 71 times more interior space than low-income country cities (18 times unweighted).
- Population density (2015, N = 1,010):
  - Regression of log city population density on log national per capita GDP: coefficient -0.50*** (R2 = 0.34).
  - Population-weighted: -0.53*** (R2 = 0.39).
  - Interpretation: agglomerations of high-income countries are 5-6 times less dense than those of low-income countries.
- Occupant density (sum of building heights per capita) (2015, N = 1,010):
  - Regression of log occupant density on log national per capita GDP: coefficient -0.84*** (R2 = 0.33).
  - Population-weighted coefficient: -1.24*** (R2 = 0.39).
  - Interpretation: occupant density more than halves when income doubles; giants of high-income countries have 60.8 times denser housing units than the ones of low-income countries (16.2 times unweighted).
- UN-Habitat (1993) floor area per person (181 cities, 1993):
  - High-income country agglomerations: about 29-30 sq m per capita.
  - Low-income country agglomerations: about 7-8 sq m per capita.
  - Log elasticity of floor area per person wrt log per capita GDP: 0.47***-0.56*** (R2 = 0.56-0.50).

### 3.5. Summary elasticities and accounting identity
- From Table 3 (columns without city population control, main sample N = 1,010):
  - Land area elasticities: 0.52/0.58 (row 3).
  - Building heights elasticities: 0.34/0.71 (row 4).
  - Occupant density elasticities: -0.84/-1.24 (row 7).
  - City population size-income elasticities: -0.00/0.04 (full sample row 1); 0.02/0.06 (main sample row 2).
  - Sum of components (Rows 3 + 4 + 6) close to 0.00 (row 8), consistent with near-zero population-income elasticity.
- Interpretation:
  - Interior space elasticity with respect to income is close to 1 and decomposes into land area and building heights elasticities.
  - Rich-country cities both consume more land and build up; poor-country cities densify existing structures (greater crowding) rather than expand interior space per capita.

---

### 4. City Economic Development and City Population Sizes

### Data and sample
- CIESIN(2017) polygons: 31,361 urban polygons/agglomerations of at least 1,000 inhabitants in 223 countries (2000); NGDC(2015) night lights used.
- Theil decomposition (night lights across agglomerations): within component and between component account for 60% and 40% (63% and 37% when using population weights).

### Urban size–night lights relation: examples and pooled results
- U.S. (year 2000, N = 5,034): log sum of night lights on log population slope = 1.04***; population-weighted slope = 0.92***.
- India (year 2000, N = 2,733): slope = 1.11***; population-weighted slope = 1.06***.
- Restricting to agglomerations above 300,000 inhabitants:
  - U.S.: slope = 0.87*** (N = 85).
  - India: slope = 1.04*** (N = 107).
- Pooled U.S. and India with country fixed effects: slope = 1.06***, R-squared = 0.80 (N = 7,767).
- World pooled baseline (log night lights on log population, no country FE): slope = 0.52***, R-squared = 0.18 (Table 8, Row 1, Col. (1)).
- World with country fixed effects: slope ≈ 1.11***, R-squared = 0.83 (Table 8, Row 2, Col. (1)).
  - Interpretation: an urban wage premium for the world of about 10% (coefficient ≈ 1.10).

### Country slopes, levels, and relation to national income
- Estimated slope of log night lights vs. log population is close to 1.10 for most countries; slope coefficient not correlated with national per capita GDP (regression effect ~ -0.00; R2 = 0.00).
- Country fixed effects (level differences relative to the U.S.) strongly correlated with national per capita GDP:
  - Coefficient of log per capita GDP: 1.00***, R2 = 0.68, N = 170 (Table 8, Row 4, Col. (1)).
  - Interpretation: high R-squared indicates population is a poor cross-country measure of urban economic development but a good within-country predictor when technology/parameters are shared.

### Key findings and implications
- Urban systems behave similarly across countries: within-country urban wage premium (how city per capita income varies with city size) is close to 10% for most countries.
- Across countries, level differences in city economic size for a given population are almost entirely explained by national income per capita.
- Urbanization patterns differ by country income:
  - Rich country cities disproportionately build “up” and “out”.
  - Poor country cities disproportionately build “in” (greater population density and crowding).
- Policy and empirical caution:
  - Avoid using city population differences alone as measures of economic size in cross-country analyses.
  - SUM provides a framework explaining how similar populations can imply very different urban forms and economic outcomes across countries.

---

### Tables and selected regression highlights (key numeric points)
- Population elasticity wrt national per capita GDP (full sample, 2015): -0.00 [0.02] (N = 1,773).
- Land area elasticity (main sample, 2015): 0.52*** [0.13] (N = 1,010).
- Average building heights elasticity (main sample, 2015): 0.34*** [0.06] (N = 1,010); population-weighted: 0.71*** [0.10].
- Interior space elasticity (main sample, 2015): 0.86*** [0.15] (unweighted); 1.28*** [0.13] (weighted).
- Population density elasticity (main sample, 2015): -0.50*** [0.11].
- Occupant density elasticity (main sample, 2015): -0.84*** [0.13]; weighted: -1.24*** [0.12].
- Evolution over time (interior space, unweighted): 1975: 0.31***; 1990: 0.50***; 2000: 0.65***; 2015: 0.86***.
- Urban wage premium from night lights (global, with country FE): ≈ 1.11*** (implying ~10% premium).

---

### Policy-relevant implications and recommended empirical practice
- For cross-country analysis of cities, do not treat population as a sufficient statistic for economic size; use direct economic measures (city GDP) or satellite night lights where available.
- For within-country analysis where urban technology and parameters are plausibly common, population can serve as a first-order sufficient statistic.
- When assessing spatial policy (land use, infrastructure, housing), account for three channels that explain population differences across cities: land area, structure (building) density, and occupant density (crowding).
- Use radiance calibrated night lights (NGDC(2015)) as a robust proxy for economic activity in cross-country urban comparisons.
- Recognize divergent development paths: richer countries have expanded interior space per capita via land and height increases; poorer countries accommodate population growth mainly through increased crowding.

*Italicized source attribution: wpiea2019203-print-pdf - 1. Implications of the Standard Urban Model (SUM) (PDF chapter/section).*

### 1. Implications of the Standard Urban Model (SUM) ............................................................... 7

### 1. Implications of the Standard Urban Model (SUM)

### Purpose and research questions
- Document similarities and differences between large agglomerations in high income and low income countries, focusing on economic and physical characteristics.
- Explain how cities with similar populations (e.g., close to 19 million) can differ markedly in GDP, satellite night lights, land area, building heights, and interior space.
- Assess whether population is a sufficient statistic to characterize urbanization and economic development within and across countries.
- Evaluate whether the standard urban model (SUM) can account for observed cross-country similarities and differences in city form and size.

### Key contributions
- Assembled a large merged data set of economic and physical characteristics for the world’s largest agglomerations, including GDP, land area, and structures.
- Opened the “black box” of cities by decomposing population into component parts: land area, structure space per unit land, and population per unit interior space (crowding).
- Tested theoretical predictions of a modified SUM for both poor and rich countries, focusing on population, land area, structure density, and population density.
- Provided evidence that population is a sufficient statistic to characterize economic differences among cities within the same country, but not across countries with different urban technologies and income per capita.
- Documented that satellite night lights are strongly correlated with GDP when comparing cities across different countries, suggesting night lights may be a better measure of economic size than population.

### Context and motivation
- Historical association between city size or fraction urbanized and country income per capita weakened during the 20th century; recent literature casts doubt on the relation between urbanization based on city populations and economic development.
- Many mega-cities in poor countries accommodate large populations via greater crowding rather than larger land area or taller buildings.
- Agriculture accounts for 3% of the world’s GDP (World Bank (2018)). If two thirds of non-agricultural activities take place in cities (as shown for a large sample of countries by Gollin et al. (2015)), potentially 65% of the world’s GDP comes from cities. McKinsey (2011a) estimate that just 600 cities generate 65% of the world’s economic growth.

### Main empirical findings and stylized facts
- The elasticity of city size with respect to income per capita across countries is zero, but was positive in the past.
- Developing countries are now as likely as developed countries to have large agglomerations when population is the measure.
- Urban giants in poor countries are not large by other measures (land area, interior square feet of space, or total value of output).
- Over time, rich country cities “built up” more (more structure/height) while poor country cities “densified” more (more crowding), causing poor-country cities to outgrow rich-country cities in population.
- Population = land area × structure space per unit land × population per unit interior space (crowding).
- Population is a sufficient statistic to compare cities within a given country (common urban technology), but not across countries with differing urban technologies and income per capita.
- Satellite night lights are strongly correlated with GDP across cities in different countries; night lights may be a better proxy for economic size than population.

