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Large cities lose their growth advantage as countries urbanize

By introducing consistent global and U.S. city population datasets, this paper reveals that large cities lose their growth advantage as countries urbanize, leading to a projected 38% of the world's population living in cities over one million by 2100—a figure that falls between current trend extrapolations and proportional growth theory.

Original authors: Andrea Musso, Diego Rybski, Dirk Helbing, Frank Neffke

Published 2026-03-31

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Andrea Musso, Diego Rybski, Dirk Helbing, Frank Neffke

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: The "Growth Spurt" of Cities

Imagine the world's cities as a giant family of children growing up. For a long time, economists and planners have been arguing about how these children grow.

Theory A (The "Super-Size" Theory): Big kids grow faster than small kids. The more popular and successful a city is, the more it attracts people, money, and innovation, making it grow even faster. This suggests the world will eventually become dominated by a few massive "super-cities."
Theory B (The "Equal Growth" Theory): All kids grow at roughly the same speed. A small town and a giant metropolis both add people at a similar rate. This suggests the population will spread out more evenly.

This paper says: Both theories are right, but they apply at different times.

The authors discovered that cities go through a life cycle, much like a human being.

The Life Cycle of a City

Phase 1: The "Teenage Growth Spurt" (Early Urbanization)

When a country is just starting to urbanize (moving from farms to cities), the big cities are like teenagers hitting a growth spurt. They are the cool kids. They have the best jobs, the most schools, and the most excitement.

What happens: The giant cities grow much faster than the small towns.
The Analogy: Imagine a race where the runners at the front are sprinting, while the runners at the back are jogging. The gap between the front and the back gets wider and wider.

Phase 2: The "Adult Plateau" (Mature Urbanization)

As a country becomes fully urbanized (most people already live in cities), the dynamic changes. The big cities get so huge that they start to get "clogged."

The Problems: Traffic jams, expensive rent, crowded subways, and high crime rates start to outweigh the benefits of being big.
What happens: The growth advantage disappears. The giant cities stop sprinting and start jogging at the same pace as the small towns. Sometimes, people even start moving out of the big city center to the quieter suburbs or smaller towns.
The Analogy: The race is over. The sprinters are tired. Now, everyone is just walking at a steady, comfortable pace. The gap between the front runners and the back runners stops widening.

How They Figured This Out

The authors didn't just guess; they built two massive "time machines" using data:

The Global Time Machine (1975–2025): They used satellite images to look at the whole world. They didn't rely on messy political borders (like city limits that haven't changed in 100 years). Instead, they looked at the actual "glow" of the city—the lights and buildings—to see where people actually live.
The US Time Machine (1850–2020): They went back to old, handwritten US census records. They matched millions of individual names to see how people moved over 170 years, creating a perfect history of American city growth.

By combining these, they saw a clear pattern: As countries get more urbanized, the "growth advantage" of big cities fades away.

The Crystal Ball: What Happens by 2100?

The authors used this "life cycle" model to predict the future. They compared their prediction against the two old theories:

If the "Super-Size" theory were true: 47% of the world would live in cities with over 1 million people by 2100.
If the "Equal Growth" theory were true: 33% would live there.
If we just kept doing what we are doing now (extrapolating trends): 42% would live there.

The Authors' Prediction:
They predict 38% of the world's population will live in cities with over 1 million people by 2100.

What does this mean?
It means the world is heading toward a "Goldilocks" zone. We won't end up with a few terrifyingly huge mega-cities swallowing everything, but we also won't have a perfectly flat distribution. The growth of the giants is slowing down, but they are still growing—just not as fast as they used to.

Why Should You Care?

This isn't just about math; it's about how we build our future.

If we think big cities will keep exploding: We might pour all our money into building more skyscrapers and subways in Tokyo, New York, or Mumbai, ignoring smaller towns.
If we know the growth is slowing: We can start investing in smaller cities and regional hubs. We can plan for a world where the "cool factor" of the massive city is balanced by the livability of the medium-sized city.

The Bottom Line

Cities are like living organisms. When they are young and hungry, they grow fast and big. When they get older and full, they slow down and stabilize. The world is moving from the "hunger phase" to the "stability phase," and our cities are changing right along with us.

1. Problem Statement

The paper addresses a fundamental debate in urban economics and geography regarding the future trajectory of urban concentration:

The Conflict: Do large cities maintain a permanent growth advantage over smaller ones (Increasing Returns theory), or do all cities grow at similar rates regardless of size (Proportional Growth/Gibrat's Law)?
The Gap: Existing literature is divided, with studies often limited by inconsistent city definitions across countries and time, or restricted to short time windows. This lack of harmonized data prevents a clear understanding of how the relationship between city size and growth rate evolves over the long term.
The Question: Will the world's population continue to concentrate in mega-cities (1M+), or will this trend level off as countries mature?

2. Methodology

A. Data Construction

The authors constructed two novel, harmonized datasets to overcome historical data inconsistencies:

Global Cities Dataset (1975–2025):
- Source: Global Human Settlement Layer (GHSL) 2023 satellite imagery.
- Scope: 99 countries (94% of the world population).
- Definition: Cities are defined as contiguous clusters of built-up areas or high population density (geographic definition), dynamically adjusted to expansion.
USA Cities Dataset (1850–2020):
- Source: IPUMS full-count census microdata and Census Place Project.
- Scope: Continental USA over nearly its entire history.
- Method: Used geocoding to map 500 million individual records to ~40,000 census places, then aggregated into 1km grids.

