Donald Trump launched his bid to become US president this week with a speech that claimed, among other things, that “the American dream is dead”.

The property tycoon thinks his record in business and high net worth make him a good candidate for the White House.

One of his websites describes him as “the very definition of the American success story”. But critics have pointed out that Mr Trump’s father was a wealthy property developer who gave his son access to private schools and top universities as well as a sizeable inheritance.

That’s not quite the rags-to-riches story that we usually mean by the American Dream – the idea that anyone can make it to the top through hard work.

It seems Americans still believe in the Dream. In the latest World Values Survey, US citizens were about twice as likely as Germans to believe in the proposition that hard work – as opposed to luck and connections – is the key to success.

But research suggests America may no longer be a land of opportunity for the many, if it ever was.

Social mobility is limited…

Research by the Pew Charitable Trusts in 2012 found that 43 per cent of Americans born at the bottom of the income distribution remained there as adults, and 70 per cent never reached the middle.

A 2007 US Treasury study of tax receipts found that about 42 per cent of people in the lowest-earning fifth in 1996 were still in the same bracket 10 years later.

About 5 per cent of the lowest earners had made it to the top of the income ladder.

What about mobility between generations – the probability that you will do better than your parents and grandparents – compared to other countries?

Studies by the OECD and the economists Miles Corak and Gary Solon, among others, suggest that is significantly harder for people to rise above their family background in the US than in Canada or many western European countries (Britain is a notable exception).

…but not necessarily getting worse

Two recent major studies have found that – despite warnings from President Barack Obama and others about the urgency of the problem – rates of social mobility have not changed significantly in recent decades.

There is some disagreement among the experts, but if true this could suggest that – as some British academics think in relation to UK data – the idea that there was a golden age of social mobility in the 1950s and 1960s could be a myth.

Black Americans have a lower chance of success

Most research agrees that African-Americans will find it disproportionately hard to become top earners.

The Pew study says black people are more likely than whites to stay at the bottom of the family earnings ladder and fall from the middle.

Pew research suggests that about 22 per cent of black children will earn more than their parents compared to 46 per cent of white children.

It matters where you live…

This massive study led by Harvard economics professor Raj Chetty found that, unsurprisingly in a country as big and diverse as the United States, your life chances depend on where you grow up.

The probability of a child born to a family in the bottom fifth of earners making it to the top ranged from 4.4 per cent in Charlotte, North Carolina, to 12.9 per cent in San Jose, California.

The authors said: “The US is better described as a collection of societies, some of which are ‘lands of opportunity’ with high rates of mobility across generations, and others in which few children escape poverty.”

Michelle Obama is right about education…

The First Lady, who went from a poor neighbourhood in Chicago to Princeton and Harvard, was banging the drum for the importance of education on a visit to a London girls’ school this week.

As in the UK, getting a degree is still likely to be a good investment in terms of lifetime earnings, even with the spiralling cost of higher education.

An American born into the lowest fifth of earners is almost four times more likely to break into the top fifth after earning a college degree:

Things could be even worse than we think…

Most of the research on this subject looks at changes in family income over two or three generations.

The Scottish-born economist Gregory Clark takes a radically different approach and comes up with disturbing findings.

Instead of trying to follow the financial fortunes of different generations of the same family, he looks at elite groups with unusual surnames and sees how often people with those names pop up in high-status professions and institutions.

This has an obvious disadvantage: we don’t know for sure that people with the same unusual surname are actually related. But the advantage is that you can follow the fortunes of elite families for hundreds of years.

The results are astonishing. Someone with a Norman surname is still significantly more likely to attend the universities of Oxford and Cambridge now than the average Brit, some 950 years after the Battle of Hastings.

Similar results hold true in America and in countries as disparate as Japan and Sweden, according to Professor Clark.

This suggests that lack of social mobility could be a universal problem that endures far longer than we think – it could be centuries or even millennia before the fortunes of elite families return to the mean.

The verdict

The American Dream is alive and well… in Canada.