### Theoretical implications from the modified SUM
- In the basic SUM, city population increases with earnings opportunities relative to alternatives and with construction and transportation technologies.
- For a given city, housing price, land rent, structure density, and population density follow negative exponential functions depending on earnings and urban technology.
- Central model predictions:
  - City population varies directly with land area and structure density and inversely with housing consumption per capita.
  - The elasticity of city size with respect to earnings can be similar across countries, but the logarithmic relation between earnings and city size is shifted downward as country income per capita rises.
  - Therefore, population can be a sufficient statistic within a country (common urban technology) but is not a reliable indicator of other city characteristics across countries.
- These theoretical predictions are borne out by the assembled data.

### Methodology notes and limitations
- Merged multiple data sets because existing city databases lack comprehensive information on GDP, land area, or structures.
- Analysis focuses on correlations and descriptive decomposition rather than causal identification.
- The paper does not attempt to explain the causes of the disconnect between population-based urbanization measures and economic development; it documents how the disconnect is physically possible (via crowding, land, structure differences).

### Implications for research and policy use of population measures
- Using city population or urbanization rates as proxies for economic development can be misleading across countries with different incomes and urban technologies.
- Within-country comparisons using population remain useful as a first-order approximation when urban technology is similar.
- Satellite night lights provide a more reliable cross-country proxy for economic size than population.

*Italicized source attribution: wpiea2019203-print-pdf - 1. Implications of the Standard Urban Model (SUM) (PDF chapter/section).*

### 1.  Implications of the Standard Urban Model (SUM)

### 1.  Implications of the Standard Urban Model (SUM)

### Setting up the basic monocentric city model
- City configuration and availability of land:
  - Radius k ∈ [0, k*], where k* is the city edge and land available for housing L = ∫_0^{k*} θ k dk with 0 < θ < 1. (Equation (1))
- Household choices and landlord pricing:
  - Utility outside city u* is the reservation utility; transportation cost to center = t k.
  - Landlord pricing problem: Max r(k) = (y − t k − p_c c)/h(k) subject to u* − u(h(k), c(k)) = 0. (Equation (2))
  - Muth’s equation: dr(k)/dk = ∆t / h(k). (Equation (3))
- Assumption: real income constant own-price elasticity of demand for housing = 1, so (r(k) h(k)) = constant = v (total expenditure on housing). This yields a negative exponential housing price gradient. (Discussion following Equation (4))

### Housing price, land rent, structure density, and population density gradients
- Housing price gradient:
  - r(k) = r_0 e^{−(t/v) k}; ln r(k) = ln r_0 − (t/v) k; dr(k)/dk = −t/v. (Equation (5))
  - Interpretation: gradient flatter if v higher or t lower.
- Housing production (Cobb-Douglas):
  - H = A L^β S^{1−β}. (Equation (6))
  - Structure/land ratio from cost minimization: S/L = [(1−β) R(k)]/[β p_s]. (Equation (7))
- Land rent gradient:
  - R(k) = [A φ r(k)^{1/β}]/[p_s^{(1−β)/β}], where φ = (1−β)^{(1−β)} β^{β}. (Equation (8))
  - d ln R(k)/dk = (1/β) d ln r(k)/dk = −t/(v β). (Equation (9))
  - Land rent decreases with distance more steeply than housing price by factor 1/β.
- Structure density gradient:
  - (H/L)(k) = A φ r(k)^{(1−β)/β} / p_s^{(1−β)/β}; ln(H/L)(k) = ln(A φ) + [(1−β)/β] ln r(k) − (1−β)/β ln p_s. (Equation (10))
  - d ln(H/L)/dk = [(1−β)/β] d r(k)/dk = −t(1−β)/(v β). (Equation (11))
  - Slope steeper than housing price but shallower than land rent.
- Population density gradient:
  - With h(k) = v / r(k) (from elasticity assumption), D(k) = (H/L)(k) / h(k) = A φ r(k)^{1/β} / (v p_s^{(1−β)/β}). (Equation (12))
  - d ln D(k)/dk = (1/β) d ln r(k)/dk = −t/(β v). (Equation (13))
  - Ordering of slopes: housing price < housing density < land rent/population density (in absolute steepness) under assumptions.

### Total population and relation to central density and gradient
- Total population:
  - N = ∫_0^{k*} θ D(k) dk = ∫_0^{k*} θ D_0 e^{−(t/(β v)) k} dk. (Equation (14))
  - Let λ = t/(β v). For large cities (e^{−λ k*} → 0): N = θ D_0 / λ^2 = θ D_0 β^2 v^2 / t^2. (Equation (16))
  - ln N = ln θ + ln D_0 − 2 ln λ = ln θ + ln D_0 − 2 ln(t/(β v)). (Equation (17))
- Implications:
  - Elasticity of population with respect to central density: d ln N / d ln D_0 = 1.
  - Holding central density constant, higher v (housing expenditure) and higher β increase population; higher t lowers population.

### Varying city size within a given country: wages, rents, and elasticities
- Mechanism for cities of different sizes within a country:
  - Open-city framework: exogenous labor productivity differences ⇒ wages y differ across cities.
  - Raising city earnings y by ∆y expands city boundary by ∆k* = ∆y / t.
  - Wage–rent relation: d ln r / d ln y = 1/η where v = η y (η = fraction of income spent on housing). Derivation: d ln y = η d ln r, so d ln r / d ln y = 1/η.
- Central density elasticity with respect to income:
  - d ln D_0 / d ln y = (1 − β) / (β η). (Equation (18))
- Elasticity of city population with respect to city earnings (urban wage premium):
  - Using ∂ ln N / ∂ ln D_0 ≈ 1 and ∂ ln N / ∂ ln λ ≈ −2 and λ = t/(β η y):
  - d ln N / d ln y = (1 − β)/(β η) + 2/η = 1/(β η) + 1/η. (Equation (20))
  - Interpretation: elasticity of household population with respect to income is constant and depends on β (share of land in housing production) and η (share of housing in income). Transportation cost t does not appear because t assumed constant within country.
- Numerical calibration (U.S. example):
  - Adopt β = 0.2 and η = 0.3. Then d ln N / d ln y = (1/(β η)) + (1/η) = 20 or inverse implies a premium of 0.05 (a 10% rise in population generated by 0.5% rise in earnings).
  - Empirical literature consensus for U.S. urban wage premium ≈ 0.05 to 0.06. Reported estimates (Chauvin et al. (2016)) OLS: U.S. 0.054, Brazil 0.052, China 0.088, India 0.077 (noting IV issues for China and India).

### Other elasticities within a country
- Elasticity of central structure density with respect to income equals that of central population density: d ln(H/L)(0) / d ln y = (1 − β)/(β η). (Derived from Equation (10) and (18))
- Elasticity of absolute value of density gradient with respect to income: −1/η (density gradients fall slightly with city size).

### Comparing cities in developed (d) and developing (g) countries
- Key decomposition:
  - N = L (H/L) (N/H): total population = land area × structure density × crowding (population per unit interior space). (Equation (21))
  - More formally: N = ∫_0^{k*} θ (H/L)(k) / h(k) dk. (Equation (22))
- Parameter contrasts likely across countries:
  - y_d » y_g ⇒ v_d » v_g ⇒ h_d > h_g (higher housing consumption per household in developed cities).
  - A_d > A_g (superior building technology in developed cities).
  - Possible β_d < β_g (developed countries better able to substitute structures for land).
  - Ambiguous sign for t_d vs t_g due to competing effects (transport technology vs higher value of time).
- Implications for spatial profiles:
  - Housing price gradient flattens with higher v and lower t (Equation (5)).
  - Structure density central level higher in developed cities due to higher A and possibly higher r(0), but structure density gradient flatter in developed cities because v is higher (Equation (11) and (23)).
  - Population central density may be lower in developed cities because ln D(k) = ln(A φ) + (1/β) ln r(k) − ln v − (1−β)/β ln p_s (Equation (24)): although A higher raises central D, much higher v in developed cities reduces central D unless p_s much lower or r(0) much higher in developing cities.
  - For identical total population, developed cities expected to have larger radius k* (larger land area), higher structure density near center but lower central population density (flatter population density gradient). Figures in the source illustrate D_d(k) flatter than D_g(k).
- Cross-country implication for sufficiency of population:
  - Holding population constant, L, (H/L), and h differ systematically with GDP per capita. Thus, population N alone is not a sufficient statistic to characterize land area, structure capital, or crowding across countries.
  - However, elasticities of output, land, or structures with respect to population need not differ across countries; in some cases they may be similar, allowing pooling in some empirical contexts.
- Employment density:
  - Parallel to housing: higher structure density in developed cities but higher space per worker (N/H lower) due to substitution of space/capital for labor as wages rise ⇒ employment density lower in developed cities near center despite more built space.

