Cities' productivity is proportional to their size – unless they're British

Wokingham: unexpectedly productive. Image: wx8 at Wikimedia Commons.

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. 


 

 
 
 
 

To build its emerging “megaregions”, the USA should turn to trains

Under construction: high speed rail in California. Image: Getty.

An extract from “Designing the Megaregion: Meeting Urban Challenges at a New Scale”, out now from Island Press.

A regional transportation system does not become balanced until all its parts are operating effectively. Highways, arterial streets, and local streets are essential, and every megaregion has them, although there is often a big backlog of needed repairs, especially for bridges. Airports for long-distance travel are also recognized as essential, and there are major airports in all the evolving megaregions. Both highways and airports are overloaded at peak periods in the megaregions because of gaps in the rest of the transportation system. Predictions for 2040, when the megaregions will be far more developed than they are today, show that there will be much worse traffic congestion and more airport delays.

What is needed to create a better balance? Passenger rail service that is fast enough to be competitive with driving and with some short airplane trips, commuter rail to major employment centers to take some travelers off highways, and improved local transit systems, especially those that make use of exclusive transit rights-of-way, again to reduce the number of cars on highways and arterial roads. Bicycle paths, sidewalks, and pedestrian paths are also important for reducing car trips in neighborhoods and business centers.

Implementing “fast enough” passenger rail

Long-distance Amtrak trains and commuter rail on conventional, unelectrified tracks are powered by diesel locomotives that can attain a maximum permitted speed of 79 miles per hour, which works out to average operating speeds of 30 to 50 miles per hour. At these speeds, trains are not competitive with driving or even short airline flights.

Trains that can attain 110 miles per hour and can operate at average speeds of 70 miles per hour are fast enough to help balance transportation in megaregions. A trip that takes two to three hours by rail can be competitive with a one-hour flight because of the need to allow an hour and a half or more to get to the boarding area through security, plus the time needed to pick up checked baggage. A two-to-three-hour train trip can be competitive with driving when the distance between destinations is more than two hundred miles – particularly for business travelers who want to sit and work on the train. Of course, the trains also have to be frequent enough, and the traveler’s destination needs to be easily reachable from a train station.

An important factor in reaching higher railway speeds is the recent federal law requiring all trains to have a positive train control safety system, where automated devices manage train separation to avoid collisions, as well as to prevent excessive speeds and deal with track repairs and other temporary situations. What are called high-speed trains in the United States, averaging 70 miles per hour, need gate controls at grade crossings, upgraded tracks, and trains with tilt technology – as on the Acela trains – to permit faster speeds around curves. The Virgin Trains in Florida have diesel-electric locomotives with an electrical generator on board that drives the train but is powered by a diesel engine. 

The faster the train needs to operate, the larger, and heavier, these diesel-electric locomotives have to be, setting an effective speed limit on this technology. The faster speeds possible on the portion of Amtrak’s Acela service north of New Haven, Connecticut, came after the entire line was electrified, as engines that get their power from lines along the track can be smaller and much lighter, and thus go faster. Catenary or third-rail electric trains, like Amtrak’s Acela, can attain speeds of 150 miles per hour, but only a few portions of the tracks now permit this, and average operating speeds are much lower.

Possible alternatives to fast enough trains

True electric high-speed rail can attain maximum operating speeds of 150 to 220 miles per hour, with average operating speeds from 120 to 200 miles per hour. These trains need their own grade-separated track structure, which means new alignments, which are expensive to build. In some places the property-acquisition problem may make a new alignment impossible, unless tunnels are used. True high speeds may be attained by the proposed Texas Central train from Dallas to Houston, and on some portions of the California High-Speed Rail line, should it ever be completed. All of the California line is to be electrified, but some sections will be conventional tracks so that average operating speeds will be lower.


Maglev technology is sometimes mentioned as the ultimate solution to attaining high-speed rail travel. A maglev train travels just above a guideway using magnetic levitation and is propelled by electromagnetic energy. There is an operating maglev train connecting the center of Shanghai to its Pudong International Airport. It can reach a top speed of 267 miles per hour, although its average speed is much lower, as the distance is short and most of the trip is spent getting up to speed or decelerating. The Chinese government has not, so far, used this technology in any other application while building a national system of long-distance, high-speed electric trains. However, there has been a recent announcement of a proposed Chinese maglev train that can attain speeds of 375 miles per hour.

The Hyperloop is a proposed technology that would, in theory, permit passenger trains to travel through large tubes from which all air has been evacuated, and would be even faster than today’s highest-speed trains. Elon Musk has formed a company to develop this virtually frictionless mode of travel, which would have speeds to make it competitive with medium- and even long-distance airplane travel. However, the Hyperloop technology is not yet ready to be applied to real travel situations, and the infrastructure to support it, whether an elevated system or a tunnel, will have all the problems of building conventional high-speed rail on separate guideways, and will also be even more expensive, as a tube has to be constructed as well as the train.

Megaregions need fast enough trains now

Even if new technology someday creates long-distance passenger trains with travel times competitive with airplanes, passenger traffic will still benefit from upgrading rail service to fast-enough trains for many of the trips within a megaregion, now and in the future. States already have the responsibility of financing passenger trains in megaregion rail corridors. Section 209 of the federal Passenger Rail Investment and Improvement Act of 2008 requires states to pay 85 percent of operating costs for all Amtrak routes of less than 750 miles (the legislation exempts the Northeast Corridor) as well as capital maintenance costs of the Amtrak equipment they use, plus support costs for such programs as safety and marketing. 

California’s Caltrans and Capitol Corridor Joint Powers Authority, Connecticut, Indiana, Illinois, Maine’s Northern New England Passenger Rail Authority, Massachusetts, Michigan, Missouri, New York, North Carolina, Oklahoma, Oregon, Pennsylvania, Texas, Vermont, Virginia, Washington, and Wisconsin all have agreements with Amtrak to operate their state corridor services. Amtrak has agreements with the freight railroads that own the tracks, and by law, its operations have priority over freight trains.

At present it appears that upgrading these corridor services to fast-enough trains will also be primarily the responsibility of the states, although they may be able to receive federal grants and loans. The track improvements being financed by the State of Michigan are an example of the way a state can take control over rail service. These tracks will eventually be part of 110-mile-per-hour service between Chicago and Detroit, with commitments from not just Michigan but also Illinois and Indiana. Fast-enough service between Chicago and Detroit could become a major organizer in an evolving megaregion, with stops at key cities along the way, including Kalamazoo, Battle Creek, and Ann Arbor. 

Cooperation among states for faster train service requires formal agreements, in this case, the Midwest Interstate Passenger Rail Compact. The participants are Illinois, Indiana, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota, Ohio, and Wisconsin. There is also an advocacy organization to support the objectives of the compact, the Midwest Interstate Passenger Rail Commission.

States could, in future, reach operating agreements with a private company such as Virgin Trains USA, but the private company would have to negotiate its own agreement with the freight railroads, and also negotiate its own dispatching priorities. Virgin Trains says in its prospectus that it can finance track improvements itself. If the Virgin Trains service in Florida proves to be profitable, it could lead to other private investments in fast-enough trains.

Jonathan Barnett is an emeritus Professor of Practice in City and Regional Planning, and former director of the Urban Design Program, at the University of Pennsylvania. 

This is an extract from “Designing the Megaregion: Meeting Urban Challenges at a New Scale”, published now by Island Press. You can find out more here.