B. City Definition Algorithm: City Clustering Algorithm (CCA)

To ensure consistency across time and space, the authors applied the City Clustering Algorithm:

Step 1: Classify grid cells as "urban" or "non-urban" based on density thresholds (50 people/cell for US; semi-dense urban cluster for Global).
Step 2: Form initial contiguous clusters using a flood-fill algorithm.
Step 3: Match clusters across time intervals ( $t_1, t_2$ ) using a bipartite graph where edges represent spatial overlap.
Step 4: Define stable city boundaries as the spatial union of all clusters within a connected component of the graph. This prevents "new cluster bias" (counting new small clusters as high growth) and handles mergers/splits systematically.
Step 5: Calculate growth rates based on population changes within these stable boundaries.

C. Analytical Framework

The authors model the urban system using two key parameters:

$\beta$ (Size-Growth Slope): The slope of the relationship between city log-size and city log-growth.
- $\beta > 0$ : Large cities grow faster (Increasing Returns).
- $\beta \approx 0$ : All cities grow at similar rates (Proportional Growth).
$\alpha$ (Rank-Size Slope): The slope of the rank-size curve (Zipf's Law analogue).
- Theoretically linked to $\beta$ via the equation: $\alpha_{t+10} = \alpha_t \cdot (1 + \beta_t)$ .

Estimation Technique:
Instead of Ordinary Least Squares (OLS), which is biased by the high density of small cities, the authors use penalized cubic B-splines to estimate $\alpha$ and $\beta$ . This approach weights all parts of the size spectrum equally, providing a more robust measure of the curve's shape.

D. Projection Method

To forecast to 2100, the authors:

Regressed $\beta$ against the urban population share to establish a life-cycle relationship.
Projected future urban shares using UN and World Bank scenarios.
Calculated future $\beta$ values based on projected urbanization levels.
Iteratively updated $\alpha$ using the derived relationship.
Converted projected $\alpha$ values into the share of the population living in cities >1M.

3. Key Contributions

Harmonized Datasets: Creation of the first consistent, long-term (1850–2025) datasets for US and Global city populations using a unified geographic definition.
The Urban Life Cycle Theory: The paper demonstrates that "Increasing Returns" and "Proportional Growth" are not competing theories but sequential phases of urban development:
- Early Stage: Low urbanization $\rightarrow$ High $\beta$ (Large cities grow significantly faster).
- Late Stage: High urbanization $\rightarrow$ \beta $\approx 0$ (Growth rates equalize across sizes).
Mechanism Identification: The decline in $\beta$ is driven by the stage of urbanization, not just regional differences. Once urbanization levels are controlled for, regional differences in growth advantage largely disappear.
Suburbanization Analysis: The authors tested if suburbanization (growth shifting from cores to peripheries) explains the decline in $\beta$ . They found that while suburbanization exists, it accounts for only a small fraction of the observed trend; deeper structural forces are at play.

4. Results

The Inverse Relationship: There is a strong negative correlation between a country's urbanization level and the growth advantage of large cities ( $\beta$ $β$ ).
- In less urbanized countries (e.g., parts of Asia/Africa), 1M+ cities grow ~7.3% faster than the national average.
- In highly urbanized countries (e.g., Europe/Americas), 1M+ cities grow at or slightly below the national average.
Evolution of Distribution: As $\beta$ declines, the rank-size slope $\alpha$ increases (the distribution becomes steeper/top-heavy initially, then stabilizes). The rate of change in $\alpha$ slows as countries mature.
2100 Projections:
- Proportional Growth Model (Constant $\beta=0$ ): 33% of the world population in 1M+ cities.
- Increasing Returns Model (Constant $\beta=0.03$ ): 47% in 1M+ cities.
- Current Trend Extrapolation: 42% in 1M+ cities.
- Authors' Model (Life Cycle): 38% of the world population will live in 1M+ cities by 2100.
- Significance: This is 450 million fewer people than current trend extrapolations suggest, but 490 million more than a pure proportional growth model.

5. Significance and Implications

Policy Planning: The finding that large cities will not continue to dominate growth indefinitely suggests that future urban planning should not focus solely on mega-cities. Resources may need to be distributed more evenly across the urban system as countries mature.
Economic & Environmental Trade-offs:
- If productivity scales super-linearly with size, a slowdown in large city growth implies a slowdown in aggregate productivity gains.
- Conversely, if environmental costs (heat islands, emissions) scale super-linearly, the leveling off of large city growth could alleviate environmental pressures.
Theoretical Advancement: The paper resolves the conflict between Gibrat's Law and Increasing Returns by framing them as dynamic phases of a single process, providing a unified framework for understanding urban evolution.
Robustness: The findings hold across different city definitions (geographic vs. functional), different spatial scales (national vs. sub-regional), and various hyperparameter choices, confirming the robustness of the "urban life cycle" phenomenon.

In summary, the paper provides empirical evidence that the "growth advantage" of large cities is a transient feature of early urbanization that fades as a country develops, leading to a more balanced distribution of population across city sizes by the end of the century.