### Conclusions and empirical strategy implication
- Within a country with high population mobility and shared technology/parameters, population can act as a sufficient statistic because iso-utility conditions and common technology tie city characteristics together; the urban wage premium is a constant function of β and η (Equation (20)).
- Across countries, especially comparing developed and developing cities of the same population, population is not a sufficient statistic: land area, structure density, and interior space per household vary systematically with income and technology.
- Empirical approach signposted:
  - Use data to test SUM implications: developing-country cities are large by population but small in land area and structure capital per capita; population alone cannot characterize cross-country city differences, while within-country analyses may justify using population as a sufficient statistic in many contexts.

*Source: 1. Implications of the Standard Urban Model (SUM), wpiea2019203-print-pdf*

### 2.  Data on the World’s Largest Agglomerations

### 2.  Data on the World’s Largest Agglomerations

### Data sources and scope
- United Nations(2018): population of each urban agglomeration of at least 300,000 inhabitants every five years from 1950 to 2015 (N = 1,860). Agglomerations defined as “commuting zones” including central business districts, suburban areas, and satellite towns.
- Demographia(2005,2017): population and land area (sq km) of many agglomerations of at least 500,000 inhabitants circa 2000 (N = 360) and most agglomerations of at least 500,000 inhabitants circa 2016, used as a proxy for 2015 (N = 1,042). Notes:
  - Data imperfect for the year 2000 because many agglomerations in developing countries are omitted.
  - For 2016, estimates come from censuses and satellite imagery and are thus more reliable.
- CTBUH(2018) (Council on Tall Buildings and Urban Habitat): publicly available online database of all tall buildings in the world; research assistants extracted building characteristics (years proposed/started/completed, architectural height, height at the tip, height of the lowest occupied floor, height of the observatory, number of floors, and function “residential” or “office”).
  - Kernel distribution mode of heights is 80 meters (see Web Appendix Figure A2). Given floors of about 4 meters, this corresponds to buildings of about 20 floors.
  - Analysis restricts to 14,839 buildings above 80 meters.
  - For cities without tall buildings in CTBUH, assume they have almost no tall buildings, giving them half a building (40 m).
  - CTBUH data described as collected for more than 40 years via an extensive member network and an Editorial Board; dataset appears reliable and used to construct an index of the stock of tall buildings for each city.
- World Bank(2018) World Development Indicators: national per capita GDP (PPP and constant 2011 international $) for each country-year from 1990 to 2017.
  - Per capita GDP growth rates from Maddison(2008) (in 1990 Geary-Khamis dollars, equivalent to PPP and constant international $) used to reconstruct per capita GDP from 1950 to 1990.
  - To avoid contamination by fluctuations in factors like commodity prices, two-year moving averages are used.
- Oxford Economics(2019): per capita GDP (constant 2012 million $) for 775 agglomerations annually from 2000 to 2017. Methodology notes:
  - Used detailed national accounts data or estimates provided by city administrations; when unavailable, used per capita GDP for regions encompassing agglomerations.
  - Because estimates may have been spatially and/or temporally interpolated and/or extrapolated, quality is not considered high and this is not used as the main income data source.
- NGDC(2015): satellite night lights data used as a proxy for economic activity; available annually from 1996-2011 at fine spatial resolution.
  - Radiance calibrated version used to avoid issues related to top-coding, especially for cities. Radiance calibrated data imply that night light intensity can go beyond the typical upper-bound of 63.
- CIESIN(2017) Global Rural-Urban Mapping Project: geocoded polygons of urban extent boundaries circa 1995; provides urban population of each polygon in 1990 and 2000.
  - Using GIS, sum of satellite night lights in each polygon obtained from 1996 to 2011 and matched to agglomerations in the sample.
  - 31,361 urban polygons have a non-zero population in their sample. Minimal population in the sample is 1,000 for many countries.
  - Analysis focuses on large agglomerations of at least 300,000 inhabitants, with additional analyses including all cities above 1,000 inhabitants.

### Main sample and construction
- Main Sample: 1,010 agglomerations of at least 300,000 inhabitants in 2015 in United Nations(2018) and data on land area in Demographia(2017). (Web Appx. Fig. A3 shows their location.)
  - 405 of these agglomerations have tall buildings (per CTBUH). For other agglomerations, they are assigned half a building (40 m).
- CTBUH-derived index: used as a proxy for the stocks of all buildings, restricted to buildings above 80 meters (14,839 buildings).

### Auxiliary datasets for robustness checks
- UN-Habitat(1993): key indicators collected in 237 cities circa 1993; reliability uncertain and sample not representative of the world.
- AUE(2016): global sample of 200 cities intended to be representative of agglomerations of 100,000 people or more in 2010.
  - Data reported for 1990, 2000, and 2014 (used as a proxy for 2015) for some variables; other variables reported for “pre-1990” (proxy for 1990) and “1990-2015” (both 2000 and 2015).
  - Data created based on census estimates and satellite imagery; quality appears relatively high.
- European Commission(2018): reports for 1970, 1990, 2000 and 2015 estimates of land areas and populations for 11,836 cities of at least 50,000 inhabitants in 2015.
  - Land areas obtained using satellite images and machine learning to identify building footprints and distinguish urban agglomerations. Advantage: consistent methodology across all cities and countries; caveat: a common algorithm may miss city- or country-specific idiosyncrasies.
- OECD(2018): reports per capita GDP (in nominal USD) for 281 agglomerations in 29 countries annually from 2000-2014. Only one developing country, Mexico, is included.

### Notes on measurement choices and data quality
- Demographia 2000 data may omit many developing-country agglomerations and provides little detail on how land areas were obtained.
- CTBUH does not use a consistent definition of tall buildings according to its website; empirical mode at 80 meters motivates focusing on buildings above 80 meters.
- Oxford Economics city-level GDP estimates may involve spatial and temporal interpolation/extrapolation; treated as lower-quality for main income measures.
- NGDC radiance calibrated night lights chosen to avoid top-coding issues in intensity measures.
- CIESIN urban polygons likely attempt to capture most cities of at least 1,000 inhabitants, but urban character of small settlements (1,000 to even 10,000) is problematic for analysis focusing on large agglomerations.

*Source: wpiea2019203-print-pdf - 2.  Data on the World’s Largest Agglomerations.*

### 3.  Components of City Population Sizes

### 3.  Components of City Population Sizes

### 3.1. City Population Size and Country Economic Development
- Location of Urban giants:
  - Among the 100 top largest agglomerations in the world in 2018 (source: United Nations(2018)), only 28 are located in high income countries, and 27 are located in low or lower-middle income countries.
  - Among the top 10 mega-cities, 4 of them are located in lower-middle income countries.
- Income elasticity of city population size:
  - For 1,773 agglomerations of more than 300,000 inhabitants in 2015, there is no relationship between log population size and economic development proxied by log national per capita GDP (PPP).
  - Column (1) of row 1 in Table 3 reports the elasticity of log population size wrt log per capita GDP controlling for log country population in 2015; when weighting observations by their population size in 2015 (giving more weight to the giants), the elasticity is close to 0 and never significant.
  - Similar low elasticities are found for the main sample (N = 1,010).
  - Standard errors are clustered at the country level in all regressions.
- Robustness:
  - Low elasticities are also obtained for 300K+ agglomerations using other datasets and their population estimates for 2015: Demographia(2017) (N = 1,040), European Commission(2018) (N = 1,549), and AUE(2016) (N = 162).
  - Elasticities remain unchanged when dropping each country one by one or when removing the largest cities of each country (studying non-primate cities only).
  - National per capita GDP is strongly correlated with both city per capita GDP (source: Oxford Economics(2019); correlation 0.91-0.92) and night lights per capita (source: NGDC(2015); correlation 0.78-0.81). The between component accounts for 91-93% and 67-68% of the variation in city per capita GDP and night lights per capita, respectively.
  - Low elasticities are also found when using city per capita GDP (cols. (5)-(6)) or night lights per capita (cols. (7)-(8)), for both the full sample (N = 746-745) and the main sample (N = 694-693).
- Evolution over time:
  - For the full sample of 1,773 agglomerations controlling for total population, the elasticity of log population size wrt log national per capita GDP was:
    - -0.00 in 2015
    - 0.10*** in 2000
    - 0.21*** in 1990
    - 0.33*** in 1975
    - 0.50*** in 1960
  - Using population weights, the elasticities were:
    - 0.04 in 2015
    - 0.20** in 2000
    - 0.31** in 1990
    - 0.40*** in 1975
    - 0.42*** in 1960
  - The decrease in elasticity over time is driven by developing country cities becoming larger given a certain income level; large cities of developing countries, especially their urban giants, outgrew the cities of developed countries over time.
- Other dimensions of city size (Panel A, Row 1):
  - Cities in developing countries make up 74.2% of the total population of the sample but account for:
    - 50.3% of total land area
    - 34.4% of total interior space
    - 42.1% of total GDP
    - 23.7% of night lights
  - Results hold when focusing on 1,009 agglomerations with data across all dimensions (Row 2).
- Reclassification (Panel B, Row 1):
  - When reclassifying upper-middle income countries as developed, cities in developing countries make up 29.7% of population but account for:
    - 15.7% of land area
    - 6.1% of interior space
    - 8.1% of GDP
    - 4.3% of night lights
  - These patterns are not driven by compositional biases.
- Decomposition insight:
  - Differences among cities with comparable populations can be decomposed into three components: land area, average building height, and occupant density. Subsequent sections investigate how these vary with per capita national and city incomes.

