The British are worrying about ghettos. David Cameron’s anxiety about “communities where people from different ethnic origins never meet, never talk, never go into each others’ homes” seems to have found echoes up and down the political spectrum. The American political scientist Robert Putnam has even been invited to collaborate with Manchester-based academics on the question of immigration and social change. Professor Putnam’s work on “social capital” is justly admired, but perhaps we should have invited some economists across the Atlantic too.

David Cameron’s nervousness is understandable, but an early contribution of economists was to point out that segregation need not be the result of sinister processes. Thomas Schelling, one of last year’s Nobel laureates in economics, once showed that this was true in an absurdly simple little demonstration that, once they have witnessed it, people rarely forget.

You can prove it to yourself at home with a chessboard and a collection of black and white counters. Scatter the counters at random across the chessboard, leaving about a third of the spaces empty. Each counter will have up to eight neighbours; look for a white counter whose neighbours are more than two-thirds black, and move it to the nearest space where it is not so badly outnumbered.

The counters represent people, of course. Do the same for other “counters” and you will find a chain reaction taking place. Each counter that moves leaves an old neighbour isolated. The neighbour moves in turn. The blacks and whites separate like oil and vinegar, despite the fact that each might be happy to live in a mixed neighbourhood.

A desire not to be racially outnumbered more than two to one is nothing to be proud of, but it hardly signifies membership of the Ku Klux Klan. Professor Schelling showed that rather mild preferences could lead to levels of segregation that looked very alarming. What his model does not reveal is how destructive the results of segregation are - if, indeed they are destructive at all.

So, are ghettos a bad thing? The American economists David Cutler and Ed Glaeser have been returning to this rather pointed question, on and off, for a decade. Their initial research suggested, plausibly enough, that living in a racial enclave damaged your education and job prospects.

Follow-up work didn’t concur. Evidence started to emerge that minority groups might even benefit from self-segregation. (One small example: the research on car-pooling that I described in July, showing that blacks were more likely to get a lift to work from a black-majority area.)

Professors Cutler and Glaeser then revisited the question with a third economist, Jacob Vigdor. Armed with more data, they concluded that the overall averages are masking what is really happening. Ghettos create winners and losers. Those living inside the ethnic or religious enclave suffered as a result: they were likely to be cut off from opportunities to learn from, or be employed in, the wider world. Unless the enclave community itself is highly educated and prosperous to start with, this is a trap.

But a growing number of people benefit from the ghetto: these are “connectors”, members of minority groups who live outside the ghetto and link it to the outside world. Vigdor speculates that such people are entrepreneurs benefiting from selling services into the segregated community, or employing its members to produce something for the wider world.

Putnam emphasises the importance of “bridging social capital” - relationships that cross ethnic or religious dividing lines. If Vigdor is right, the people who act as bridges are growing in number and being rewarded for their efforts. That is reassuring, as well as making good economic sense.