Or rather, three tales - for there are at least three different ways of looking at the economic contribution of immigrants. You can look at the statistics, and see to what extent immigrant groups seem to prosper (or otherwise) relative to the locals. You can look at the disproportionate contribution of immigrant stars - the people who have not just prospered, but have in fact changed the country in some dramatic way. And you can look at the dynamic contribution of migration in shaping economies, and in particular why moving people around may be becoming a more important engine of economic growth.
If you ask the question "how well do immigrants do?", the question that immediately follows is, "which immigrants?", for the picture is very mixed. The best work on this subject probably comes from the Policy Studies Institute, which has produced a series of reports on ethnic minorities in Britain, while the Employment Policy Institute also does helpful research.
So we know quite a lot about how various immigrant groups prosper. Some clearly do very well. Among the "winners" are African and Caribbean women, who earn substantially more than white women; African-Asian and Chinese men also have a higher chance than whites of earning more than pounds 500 a week, and they are less likely to be out of work.
Of course, not all immigrants are from non-white ethnic groups. Other recent figures show that Irish people in Britain now do well, while Americans and immigrants from the EU also seem to be prospering. Incidentally, two of the Law Lords who gave that controversial verdict on General Pinochet were immigrants from South Africa.
By contrast, some immigrant groups find it hard to make economic headway here. There is very high unemployment among people from Pakistan and Bangladesh, and their households are among the poorest in the country. Caribbean men tend to do badly. There is also evidence of a "glass ceiling" - of well qualified people from immigrant communities not getting as good jobs as their qualifications would suggest they should. On the other hand, the NHS would be in a dreadful mess without the services of African and Caribbean women.
If you turn the question on its head and, instead of asking whether immigrants do well out of Britain, ask whether Britain does well out of them, I suppose the answer would be equally mixed. The country clearly benefits enormously from the contribution of some communities and does not seem to benefit much from that of others.
Looking ahead, I suspect that the performance of immigrant communities will tend to improve rather than deteriorate, for several reasons. For a start, any ethnic disadvantage from being seen as "different" will fade away. This is partly because mixed relationships are booming: half of the Caribbean men and one-third of Caribbean women have white partners. But it is also because some of the professions in which immigrants have been particularly successful - such as entertainment and sport - are strong growth industries.
In the US, it used to be said that blacks could make it to the top only in music and sport, as though success there were somehow not as valuable or worthwhile as success in business or the law. In fact, those are two terrific professions to be good at; a few stars have a disproportionate impact on the economy.
That leads to the second area in which immigrants make a special contribution: the stars. Immigrant stars burst out in just about every walk of life. If you include second-generation immigrants as well as first, political stars would include Sir Leon Brittan, Michael Portillo and Michael Howard on the right, and Paul Boateng, Keith Vaz, Bernie Grant and Diane Abbott on the left. There is a vast range of success stories in the business community, too - Lord Paul, who runs the industrial group Caparo, and Lord Hamlyn, the publisher, were among the prominent contributors to Labour at the last election.
Lakshmi Mittal, another big contributor, is ranked as Britain's third- richest person and richest Asian, a little ahead of the Hinduja brothers, who are supporting the spirit section of the Millennium Dome - and have been substantial supporters of the Tories.
I haven't seen any comparable statistics, but I would suspect that immigrant businesspeople play a larger role in the economy here than they do in France or Germany, though naturally not in the US. It is self-evidently possible for immigrant business people to "make it" in Britain - so many have.
But the more interesting question is whether any have really changed the nature of our economy. I can think of three post-war examples. One is Siegmund Warburg, who came from Germany in the Thirties and founded the merchant bank SG Warburg. He virtually invented the contested take- over, and played a crucial role in recovering the City's international business in the Fifties and Sixties.
A second example is the Grade family, which came from the Ukraine in the early years of this century. As a family, they were immensely successful in showbiz, with Lew and Leslie Grade and Bernard Delfont all making great successes of their lives. But Lew stood out as the most important single person in developing commercial TV in Britain. Yes, the industry would have grown, but I don't think it would have achieved its popularity so quickly without his leadership at ATV - or had the impact on the stodgy BBC that it did.
My third example would be the Saatchi brothers, whose family came from Baghdad to revolutionise our advertising industry. Two of the world's largest ad groups are now British, the original Saatchi empire (which ejected the brothers, who now run a new agency) and WPP, run by a former Saatchi executive.
The fact that Britain punches above its weight in financial services, the entertainment industries and advertising all has something to do with immigrants.
Looking ahead, I'm fairly sure that migration will become more important, not less. It is not just that a society open to immigrants tends to attract good brains. Only this week a report by the Government suggested that teeenagers from ethnic minorities are far more likely to be in full-time education at 18 than their white counterparts.
That human capital - as opposed to financial capital, industrial plant, natural resources and so on - has become the most important single determinant of economic success. Finance? The world markets are awash with money seeking a good home. Manufacturing capability? Foreign direct investment transfers the knowledge of how to make things within a matter of weeks. Resources? They seem to be getting ever cheaper in real terms. What matters is people. Any country that can become a magnet for talented people will be assured of economic success.
But who are these talented people? What are the talents of the future? In some areas it is easy to see. The City has become a magnet for talent, for if you want to make a pot of money in international finance it is arguably the best place in the world to do so. In the entertainment industries, Britain is a magnet for talent, and sport - well that has become a global business, and we do seem to be able to attract foreign talent to come and work here.
But in other areas it is very hard to know what talent really is. Who could have predicted that writing software for video games would be a great growth industry in Britain? On paper an economically literate immigration policy should seek to attract the highest skilled, and that is certainly what some countries seek to do. But you also need pirates - people who don't have the formal qualifications, but have an overriding desire to make a better life for themselves and their families. I am not suggesting that we should welcome every container-load of refugees who sneak in at Dover. But just a few may become the Lew Grades of the next century.Reuse content