*Source: wpiea2019203-print-pdf - 3.  Components of City Population Sizes*

### 3.2. City Land Area and Country Economic Development
- Income elasticity of city land area (main sample N = 1,010):
  - Regressing log city land area (sq km) on log national per capita GDP (PPP) gives coefficient 0.52*** (R2 = 0.19) — reported in column (1) of row 3 in Table 3.
  - Interpreted: land area of urban agglomerations increases by 52% when per capita income doubles.
  - Alternatively, agglomerations in high-income countries consume on average 6.0-6.8 times more land than cities in low-income countries.
  - When weighting by city population, coefficient becomes 0.58*** (R2 = 0.17).
  - Controlling for log city population size yields elasticities 0.50***-0.54*** (R2 = 0.67-0.79, cols. (3)-(4)).
  - Implication: more land available per capita in cities of richer countries due to higher incomes and better commuting technologies; higher incomes induce more housing consumption and higher capital-labor ratios, increasing land per capita needed for both housing and production.
- Robustness checks:
  - Log land area in Demographia(2017) correlates with log land area in AUE(2016) (0.91; N = 140) and European Commission(2018) (0.78-0.87; N = 1,007).
  - Elasticity remains close to 0.5 using AUE(2016) (col. (2)); using residential built-up or non-residential built-up area yields very similar elasticities (built-up areas account for 70% of total land area, of which two thirds is “residential”).
  - Using European Commission(2018) data, elasticities become smaller only if using total land area (col. (3)), not if using built-up area estimates (col. (4)).
  - Dropping each country one by one leaves elasticities unchanged except when dropping the U.S., where elasticities are lower at 0.36***-0.43***; U.S. cities disproportionally consume land given income level.
  - Dropping primate cities raises elasticities to 0.66***-0.71*** (N = 863).
  - City land area in Demographia(2017) is available for 1,010 out of 1,773 agglomerations; regressions of a dummy for availability on log national per capita GDP find negative significant coefficients (0.015/0.026**; N = 1,773), indicating the dataset misses large agglomerations in developed countries. Results hold if weights make the main sample representative of the income distribution of the full sample (col. (5)).
  - Using other per capita income measures: similar elasticities for city per capita GDP (Oxford Economics(2019); N = 694; col. (6)); lower elasticities for night lights per capita (0.31***-0.35***; NGDC(2015); N = 1,009; col. (7)).
- Evolution over time:
  - Balanced sample of 232 cities (in both Demographia(2005) and Demographia(2017)) shows elasticity decreases by 0.31-0.29 between 2000 and 2015; given 2015 elasticities of 0.52-0.58, that implies elasticities of about 0.83-0.87 in 2000 (balanced sample caveat).
  - AUE(2016) (N = 162) elasticities: 0.55***-0.61*** in 2015 (col. (3)), 0.62***-0.65*** in 2000 (col. (8)), 0.72***-0.75*** in earlier period (col. (9)) — indicating reduction over time.
  - Using built-up area data from European Commission(2018), elasticities are relatively similar in 2015, 2000, 1990 and 1975 (cols. (5) and (10)-(12)).
  - Interpretation: elasticity of land use wrt income per capita either decreased or remained stable over time; land expansion either became relatively more important or remained as important for poorer countries.
  - In AUE(2016), lower elasticities over time arise from cities in developing countries using relatively more land over time; European Commission(2018) shows across-the-board increases in city land areas.

*Source: wpiea2019203-print-pdf - 3.  Components of City Population Sizes*

### 3.3. City Building Heights and Country Economic Development
- Constructing average building height:
  - Average height = sum of tall building heights (m) divided by land area (sq km); analysis restricted to main sample of 1,010 agglomerations.
- Income elasticity of building height:
  - Regressing log average building height (m) on log national per capita GDP (PPP) yields coefficient 0.34*** (R2 = 0.06).
  - When weighting by city population, coefficient becomes 0.71*** (R2 = 0.16).
  - Controlling for log city population size, elasticities are 0.33*** and 0.68*** respectively (R2 = 0.16 and 0.35).
  - Interpretation: average building heights increase by about one third when per capita income doubles; elasticity doubles when giving more weight to the giants.
  - Alternatively, cities in high-income countries have on average 11 times taller tall buildings than cities in low-income countries (3 times without weights).
- Robustness and measurement considerations:
  - Data from CTBUH(2018) capture tall buildings above 80 m (~20 floors).
  - Emporis(2019) captures high-rise buildings above 35 m and classifies skyscrapers above 100 m. Correlations:
    - Correlation between number of skyscrapers (Emporis) and number of buildings above 100 m (this data) is 0.85 (0.86 with weights; N = 94).
    - Correlation between Emporis number of skyscrapers and their Skyline Index is 0.88 (0.86 with weights; N = 100).
  - Regressing Skyline Index on number of skyscrapers and then residuals (capturing 35-100 m buildings) on national per capita GDP yields no effect (population weights or not).
  - Land area known for 1,040 cities from Demographia(2017); only 405 have tall buildings in building data. Assumed height of 40 m for remaining 635 cities; elasticities remain similar if:
    - dropping cities without buildings (col. (2))
    - giving these cities one third (27 m) or two thirds (53 m) of a building (cols. (3)-(4))
  - Elasticities unchanged if heights not imputed using number of floors (col. (5)) or if using raw architectural heights.
  - Results hold when limiting to countries where CTBUH(2018) website languages are official (col. (6)).
  - Using only taller buildings (25th percentile height 100 m, col. (7); median height 125 m, col. (8); mean height 135 m, col. (9)) yields similar results.
  - Results hold using weights making main sample representative of income distribution of full sample (col. (10)).
  - Addressing possible reporting bias:
    - Dropping countries in bottom or top 10% in income per capita does not change elasticity (cols. (11)-(12)).
    - Dropping cities in top 10% by number of buildings does not change results (col. (13)).
    - Dropping cities in bottom or top 10% of city size does not change results (cols. (14)-(15)).
    - Elasticities unchanged if dropping each country one by one.
- Building use and sub-sample elasticities:
  - 48% of buildings and 47% of the building stock are used for residential purposes.
  - Shares for offices: 44% of buildings and 47% of building stock.
  - Elasticities for non-residential buildings: 0.23*** and 0.61*** (not shown).
  - Elasticities for office buildings: 0.19*** and 0.59*** (not shown).
  - For residential buildings: 0.03 without weights and 0.48*** with weights (not shown).
  - Elasticities increase if using city per capita GDP (col. (16)), decrease when using lights (col. (17)).
- Evolution over time:
  - Land area used to compute average building heights observed for 2015 from Demographia(2017).
  - For 232 cities that exist in Demographia(2005) and Demographia(2017), elasticity increased by 0.19 (unweighted) and 0.25 (weighted) between 2000 and 2015.
  - Given 2015 elasticities of 0.34 (unweighted) and 0.71 (weighted), implied elasticities circa 2000 would be approximately 0.15 and 0.46 respectively for that balanced sample.

*Source: wpiea2019203-print-pdf - 3.  Components of City Population Sizes*

### 2000.   If  we  use  land  areas  fromAUE(2016),  we  find  that  the  unweighted  elasticity  increased

### wpiea2019203-print-pdf - 2000.   If  we  use  land  areas  fromAUE(2016),  we  find  that  the  unweighted  elasticity  increased

### Elasticities of building heights and land area over time
- Using AUE(2016) land areas, the unweighted elasticity increased from 0.25* in 1990 to 0.47*** in 2000 and 0.71*** in 2015; the weighted elasticity increased from 0.50*** to 0.62*** and 0.91*** (col. (18)-(20)).
- Using European Commission (2018) land areas, the unweighted elasticity increased from 0.05 in 1975 to 0.23** in 1990, 0.37*** in 2000 and 0.60*** in 2015; the weighted elasticity increased from 0.44** to 0.60***, 0.74*** and 0.95*** (col. (21)-(24)).
- Across different data sets, elasticities increase by about 0.15-0.20 between 1975 and 1990, 0.15-0.20 between 1990 and 2000, and 0.20-0.30 between 2000 and 2015.
- Higher elasticities over time in AUE(2016) and European Commission(2018) stem from:
  - Cities in developing countries having decreasing average building heights while land area disproportionately increases.
  - Cities in developed countries having increasingly taller buildings.
- If focusing on larger cities, rising elasticities are mostly due to taller buildings in richer countries.
- Similar patterns obtained using built-up areas instead of total land areas (not shown).

