It’s always satisfying when a simple theory comes along which seems to make sense of messy and complicated things. We ran a piece last year on the theoretical physicist Geoffrey West, who seems to have hit upon a “grand, unified theory of cities”. It runs as follows: if a city doubles in size, then, all else being equal, a whole range of things from crime to wages will increase by around 15 per cent. 

The explanation for this impossibly neat correlation lies in the idea that if you put lots of people, businesses and infrastructure in one place, the increase in interactions and shared ideas will drive up economic productivity, innovation, and a host of other factors. Diseases spread faster in densely populated cities; it should come as no surprise that ideas and expertise do, too. 

This month, the Organisation for Economic Co-operation and Development, which encourages trade and economic progress among its 34 member countries, unveiled its own grand unified theory of cities’ productivity and size. In two tome-like reports, based on some of the most accurate city-level data ever collated, they concluded that, if you double the size of a city, you generally increase its productivity per capita by between 2 and 5 per cent.

That may not sound all that impressive – it’s much less than West’s version, for a start. But nonetheless, it means that a city like Paris should be anything up to 50 percent more productive than a settlement of 50,000 people. What’s more, it means that simply moving to a city makes an individual more productive:

If you were to take a random person from a small city and relocate that person to a larger city without changing his or her characteristics, the person would, on average, be more productive in the larger city… This effect would occur no matter whether the randomly picked person worked in a high-skilled or low-skilled occupation.

There are several explanations for this effect. Firstly, there are more jobs in cities, so that individual is more likely to find one. Also, they are more likely to be in a more specialised and innovative firm, and more likely to be a good match for their skills. Due to higher competition in cities, meanwhile, businesses which aren’t pulling their weight tend to be forced out. There’s also that “network”, or “agglomeration” effect we saw in action in West’s research. 

The theory is borne out when you plot US cities’ productivity differential (which is loosely based on wages) against their population size. There are outliers, but as you can see, the statistical relationship is relatively strong:

Source: “The Metropolitan Century” (OECD).

There’s also this bar chart, which plots OECD cities in North America and Europe against size. (In Asia and Central America the rule doesn’t work so well, for reasons too complex to go into here.)

So: the bigger a city gets, at least in the western world, the more productive it becomes. Great. Glad we’ve got that sorted.

Except, actually, we don’t. Take a look at the same factors plotted using UK cities:

There are two odd effects at play here. First, cities don’t increase in productivity in the way you’d expect as they increase in size. Second, as the report notes, London’s productivity is “larger than would be expected given its size”. 

If you’ve had even half an ear turned to the arguments over devolution to UK cities, you might be able to guess at a few of the theories which could explain London’s productivity bottleneck. The OECD researchers themselves don’t have any conclusive answers, but here are a few possibilities:

1. Skills drain. High average levels of education have a big effect on city productivity, even among lesser educated people. In the UK, graduates tend to move to London – which is why many cities are keen to gain control of their skills budget as part of their devolution deals. 

2. Geography. The UK is relatively small, which is perhaps why graduates feel able to move en masse to London, while those in the US may be less likely to move across the country to New York. 

3. Governance. US cities, and those in larger European countries, tend to have more control of their own affairs than UK cities. The OECD also found that capital cities tend to grow faster, and be more productive, than other cities, which may partially explain London’s impressive productivity levels. 

There’s also another possibility, which is that smaller cities are more productive than you’d expect, which flattens out the graph. This could be, again, a matter of geography. Three of the significant outliers – Bracknell, Wokingham, Milton Keynes – are London commuter towns, which the researchers believe could explain their higher productivity. 

The OECD also found that cities increase in productivity if other populous cities are “nearby”; they define nearby as “within 300km”.  

And Britain simply isn’t that big. That could be distorting the trend:

The black line is about 300km long.

So are small UK cities over-productive, or are big ones besides London under-productive? And is London an innocent outlier, or is it a succubus pulling skills from other cities? Answers on a postcard, please.