Part of a series “old econ papers”
Zipf’s Law for Cities: An Explanation: rank cities by population. The largest city has rank 1, second largest rank 2, etc. In many countries, approximately:
So if the largest city has 8 million people, the second may have around 4 million, the fourth around 2 million.
Why should city sizes line up like this at all?
Gibrat’s law: large cities have roughly similar distributions of percentage growth, independent of their current size. A city of 5 million people is not expected to grow five times faster in percentage terms than a city of 1 million.
Does Zipf’s law actually hold?
Results change depending on:
- what counts as a city;
- whether you use administrative boundaries or actual urban agglomerations;
- how many small cities you include;
- which country and time period you look at.
Recent work is still finding strong scaling regularities, 2025 PNAS Nexus paper uses globally consistent remote-sensing definitions rather than relying entirely on each country’s administrative statistics, and still finds common scaling patterns across countries.
The follow-up I find more interesting
A 2024 PNAS Nexus paper builds networks between cities from the locations of multinational firms. Cities which are more globally connected than expected for their population also tend to produce more GDP than expected for their population.
They look at the US, EU and China. Adding global firm-network connectivity improves the description of city GDP beyond population alone.
This is correlational estimate, but I think the framing is better:
A million people who barely interact economically with the outside world are not equivalent to a million people sitting inside a dense network of companies, universities, suppliers and customers.
Maybe “size” is the wrong primitive
Perhaps the more fundamental objects are distributions of:
- firm connections;
- migration links;
- knowledge flows;
- transport links;
- scientific collaborations;
- supply chains.
This would also connect city-size distributions to other fat-tailed distributions in economics like firm sizes, wealth or scientific impact.