### City interior space and income (elasticities and evolution)
- Interior space elasticity decomposition (not weighting by population): 0.52*** + 0.34*** = 0.86***.
- Interior space elasticity decomposition (weighting by population): 0.58*** + 0.71*** = 1.29***.
- Direct regression of log sum of building heights on log national per capita GDP confirms interior space elasticity: interior space approximately doubles when per capita income doubles.
- The elasticity is 50% higher when more weight is given to larger cities, due to taller buildings there.
- Comparative magnitudes: cities in high-income countries have on average 71 times more interior space than cities low-income countries (18 times when not using weights).
- Evolution over time (unweighted interior space-income elasticities):
  - 1975: 0.31***.
  - 1990: 0.50***.
  - 2000: 0.65***.
  - 2015: 0.86*** (see Col. (1)-(4) of row 1 in Table7).
- Evolution over time (weighted interior space-income elasticities):
  - 1975: 0.79***.
  - 1990: 0.95***.
  - 2000: 1.08***.
  - 2015: 1.28*** (row 2).
- These increases are disproportionately driven by richer countries building up; area-income elasticities did not increase comparably.

### City population density and income
- Cross-section (2015, N = 1,010):
  - Regression of log city population density on log national per capita GDP: coefficient -0.50*** (R2 = 0.34; N = 1,010; col. (1) of row 6 in Table3).
  - Population-weighted coefficient: -0.53*** (R2 = 0.39; N = 1,010; col. (2)).
- Interpretation: agglomerations of high-income countries are 5-6 times less dense than those of low-income countries.
- Robustness checks yield similar elasticities.
- Evolution over time depends on land area data set:
  - Using Demographia(2017): density-income elasticity slightly increased over time by about 0.14-0.16; given -0.50/-0.53 in 2015, implies -0.34/-0.39 in 2000.
  - Using AUE(2016): elasticities remained similar over time, at -0.46***/-0.46*** in 1990 and -0.48***/-0.53*** in 2015.
  - Using European Commission(2018): elasticities decreased over time, from -0.17/-0.23*** in 1975 to -0.44***/-0.49*** in 2015.
- Different land area data sets produce different pictures of population density patterns.
- Similar patterns obtained using built-up areas instead of total land areas (not shown).

### City occupant density and income (within-unit crowding)
- Occupant density defined as sum of building heights (m) per capita proxy (assumes cities without tall buildings have half a tall building (40 m)).
- Cross-section (2015, N = 1,010):
  - Regression of log city occupant density on log national per capita GDP: coefficient -0.84*** (R2 = 0.33; N = 1,010; col. (1) of row 7 in Table3).
  - Population-weighted coefficient: -1.24*** (R2 = 0.39; col. (2)).
- Interpretation:
  - Occupant density more than halves when income doubles.
  - Giants of high-income countries have 60.8 times denser housing units than the ones of low-income countries (16.2 times when not using weights).
- UN-Habitat(1993) floor area per person (181 cities, 1993):
  - Residents of high-income country agglomerations: about 29-30 sq m per capita.
  - Residents of low-income country agglomerations: about 7-8 sq m per capita.
  - Log elasticity of floor area per person with respect to log per capita GDP: 0.47***-0.56*** (R2 = 0.56-0.50).
  - Restricted sample (128 agglomerations of at least 300,000 inhabitants in 2015): elasticities 0.44*** and 0.56***.
- Evolution of occupant density elasticities:
  - Unweighted elasticity decreased from 0.02 in 1975 to -0.25, -0.52*** and -0.84*** in 1990, 2000 and 2015, respectively (see Col. (5)-(8) of row 1 in Table7).
  - Weighted elasticity decreased from -0.47** in 1975 to -0.68***, -0.91*** and -1.24*** in 1990, 2000 and 2015, respectively (row 2).
- Decreases driven by occupant densities increasing in poor-country cities and decreasing in rich-country cities.

### Summary of main elasticities and accounting identities
- In columns (1)-(2) of Table3 (no control for city population size), estimated elasticities:
  - Land area elasticities: 0.52/0.58 (row 3).
  - Building heights elasticities: 0.34/0.71 (row 4).
  - Occupant density elasticities: -0.84/-1.24 (row 7).
- Estimated city population size-income elasticities: -0.00/0.04 (row 1) for full sample; 0.02/0.06 for main sample (row 2).
- The sum of the three component elasticities is close to 0.00 (row 8), consistent with the estimated elasticities of city population size.
- Implications:
  - Interior space elasticity with respect to income is close to 1 and decomposes into land area and building heights elasticities.
  - Cities can increase space per capita by building out or building up.
  - Cities in richer countries both consume more land and "skyscraperize"; cities in poorer countries do not expand interior space per capita as fast and pack in more inhabitants in existing structures.
  - For the largest cities, richer-country giants disproportionately build up; largest cities in poorer countries disproportionately densify existing structures.

### Interpretation of cross-country differences and drivers
- Higher incomes lead to higher land values, explaining greater land use and taller buildings in richer countries.
- Building heights increased disproportionately in rich countries for a given income level → possible improvements in building technologies and/or regulatory permissiveness over time in rich countries.
- Land areas disproportionately increased in poor countries for a given income level → possible improvements in transportation technologies there.
- Net urban technology improvement has been relatively greater in richer countries, driven more by increases in heights than by land expansion in poor countries.
- The massive relative increase in population in poor-country cities likely resulted from rural earnings decreasing faster than city earnings.

*Source: wpiea2019203-print-pdf - 2000.   If  we  use  land  areas  fromAUE(2016),  we  find  that  the  unweighted  elasticity  increased*

### 4.  City Economic Development and City Population Sizes

### 4.  City Economic Development and City Population Sizes

### Data and sample
- Analysis focused on 31,361 urban polygons/agglomerations of at least 1,000 inhabitants in 223 countries in 2000 (CIESIN(2017)).
- Night lights data (sum of radiance calibrated night lights in 2000) from NGDC(2015).
- When using Theil decompositions, the within component and the between component account for 60% and 40% (63% and 37% when using population as weights) of the variation in night lights across agglomerations.
- For cross-country analyses restricted to countries with at least 5 cities of 1,000 inhabitants or more: 171 countries, N = 28,259.

### Relationship for Cities in the U.S. and India
- Samples: U.S. N = 5,034; India N = 2,733 (year 2000).
- Log sum of night lights regressed on log population:
  - Slope for the U.S.: 1.04***.
  - Slope for India: 1.11***.
- Using city populations as weights (gives more weight to giants):
  - Weighted slope for the U.S.: 0.92***.
  - Weighted slope for India: 1.06***.
- Restricting to agglomerations above 300,000 inhabitants (N = 85 for U.S., N = 107 for India):
  - Slope for the U.S.: 0.87***.
  - Slope for India: 1.04***.
- Pooling U.S. and India samples with country fixed effects:
  - Slope: 1.06***, R-squared: 0.80, N = 7,767 (not shown).
- Pooled without fixed effects:
  - Slope: 0.39***, R-squared: 0.13 (not shown).
- U.S. fixed effect coefficient (relative to India): 3.74*** (implying U.S. cities have 3.74 log points more night lights than India cities).
- Example levels: log sum of night lights = 7.9 for the average U.S. city in the sample; 16.0 for New York.

### Relationship for the Whole World (Urban Wage Premium)
- Pooling all cities (baseline regression of log night lights on log population):
  - Slope: 0.52***, R-squared: 0.18 (see Column (1) of Row 1 in Table 8).
- Adding country fixed effects:
  - Slope: 1.11***, R-squared: 0.83 (Col. (1) of Row 2).
  - Interpretation: coefficient of about 1.10 suggests an urban wage premium for the world of 10%.
- Alternative datasets and samples (selected):
  - United Nations (2018): 1,590 cities above 300,000 inhabitants (2015) — results reported in column (2).
  - Oxford Economics (2019): 593 cities (2000 and 2015) — columns (3)-(4); includes city per capita GDP.
  - European Commission (2018): 11,261 cities above 50,000 inhabitants (2015) — column (5); uses their night lights estimates.
  - OECD (2018): 250 cities (2003 and 2012) — columns (6)-(7); city per capita GDP provided; Mexico only developing country included.
- Overall finding across datasets: with only one exception (col. (2) of row 2), the urban wage premium for the world is close to, or above, 10%.
- Using number of observations in the country as weights yields similar coefficients and R-squared (col. (8)).
- Caveats on interpreting urban wage premium from night lights or GDP per capita:
  - Omitted variable bias: education/human capital may rise with city size, biasing coefficients upward.
  - Variation in the share of labor in output with city size could bias estimated urban wage premium upward if labor share varies inversely with city size.
  - Authors anticipate the estimated elasticity may be biased upward; do not quantify how bias varies with country income.

