BRITAIN’S measly productivity growth gives politicians sleepless nights. Since 2007 output per hour has hardly budged, while in America it has jumped by 9%. Unless productivity picks up, wages cannot grow: small wonder that Sajid Javid, the business secretary, calls it “the economic challenge of our age”. Standard remedies to boost productivity include investing in education, health care and technology. But Britain’s government thinks that by tackling another big problem—the bubbly housing market—it will make productivity soar. Is it right?

Britain is crying out for new homes. The country needs to add about 250,000 per year to satisfy demand; in 2014 it built probably 150,000. As part of a 15-point “productivity plan”, on July 10th George Osborne, the chancellor, announced big changes to planning regulations, in a bid to stimulate housebuilding. A much-hyped “zonal” system will grant automatic planning permission on suitable brownfield sites, a policy borrowed from American cities. Londoners will be able to add extra storeys onto their houses up to the height of adjoining buildings. Around transport hubs the government will cajole local planning bodies into building high-density housing (it isn’t clear how).

Mr Osborne also wants to give central government the power to force through planning applications when local authorities dawdle. Councils that fail to make decisions “on time”—which probably means within 13 weeks—will suffer penalties. (The delays are partly a problem of the chancellor’s creation: local councils’ spending per person has been cut by 20% in real terms in the past five years.)

To understand how all this could boost productivity, consider the geography of the job market. London is by far the most productive part of the country, thanks to its clusters of finance, technology and nerds. Since the recession Britain has created 2m jobs, one-third of them in the capital. London could create more still, but its lack of housing hems it in. The average house there now costs £370,000 ($577,000), nearly double the national average; in some boroughs the ratio of prices to earnings exceeds 20:1. Soaring demand has met stagnant supply. In the past decade the number of homes in London has grown by just 9%.

Workers are cramming in more tightly. The average number of people per dwelling in London has risen from 2.3 to 2.5 in the past decade (see map). Others are moving out of London, taking jobs in less productive places or wasting time on marathon commutes. From 2005 to 2014 the number of people commuting into the capital rose by 32%. One paper published in 2010 found that absenteeism among German workers would be 15-20% lower if they did not commute. If it were somehow possible to scrap commuting altogether, British workers would see a productivity boost worth about £12 billion a year, according to the Centre for Economics and Business Research, a research group.

Mr Osborne’s planning shake-up ought to ease the housing shortage a little. But other proposals may worsen it. Housing associations (non-profit outfits that provide social housing) will be forced to cut rents by 1% a year for the next four years. Despite making homes more affordable to tenants in the short term, it will make it less attractive to build, reducing supply. According to the Office for Budget Responsibility, a fiscal watchdog, housing associations will now construct 14,000 fewer affordable homes by 2019-20 than previously planned—a steep drop for the sector, which built 37,000 homes last year.

And there is no guarantee that relaxing planning laws will produce a long-term increase in the rate of housebuilding, argues Neal Hudson of Savills, an estate agent. For years land has been an appreciating asset; as a result many landowners’ price expectations are firmly set. There are limited incentives for them to sell at a faster rate, since that might lower the price they can get. They will be particularly unhurried where land is already generating income through other uses. Moreover, building firms are not in the best shape. Having cut back during the financial crisis, they may struggle to ramp up production.

Most ominous of all is Mr Osborne’s promise to exploit brownfield land but “keep on protecting” the green belt, the rings of development-free land (much of it not particularly green) around cities. Nathaniel Lichfield & Partners (NLP), a planning consultancy, suggests that just 1m homes could fit into existing brownfield sites. That is nowhere near enough: more than 3m extra houses will be required in just the next 15 years, NLP reckons. And brownfield sites tend not to be located where demand for housing is high, meaning that the productivity-boosting effects of redeveloping it are limited. Paul Cheshire of the London School of Economics points out that there is enough green-belt land in Greater London alone to build 1.6m houses at average densities. Few politicians want to bulldoze the green belt. But if housing supply is to increase, and with it productivity, that may have to change.