Large cities lose their growth advantage as urban systems mature

TL;DR

This paper asks whether the world will continue concentrating population in large cities or whether that trend will slow as urban systems mature. It proposes a life-cycle model in which large-city growth advantages decline over time, unifying increasing returns and proportional growth as two phases of one process. The authors leverage two harmonized datasets—the global city dataset from satellite data (1975–2025) and the U.S. city dataset from census microdata (1850–2020)—and a City Clustering Algorithm to estimate the rank-size slope alpha and size-growth slope beta, linking them to changes in urban concentration. Projections indicate about 38% of the world population living in 1M+ cities by 2100, lying between proportional-growth and current-trend benchmarks, with regional variation in the strength and timing of the growth advantage. The work has implications for urban policy and growth accounting, highlighting how maturation of urban systems reshapes the potential for reallocation-driven productivity gains.

Abstract

The share of the world population living in cities with more than one million people rose from 11\% in 1975 to 24\% in 2025 (our estimates). Will this trend towards greater concentration in large cities continue or level off? We introduce two new city population datasets that use consistent city definitions across countries and over time. The first covers the world between 1975 and 2025, using satellite imagery. The second covers the U.S. between 1850 and 2020, using census microdata. We find that urban growth follows a characteristic life cycle. Early in urbanization, large cities grow faster than smaller ones. As urban systems mature, growth rates equalize across sizes. We use this life cycle to project future population concentration in large cities. Our projections suggest that 38\% of the world population will be living in cities with more than one million people by 2100. This estimate is higher than the 33\% implied by the well-known theory of proportional growth but lower than the 42\% obtained by extrapolating current trends.

Figures (4)

• Figure 1: The growth advantage of large cities varies systematically across regions: it is strong in Asia and Africa and weak in Europe and the Americas. (A) We compare the average growth rate of a country's cities, denoted by $g_{\text{national}}$, with the average growth rate of specific sub-groups of its cities (e.g., the largest city, 1M$+$ cities, etc.), denoted by $g_{\text{group}}$. Each bar in the chart shows the ratio $g_{\text{group}} \ / \ g_{\text{national}} - 1$ for a given region. (B)Size-growth curve by region. These curves are obtained by fitting a penalized cubic B-spline ($\lambda = 100$) to the relationship between city log-size in year $t$ and city log-growth between year $t$ and $t + 10$ (Methods \ref{['methods:measurement']}). (C)Size-growth slopes$\beta$ by country. $\beta$ is obtained by first estimating the national size-growth curve (as in panel (B)), and then averaging the local slope of this curve across the size spectrum (see left inset and Methods \ref{['methods:measurement']}). The map shows the mean value of $\beta$ between 1975 and 2025; hatched indicates no data.
• Figure 2: The growth advantage of large cities weakens as countries urbanize. (A) Size-growth curve by urbanization group (Methods \ref{['methods:measurement']}) (Inset) $\beta$ vs. urban population share (fit with a penalized cubic B-spline with $\lambda = 100$). (B-C) Size-growth curves in South Korea and the USA across different time periods. (Insets) $\beta$ vs. time (bootstrapped confidence intervals $n = 1000$). (D) Country-level regression with regional dummies ($\beta_{t, \text{country}} \sim \delta_{\text{region}} + \text{urban population share}_{t, \text{country}}$). Regional differences in $\beta$ become significantly smaller once we control for the level of urbanization.
• Figure 3: Historical trends and projections for national city size distributions. (A) Rank-size curves for the USA and South Korea. These curves are obtained by fitting penalized cubic B-splines ($\lambda = 1$) to the relationship between city log-rank and city log-size in a fixed year. The USA plot displays also a scatter of the underlying data points. (B-C) The rank-size slope $\alpha$ is estimated by averaging the local slope of the rank-size curve across ranks and then taking the absolute value (Methods \ref{['methods:measurement']}). Note that $\alpha$ is a spline-based analogue of the Zipf exponent. (B) Change in $\alpha$ for South Korea and the USA from a base year $t_0$ (South Korea $t_0 = 1975,2000$; USA $t_0=1850,1930$). (C) Change in average $\alpha$ across more/less urbanized countries since 1975 (binned scatter plot by year with bootstrapped confidence intervals; $n = 1000)$. (D) Average $\alpha$ across groups of countries in different years. 2100 values are projected using the technique in Methods \ref{['methods:projections']}. (E) Share of the world population in 1M$+$ cities in 1975, 2025, and 2100. 2100 values are projected under four urban growth models, which differ in their estimates for the future trajectories of $\beta$: proportional growth (PG; $\beta = 0$), increasing returns (IR; $\beta = 0.03$), current trend extrapolation (EX; $\beta$ equal to the country's average between 1975-2025), and our model (OM; time-varying $\beta$ according to the country's urbanization). See Methods \ref{['methods:projections']}.
• Figure 4: The City Clustering Algorithm rozenfeld2008lawsa computes stable city boundaries for a time interval $(y_1, y_2)$. This algorithm proceeds in five steps: (A) It takes two grids as input, one for each year, containing estimates of population or built-up area. (B) It classifies grid cells as either urban or non-urban using a threshold on these population/built-up area estimates. (C) It groups contiguous urban grid cells to form clusters. (D) It matches clusters across years when they overlap spatially, forming a bipartite graph. (E) It defines a city's boundary as the spatial union of all clusters within a single connected component of the graph.