### Urban Wage Premium for Each Country and Country Effects
- Estimated slope of log night lights vs. log population is close to 1.10 for most countries (Figure 11).
- Slope coefficient is not correlated with national per capita GDP:
  - Regression of country slope on national per capita GDP yields effect -0.00 (R2 = 0.00, col. (1) of row 3).
  - Restricting to countries with at least 10, 25, or 50 cities yields coefficients -0.02 (N = 144; R2 = 0.01), -0.02 (N = 106; R2 = 0.02), and 0.01 (N = 68; R2 = 0.00), respectively (not shown).
  - Restricting sample to cities above 300,000 inhabitants: coefficient -0.03 (N = 44; R2 = 0.01; not shown).
- Using alternative datasets or weighting by number of city-year observations still shows little or no correlation between country slopes and national per capita income (cols. (2)-(8) of row 3); R-squared usually small.
- Country fixed effects (relative to the U.S.) plotted against national per capita GDP (PPP, constant 2011 international dollars) in 2000 show a strong and significant negative relationship:
  - Coefficient of log per capita GDP: 1.00***, R2 = 0.68, N = 170 (col. (1) of row 4).
  - Restricting to countries with at least 10, 25, or 50 cities, coefficients remain positive and significant: 1.01*** (N = 144; R2 = 0.68), 1.02*** (N = 106; R2 = 0.74), 1.08*** (N = 68; R2 = 0.72) (not shown).
  - Restricting to cities of at least 300,000 inhabitants: coefficient 0.95*** (N = 44; R2 = 0.67, not shown).
- Interpretation: high R-squared indicates population is a poor measure of urban economic development across countries but a good measure within countries.
- Level differences between countries remain strongly correlated with national per capita income across alternative datasets and weighting schemes (cols. (2)-(8) of row 4).

### Key findings and implications
- Urban systems behave relatively similarly across countries: the urban wage premium (how city per capita income varies with city size within a same country) is close to 10% for most countries.
- Model illustration: if the share of land in housing and the share of housing in income are both one third, the urban wage premium is about 8%.
- Rich country cities are much wealthier than poor country cities for a given city size; these level differences are almost entirely explained by national income levels.
- Consequently, across countries, city size does not correlate with city per capita income, but within countries population is a sufficient statistic to characterize city differences.
- Urbanization patterns differ by country income:
  - Rich country cities disproportionately build “up” and “out”.
  - Poor country cities disproportionately build “in” with much greater population density.
  - Rich country cities have greater structure density, but poor country cities have relatively greater crowding.
- Policy and empirical caution:
  - Use caution when using differences in city population as a measure of city size or urbanization in empirical or policy analyses, especially in cross-country comparisons.
  - The SUM potentially explains differences in the relationship between city population sizes and economic development across countries and remains relevant.

*Source: IMF Working Paper — Chapter 4, "City Economic Development and City Population Sizes"*

### REFERENCES

### REFERENCES

### Major themes covered in the cited literature
- Urbanization drivers and consequences: Atlantic trade, colonial legacies, industrialization, demography, rural-urban migration, political economy of urbanization, and historical experiments (e.g., Acemoglu et al.; DeLong & Shleifer; Gollin, Jedwab & Vollrath; Nunn & Qian; Jedwab & Moradi).
- Spatial structure, land use, and urban form: monocentric models, negative exponential population densities, rent gradients, agglomeration economies, land-use regulation and building-height restrictions, and squatting/formalization (e.g., Muth; Mills; Brueckner; Bertaud & Brueckner; Saiz).
- Measurements and data sources: use of nightlights and satellite data, Global Radiance Calibrated Nighttime Lights, GRUMP, CTBUH skyscraper data, Demographia land areas, Oxford Economics city GDP estimates, World Bank and UN urbanization statistics (e.g., Henderson et al.; Donaldson & Storeygard; NGDC; CIESIN; CTBUH; Demographia; Oxford Economics).
- City growth, sprawl, transportation, and infrastructure impacts: highways, subways, colonial railways, and transport revolutions (e.g., Baum-Snow; Gonzalez-Navarro & Turner; Jedwab & Storeygard).
- Comparative urban studies across income levels and regions: developing vs. developed countries, African urbanization, Latin America, China, India, Brazil, and the United States (e.g., Glaeser; Henderson et al.; Bruederle & Hodler; Chauvin et al.; Deng et al.).
- Built environment metrics: tall building heights, average building height, interior space measures, and their relation to GDP and population (e.g., Ahlfeldt & McMillen; Barr; Liu, Rosenthal & Strange; CTBUH).

### Data and sources explicitly referenced
- World Bank (2018) — national per capita GDP (PPP, constant 2011 international $)
- United Nations (2018) — city population
- Oxford Economics (2019) — city GDP (cst 2012 million $)
- NGDC (2015) — radiance calibrated night lights
- Demographia (2017) — city land area
- CTBUH (2018) — tall building heights and sum of tall building heights
- Additional datasets and compilations: AUE Atlas of Urban Expansion (2016), CIESIN GRUMPv1 (2017), Global Human Settlement (European Commission 2018), NGDC Global Radiance Calibrated Nighttime Lights (2015), UN-Habitat Global Urban Indicators Database Version 1 (1993), World Development Indicators (World Bank 2018), OECD Metropolitan Areas Database (2018), Emporis (2019), McKinsey Urban world series (2011, 2012)

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### TABLES AND KEY STATISTICS

### Table 1: RELATIVE SIZE OF SELECTED URBAN AGGLOMERATIONS, CIRCA 2015
- Reference city: New York
  - National Per Capita GDP ($, PPP): 52,354
  - City Population (000s): 18,648
  - City GDP (millions $): 1,489,896
  - City Sum of Night Lights: 5,077,941
  - City Land Area (sq km): 11,875
  - City Avg. Tall Building Height (m): 131
  - City Sum of Tall Building Heights (km): 54
- Percentage differences (%) relative to New York City (Columns (2)-(7)):
  - Beijing: 13,089 -1 -77 -81 -65 -83 -94
  - Sao Paulo: 14,659 12 -71 -79 -74 -59 -89
  - Mexico: 16,753 14 -81 -79 -80 -72 -94
  - Cairo: 9,947 1 -94 -85 -84 -88 -98
  - Mumbai: 5,759 4 -92 -95 -63 -76 -91
  - Dhaka: 3,141 -6 -97 -99 -97 -90 -100
- Notes: Average tall building height in column (6) computed by dividing the city sum of tall building heights by city land area.

### Table 2: RELATIVE SIZE OF CITIES IN DEVELOPING COUNTRIES, CIRCA 2015
- Panel A: % in Developing Country Cities, Including Upper-Middle Income Countries
  - 1. Unbalanced Sample: Population 74.2, Land Area 50.3, Interior Space 34.4, National PCGDP 42.1, Night Lights 23.7
    - Observations: 1,773; 1,010; 1,773; 1,773; 1,765
  - 2. Balanced One (Data for the 5 Dim.): Population 74.4, Land Area 50.3, Interior Space 34.7, National PCGDP 42.1, Night Lights 27.2
    - Observations: 1,009 for all five variables
- Panel B: % in Developing Country Cities, Excluding Upper-Middle Income Countries
  - 1. Unbalanced Sample: Population 29.7, Land Area 15.7, Interior Space 6.1, National PCGDP 8.1, Night Lights 4.3
    - Observations: 1,773; 1,010; 1,773; 1,773; 1,765
  - 2. Balanced One (Data for the 5 Dim.): Population 30.6, Land Area 15.6, Interior Space 6.2, National PCGDP 8.3, Night Lights 4.7
    - Observations: 1,009 for all five variables
- Notes: Developing country classification based on World Bank 2016 (low-income, lower-middle income, upper-middle income). Balanced sample includes agglomerations for which all 5 variables are available.

