Primate cities

Why does one country's largest city dwarf every rival while another's cities sit evenly spaced in size?

Some countries have a city that swallows the frame. Paris is several times Lyon; Bangkok is more than an order of magnitude above anything else in Thailand; Lima and Budapest each sit in a class of one. Other countries have no such city — Germany's largest is under twice its second, and the next dozen descend in gentle steps. The instinct is to ask what made the giant grow. But perhaps the better question is which of the two patterns needs explaining at all.

Try the simplest possible model of urban growth and see what it produces. Suppose every city, whatever its size, grows in a given decade by a percentage drawn from the same distribution — some good decades, some bad, independent of how big it already is. No city has an inherent advantage. Nothing is planned.

What does that give you after a few centuries? Not equality. Because growth is proportionate, a run of good decades multiplies rather than adds, and a few cities compound far ahead of the rest. Run it long enough, with some floor on how small a place can be and still count as a city, and the size distribution settles into a remarkably specific shape: the second city about half the first, the third about a third, the tenth about a tenth. That is the rank-size or Zipf pattern, and it turns up across many countries and many centuries.

Notice what has just happened. The even ladder is the thing that comes free. It needs no planning, no policy, no geography — only proportionate random growth over a long time. So the country that needs explaining is not Germany. It is France.

What breaks the model, then? Only one thing can: a growth advantage that attaches to being the largest and stays attached. Random advantages shuffle; that is what keeps the ladder. A persistent one compounds without limit.

And compounding is brutal in a way worth feeling concretely. Two cities of equal size, one growing 2 per cent a year and the other 1.5 — half a percentage point, nothing you would notice in a decade — are 2.1 times apart after 150 years. To open a tenfold gap in that time you need a sustained differential of about 1.5 percentage points a year. So primacy is not the residue of a lucky century; it is evidence of a mechanism that kept feeding the same city, decade after decade.

What could do that? The strongest candidate is political. A unitary state that concentrates administration, licensing, courts, contracts and subsidy in one place makes proximity to that place a permanent business input. The advantage does not decay, because the state does not move. Cross-country work in the 1990s found primacy strongly associated with political instability and with autocratic rule — one estimate put the largest city in a dictatorship roughly 50 per cent larger than an otherwise comparable democracy's — and with closed trade regimes, since a protected economy trades with its own capital instead of the world.

Second, network topology. A rail and road network built radially from one point gives that point the only national market access there is, and every later investment follows the existing lines. France, Argentina and Hungary have such networks; Germany and the United States have meshes. But this is usually the state's doing again, so it is less an independent cause than the machinery through which the political one acts.

Third, and often forgotten: history of unification. Germany and Italy were assemblages of independent states, each with its own court, university, mint and market. Their flat hierarchies are fossilised political fragmentation — many capitals, none able to compound against the others, because for centuries there was no single prize to win.

Three honest qualifications.

The rank-size pattern is a tendency, not a law. It fits the middle of a country's distribution better than the top or the tail, the fitted exponent varies by country and decade, and there is a running argument about whether Zipf-like results are a real regularity or partly an artefact of how cities are counted.

Which raises the second point: primacy is partly a measurement choice. Draw the boundary at the municipality and Paris looks small and Bangkok enormous; draw it at the functional urban region and both change. The Netherlands and the German Rhine-Ruhr look non-primate largely because their agglomerations are administratively split, and a country with few cities will look lumpy from small numbers alone.

Third, colonial history is the popular explanation and is only half right. Colonial economies did build single-port extraction networks — but a port is a location advantage, and those can decay. Where primacy persisted after independence, it is generally because the new state concentrated its own administration in the same city, keeping the differential alive. The mechanism is the persistence, not the origin.

• Why some countries deliberately sited their capital away from the largest city, and whether it worked.
• How agglomeration economies — thicker labour markets, denser knowledge spillovers — turn an inherited advantage into a self-sustaining one.

Every term the collection defines is gathered in the glossary.