Here are a few things you probably already know. Britain has a productivity problem. Since the financial crisis, growth in output per worker has barely risen and the gap with other industrial countries is large. London is much more productive than the other big cities.

Now here’s something you might not know: a lot of it has to do with buses. Public transport really matters.

Cities tend to be more productive than towns or villages because of agglomeration effects: the notion that bringing people together in one large urban centre leads to new and better ways of doing things. The bigger the city the bigger the agglomeration effect.

This rule holds true in other countries. The second-biggest French city, Lyon, is more productive than Marseille, the third-biggest city, which in turn is more productive than the fourth biggest, Lille. In the US, Germany and the Netherlands the same applies.

In Britain it is a different story, however. Here, big cities such as Birmingham are less productive than smaller cities such as Oxford and Cambridge. And that’s because the problems people have in getting from their homes to the places where the jobs are shrinks the real size of UK cities. Research by the Open Data Institute in Leeds has shown that the effective size of Birmingham is about half that of the nominal population because of the problems caused by inadequate public transport.

What the Leeds researchers did was to record 40m bus departures from all over the city to see how long the journeys took in peak and off-peak times. They assumed that to be part of the Birmingham agglomeration someone should have a travel to work time of 30 minutes or less. The half-hour limit did not include waiting at bus stops or walking at either end, which would take the total door-to-door journey time to 50 minutes.

The research showed that in peak time, getting around Birmingham by bus is a painstaking process. A 3.5-mile journey from Stirchley in the south of the city to the centre takes about 20 minutes between 7am and 8am but about 40 minutes between 8am and 9am.

Contrast that with travel by tram. The West Midlands has one tramline, linking Wolverhampton with Birmingham. Someone who gets on at West Bromwich for the 8.5-mile journey to Birmingham knows that it will take 30 minutes, regardless of whether it is during the rush-hour or not.

Now consider the public transport infrastructure in Britain and France. The second, third and fourth-biggest cities outside of Paris – Lyons, Marseille and Lille – have eight Métro lines between them (four in Lyon and two each in Marseille and Lille). The UK equivalents have none.

Manchester has a tramway system to match that of Lyon, with about 100 stations in each city. But Marseille (three lines) and Lille (two lines) are far better connected than Birmingham, with its one line, and Leeds (none).

Tom Forth, the head of data at the Open Data Institute, said in a recent piece for CityMetric – an online magazine that specialises in urban issues – that Birmingham and Lyon are comparable cities but Birmingham has a 33% productivity shortfall with Lyon. But the two cities are only comparable on the assumption that Birmingham can make full use of its population of almost 2 million. If the real size of Birmingham – for agglomeration purposes – is 900,000, the productivity gap shrinks to only 9%.

“Our hypothesis is that, by relying on buses that get caught in congestion at peak time for public transport, Birmingham sacrifices significant size and thus agglomeration benefits to cities like Lyon, which rely on trams and metros.”

As Forth notes, Transport for the West Midlands – the public body that coordinates transport in the region – knows there is a problem and is taking steps to cut journey times. There is investment in bus lanes, seven sprint bus routes are in the pipeline, two tram extensions are under construction and railway stations are being reopened.

Improving the bus system would bring about significant productivity gains. If, for example, journey times became as reliable at peak hours as they are off-peak, the effective size of Birmingham would increase from 900,000 to 1.3 million people. Assuming UK cities would enjoy the same agglomeration benefits as those in France, Forth calculates that would mean an increase in output per head of 7%.

To punch at its full weight, however, Birmingham would require investment in new transport infrastructure – trams and metros. The same applies to the other metropolitan cities outside London.

The messages from all this are clear. First, transport infrastructure makes a real difference to the effectiveness of local economies and the lack of investment in places such as Birmingham has come at a price.

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As a report on how to rebuild the regional economies of the UK published last week noted, it is time the Treasury revised its assessment criteria for transport projects to give more weight to the less prosperous parts of the UK. The payoff in productivity terms would be considerable.

Second, if money is the issue the government should think about scrapping HS2 and reallocating the tens of billions it is going to cost to smaller-scale local projects. It would not be nearly as sexy but, pound for pound, the benefits of improving the bus network in Birmingham or criss-crossing the West Midlands with trams would bring much more to the local economy than cutting the journey time to London on HS2.

Finally, the story of Birmingham’s buses makes the strongest of cases for power and money to be devolved. The people who know just how long it takes to get from Stirchley to New Street station should be given the responsibility for doing something about it.