### Table 3: SUMMARY OF ELASTICITIES AND DECOMPOSITION OF POPULATION, 2015
- Elasticities of city outcomes with respect to National Per Capita GDP (columns show different controls; standard errors in brackets)
  - 1. Population Size (Full Sample; N = 1,773): -0.00 [0.02]; 0.04 [0.08]; -0.00 [0.02]; 0.04 [0.08]
  - 2. Population Size (Main Sample; 1,010): 0.02 [0.03]; 0.06 [0.09]; 0.02 [0.03]; 0.06 [0.09]
  - 3. Total Land Area (Main Sample; 1,010): 0.52*** [0.13]; 0.58*** [0.12]; 0.50*** [0.11]; 0.54*** [0.12]
  - 4. Avg. Build. Heights (Main Sample; 1,010): 0.34*** [0.06]; 0.71*** [0.10]; 0.33*** [0.06]; 0.68*** [0.11]
  - 5. Interior Space (Main Sample; 1,010): 0.86*** [0.15]; 1.28*** [0.13]; 0.83*** [0.12]; 1.22*** [0.14]
  - 6. Population Density (Main Sample; 1,010): -0.50*** [0.11]; -0.53*** [0.12]; -0.50*** [0.11]; -0.54*** [0.12]
  - 7. Occupant Density (Main Sample; 1,010): -0.84*** [0.13]; -1.24*** [0.12]; -0.83*** [0.12]; -1.22*** [0.14]
  - 8. Sum of Rows 3, 4 and 6: 0.02 [0.03]; 0.05 [0.09]; -0.00 [0.00]; -0.00 [0.00]
  - 9. Diff. btw Row 8 and Row 2: 0.00 [0.00]; -0.00 [0.00]; -0.02 [0.03]; -0.06 [0.09]
  - 10. Diff. btw Row 8 and Row 1: 0.02 [0.02]; 0.01 [0.02]; 0.00 [0.02]; -0.04 [0.08]
- Sample definitions and controls:
  - Full sample: 1,773 urban agglomerations (≥ 300,000 inhabitants, 2015)
  - Main sample: 1,010 agglomerations with land area available
  - Rows 1-2 control for log total population of the city’s country. Columns (3)-(4) control for log total population of the city in rows 3-7.
  - Standard errors clustered at the country level.

### Table 4: POPULATION-INCOME ELASTICITY, ROBUSTNESS CHECKS
- Robustness checks (row 1 = No Pop. Weights; row 2 = Pop. Weights). Standard errors in brackets; observations by column:
  - Checks and estimates (columns (1)-(6)):
    - (1) 2015: No Pop. Weights 0.00 [0.02]; Pop. Weights 0.04 [0.08]; Observations 1,773
    - (2) Demographia: No Pop. Weights 0.00 [0.03]; Pop. Weights 0.00 [0.03]; Observations 1,040
    - (3) GHS AUE: No Pop. Weights 0.01 [0.05]; Pop. Weights 0.01 [0.04]; Observations 1,549
    - (4) City PCGDP: No Pop. Weights 0.08 [0.07]; Pop. Weights 0.09 [0.07]; Observations 162
    - (5) City Lights: No Pop. Weights 0.15 [0.10]; Pop. Weights 0.18* [0.09]; Observations 746
    - (6) PC: No Pop. Weights -0.07 [0.06]; Pop. Weights -0.05 [0.06]; Observations 745
  - Additional checks (columns (7)-(12)):
    - (7) City PCGDP 2000: No Pop. Weights 0.15 [0.09]; Pop. Weights 0.18* [0.09]; Observations 694
    - (8) City Lights 1990: No Pop. Weights -0.07 [0.06]; Pop. Weights -0.04 [0.06]; Observations 693
    - (9) PC 1975: No Pop. Weights 0.10*** [0.02]; Pop. Weights 0.20** [0.10]; Observations 1,765
    - (10) 1960: No Pop. Weights 0.21*** [0.03]; Pop. Weights 0.31** [0.12]; Observations 1,764
    - (11) (additional year) No Pop. Weights 0.33*** [0.05]; Pop. Weights 0.40*** [0.12]; Observations 1,763
    - (12) (additional year) No Pop. Weights 0.50*** [0.08]; Pop. Weights 0.42*** [0.06]; Observations 1,760
- Notes: City population sizes in the same year used as weights in row 2.

### Table 5: LAND AREA-INCOME ELASTICITY, ROBUSTNESS CHECKS
- Baseline and alternative measures, No Pop. Weights (row 1) and Pop. Weights (row 2); standard errors in brackets; observations listed.
  - Baseline (column (1)):
    - No Pop. Weights 0.52*** [0.13]; Pop. Weights 0.58*** [0.12]; Observations 1,010
  - AUE (column (2)):
    - No Pop. Weights 0.55*** [0.13]; Pop. Weights 0.61*** [0.13]; Observations 162
  - GHS Built (B) (column (3)):
    - No Pop. Weights 0.27*** [0.07]; Pop. Weights 0.32*** [0.10]; Observations 1,749
  - Repr. World (column (4)):
    - No Pop. Weights 0.51*** [0.09]; Pop. Weights 0.53*** [0.11]; Observations 1,749
  - City PCGDP (column (5)):
    - No Pop. Weights 0.52*** [0.13]; Pop. Weights 0.58*** [0.12]; Observations 1,010
  - City Lights (column (6)):
    - No Pop. Weights 0.49*** [0.10]; Pop. Weights 0.59*** [0.09]; Observations 694
  - Additional time and data checks (columns (7)-(12)):
    - AUE 2000 No Pop. Weights 0.31*** [0.07]; Pop. Weights 0.35*** [0.07]; Observations 1,009
    - AUE 1990 No Pop. Weights 0.62*** [0.11]; Pop. Weights 0.65*** [0.12]; Observations 161
    - GHSB 2000 No Pop. Weights 0.72*** [0.09]; Pop. Weights 0.75*** [0.11]; Observations 1,611
    - GHSB 1990 No Pop. Weights 0.48*** [0.07]; Pop. Weights 0.49*** [0.10]; Observations 1,741
    - GHSB 1975 No Pop. Weights 0.48*** [0.07]; Pop. Weights 0.51*** [0.11]; Observations 1,739
    - (final column) No Pop. Weights 0.53*** [0.07]; Pop. Weights 0.54*** [0.12]; Observations 1,736
- Notes: The income elasticity of land area remains similar across robustness checks. Row 2 uses city population sizes in the same year as weights.

### Table 6: BUILDING HEIGHTS-INCOME ELASTICITY, ROBUSTNESS CHECKS
- Baseline and multiple robustness checks; No Pop. Weights (row 1) and Pop. Weights (row 2); standard errors in brackets; observations shown.
  - Baseline (column (1)):
    - No Pop. Weights 0.34*** [0.06]; Pop. Weights 0.71*** [0.10]; Observations 1,010
  - No Build. (column (2)):
    - No Pop. Weights 0.34** [0.16]; Pop. Weights 0.57*** [0.17]; Observations 405
  - Build 1/3 (column (3)):
    - No Pop. Weights 0.43*** [0.07]; Pop. Weights 0.78*** [0.10]; Observations 1,010
  - Build 2/3 (column (4)):
    - No Pop. Weights 0.28*** [0.06]; Pop. Weights 0.66*** [0.10]; Observations 1,010
  - No Floors (column (5)):
    - No Pop. Weights 0.34*** [0.06]; Pop. Weights 0.73*** [0.10]; Observations 1,010
  - Engl. Mand. (column (6)):
    - No Pop. Weights 0.50*** [0.10]; Pop. Weights 0.87*** [0.20]; Observations 534
  - Additional quantile and representation checks (columns (7)-(12)):
    - ≥25th Pctile: No Pop. Weights 0.30*** [0.06]; Pop. Weights 0.67*** [0.10]; Observations 1,010
    - ≥Median: No Pop. Weights 0.25*** [0.06]; Pop. Weights 0.63*** [0.10]; Observations 1,010
    - ≥Mean: No Pop. Weights 0.23*** [0.06]; Pop. Weights 0.61*** [0.10]; Observations 1,010
    - Repres. World: No Pop. Weights 0.35*** [0.06]; Pop. Weights 0.71*** [0.10]; Observations 1,010
    - No Bottom Inc.: No Pop. Weights 0.29*** [0.08]; Pop. Weights 0.73*** [0.10]; Observations 908
    - No Top Inc.: No Pop. Weights 0.49*** [0.10]; Pop. Weights 0.82*** [0.15]; Observations 922
  - Additional checks (columns (13)-(18) and (19)-(24)) report a variety of No Top Stock, No Bottom Pop., No Top Pop., City PCGDP, City Lights PC, AUE 2015 and AUE/GHS time slices with corresponding estimates; examples:
    - No Top Stock: No Pop. Weights 0.24*** [0.06]; Pop. Weights 0.49*** [0.10]; Observations 969
    - City PCGDP: No Pop. Weights 0.39*** [0.06]; Pop. Weights 0.73*** [0.11]; Observations 908
    - AUE 2015: No Pop. Weights 0.71*** [0.14]; Pop. Weights 0.91*** [0.14]; Observations 140
- Notes: The income elasticity of building heights remains robust across specifications, samples, and time slices.

*References list, tables, and notes as provided in the source PDF.*

### 1. No Pop. Weights0.47***0.25*0.60***0.37***0.23**0.05

### 1. No Pop. Weights0.47***0.25*0.60***0.37***0.23**0.05

### Robustness of Height and Density Elasticities
- Table (first block) summary: income elasticity of building heights under robustness checks.
  - Row 1 (No Pop. Weights): 0.47*** 0.25* 0.60*** 0.37*** 0.23** 0.05
    - Standard errors (brackets): [0.10] [0.13] [0.09] [0.10] [0.11] [0.08]
  - Row 2 (Pop. Weights): 0.62*** 0.50*** 0.95*** 0.74*** 0.60*** 0.44**
    - Standard errors (brackets): [0.14] [0.15] [0.10] [0.09] [0.15] [0.19]
  - Observations: 139 139 1,007 1,001 989 942
- Note: Row 2 uses city population sizes in the same year as weights.

### Volume- and Occupant-Density Income Elasticity, Evolution (Table 7)
- City Interior Space (columns (1)-(4)) and City Occupant Density (columns (5)-(8)) across years 2015, 2000, 1990, 1975.
  - Row 1 (No Pop. Weights):
    - City Interior Space: 0.86*** (2015) [0.15]; 0.65*** (2000) [0.15]; 0.50*** (1990) [0.16]; 0.31*** (1975) [0.12]
    - City Occupant Density: -0.84*** (2015) [0.13]; -0.52*** (2000) [0.14]; -0.25 (1990) [0.17]; 0.02 (1975) [0.13]
  - Row 2 (Pop. Weights):
    - City Interior Space: 1.28*** (2015) [0.13]; 1.08*** (2000) [0.15]; 0.95*** (1990) [0.19]; 0.79*** (1975) [0.21]
    - City Occupant Density: -1.24*** (2015) [0.12]; -0.91*** (2000) [0.16]; -0.68*** (1990) [0.22]; -0.47** (1975) [0.23]
  - Observations:
    - City Interior Space columns: 1,010 1,006 1,005 1,005
    - City Occupant Density columns: 1,010 1,006 1,005 1,005
- Note: Row 2 uses city population sizes in the same year as weights.

### Relation between Urban Size Premium and Income, Robustness (Table 8)
- Measures and samples vary by column (Lights, PCGDP, PCGDP, Lights, PCGDP, PCGDP, Lights).
- Row 1: World Elasticity, No Country FE
  - Elasticities: 0.52*** 0.95*** 0.85*** 1.09*** 1.35*** 1.17*** 1.14*** 0.14***
  - Standard errors (brackets): [0.01] [0.05] [0.06] [0.04] [0.02] 0.04] [0.03] [0.01]
  - Number of Cities: 28,259 1,590 593 593 11,261 250 250 28,259
  - R-Squared: 0.18 0.17 0.25 0.49 0.27 0.79 0.80 0.01
- Row 2: World Elasticity, Country FE
  - Elasticities: 1.11*** 0.97*** 1.08*** 1.12*** 1.25*** 1.09*** 1.09*** 1.16***
  - Standard errors (brackets): [0.00] [0.03] [0.03] [0.02] [0.01] [0.02] [0.02] [0.01]
  - Number of Cities: 28,259 1,590 593 593 11,261 250 250 28,259
  - R-Squared: 0.83 0.72 0.94 0.93 0.80 0.96 0.95 0.78
- Row 3: Effect of LPCGDP on Slope Coef.
  - Coefficients: -0.00 -0.13** -0.03 -0.09** -0.16*** -0.07 -0.11 -0.07*
  - Standard errors (brackets): [0.01] [0.06] [0.04] [0.04] [0.02] [0.06] [0.06] [0.04]
  - Number of Countries: 171 54 32 23 21 34 13 17 1 (as listed)
  - R-Squared: 0.00 0.12 0.01 0.15 0.33 0.07 0.11 0.22
- Row 4: Effect of LPCGDP on Level Diff.
  - Coefficients: 1.00*** 1.34*** 1.34*** 1.38*** 1.42*** 1.03*** 1.05*** 0.97***
  - Standard errors (brackets): [0.06] [0.11] [0.05] [0.07] [0.07] [0.12] [0.12] [0.06]
  - Number of Countries: 170 54 32 23 21 34 13 17 0 (as listed)
  - R-Squared: 0.68 0.77 0.95 0.92 0.75 0.95 0.94 0.64
- Min. City Pop. Size (000s): 130 0 22 239 250 422 439 1
- Notes:
  - Row 1: elasticity of city sum of night lights or city GDP with respect to city population size.
  - Row 2: same elasticity including country fixed effects.
  - Row 3: effect of log national per capita GDP (PPP and constant 2011 international $; source: World Bank (2018)) on estimated slope coefficient.
  - Row 4: effect of national per capita GDP on estimated level difference (relative to the United States).
  - Column sources: CIESIN(2017), United Nations(2018), Oxford Economics(2019), European Commission(2018), OECD(2018).
  - Night lights: NGDC(2015) or European Commission(2018) depending on column.
  - Column (8): regression weights are total number of city-observations (≥5) in each country in first-step regressions.

### Key Regression Results from Figures (selected)
- Figure 5: Economic development and city population sizes, 2015 (N = 1,773)
  - Regression: Y = 6.64*** - 0.00 X; R2 = 0.00; N = 1,773
- Figure 6: Economic development and city land areas, 2015 (N = 1,010)
  - Regression: Y = 0.62* + 0.52*** X; R2 = 0.19; N = 1,010
- Figure 7: Economic development and city average heights, 2015 (N = 1,010)
  - Regression: Y = -3.87* + 0.34*** X; R2 = 0.06; N = 1,010
- Figure 8: Economic development and city population densities, 2015 (N = 1,010)
  - Regression: Y = 6.24*** - 0.50*** X; R2 = 0.34; N = 1,010
- Figure 9: Economic development and city occupant densities, 2015 (N = 1,010)
  - Regression: Y = 10.11*** - 0.84*** X; R2 = 0.29; N = 1,010
- Figure 10: City population and city night lights, U.S. and India, circa 2000
  - U.S. (N = 5,034): Y = -0.74*** + 1.04*** X; R2 = 0.80
  - India (N = 2,733): Y = -5.21*** + 1.11*** X; R2 = 0.65
- Figure 11: Estimated slope coefficients and national incomes, 2000 (N = 171)
  - Regression: Y = 1.13*** - 0.00 X; R2 = 0.00; N = 171
- Figure 12: Estimated level differences and national incomes, 2000 (N = 170)
  - Regression: Y = -6.67*** + 1.00*** X; R2 = 0.68; N = 170
- Figure A8: Economic development and city volumes, 2015 (N = 1,010)
  - Regression: Y = -3.25*** + 0.86*** X; R2 = 0.19; N = 1,010
- Figure A9: Economic development and city floor area per person, 1993 (N = 181)
  - Regression: Y = -39.82*** + 6.54*** X; R2 = 0.56; N = 181

### Observed empirical patterns
- Positive interior volume (sum of tall building heights) elasticity with national income:
  - Examples: 0.86*** (2015 unweighted), 1.28*** (2015 population-weighted).
- Negative occupant density elasticity with national income:
  - Examples: -0.84*** (2015 unweighted), -1.24*** (2015 population-weighted).
- Stronger estimated urban size elasticities when country fixed effects are included (Row 2, Table 8).
- National per capita GDP influences level differences across countries (Row 4, Table 8) with coefficients around 1.00*** to 1.42*** depending on sample.

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### Web Appendix: Details on Building Heights Data
- Original CTBUH(2018) data set: 27,652 tall buildings (accessed between January 2017 and January 2018).
- After keeping “buildings” and “tower-buildings” completed or topped out: 19,132 buildings.
- Height data availability:
  - Architectural height: available for 84.7% of buildings.
  - Height to tip: 60.6%.
  - Height to highest occupied floor: 11.6%.
  - Height to observatory: 1.1%.
  - Number of floors above ground: 98.2%.
- Imputation strategy:
  - Architectural height used as main measure; when missing, imputed using height to tip (correlation = 0.99), then height to highest occupied floor (correlation = 0.98), then height to observatory (correlation = 0.96).
  - Regression of height on number of floors yields coefficient 3.8*** (95% conf. interval = [3.77; 3.87]), implying a floor corresponds to 4 meters for most buildings.
  - Result: consistent height measure for 99.6% of buildings.
- Coverage cutoff:
  - Kernel distribution mode at 80 m suggests data set captures buildings above 80 m primarily; remaining sample: 14,839 buildings > 80 m.
- Year of completion:
  - Year of completion available for 96.6% of buildings; imputed using year construction started (correlation = 0.99) and year proposed (0.97).
  - Average timing: completed 5.5 years after construction proposed and 3.3 years after construction started.
  - Year of completion obtained for 96.8% of buildings.
- Function shares (for buildings with known function, 98.9%):
  - Residential: 49.9%
  - Offices: 41.8%
  - Hotels: 11.8%
  - Retail: 3.9%

*Source: wpiea2019203-print-pdf*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019203-print-pdf.pdf_