There is a famous Monty Python sketch called "Four Yorkshiremen". It portrays tuxedo-wearing men sipping fine red wine, chomping on cigars and eagerly reminiscing about their impoverished childhoods. The conversation quickly turns into a bizarre arm's race of boasting about humble origins when even living in a hole is seen as the height of luxury. Soon, one man is claiming to have grown up "in a lake", prompting one companion to exclaim:

"You were lucky to have a lake! There were a hundred and fifty of us living in t' shoebox in t' middle o' road."

Yet, listening to the endless drum beat of speeches from both the Republican and Democratic conventions in the past week, it seemed they were mimicking the Pythons' finest work. According to their own stories, speaker after speaker detailed their family's rise from poverty to success in the space of a generation or two. In order to praise the powerful myth of the American Dream, both Republicans and Democrats battled to outdo each other with origin stories of deprived woe.

Here, for example, is Rick Santorum, praising the memory of his Italian immigrant coal-mining grandfather. "My grandfather mined coal until he was 72 years old … working the mines may not have been the dream he dreamed – I never dared to ask him – but I think his answer would have been that America gave him more than he had ever hoped," Santorum opined, though surely anyone would hope for more than working in a coal pit until well past 70.

But that was just for starters. Former Minnesota Governor Tim Pawlenty could top that.

"My dad was a truck driver. My mom was a homemaker. She died when I was 16, and my dad lost his job not long after that."

Wow. That must have been tough. But not as tough as Florida Senator Marco Rubio's grandfather's experience. "He was born to a farming family in rural Cuba. Childhood polio left him permanently disabled," Rubio explained.

Some Republicans went back a little further. Kentucky Senator Rand Paul talked about his great-grandfather. "No sooner had he stepped off the boat then his father died. He arrived in Pittsburgh as a teenager with nothing, not a penny," he said. Even – staggeringly – super-rich Mitt Romney joined in. "My dad had been born in Mexico and his family had to leave during the Mexican revolution," Mitt said. "I grew up with stories of his family being fed by the US government as war refugees."

Make no mistake, though, this posturing was a thoroughly bipartisan affair. Here is new Democratic Hispanic leader Julian Castro, the mayor of San Antonio:

"My grandmother was an orphan … She never made it past the fourth grade. She had to drop out and start working to help her family. My grandmother spent her whole life working as a maid, a cook and a babysitter, barely scraping by."

Or listen to Illinois congressional candidate Tammy Duckworth. "Mom took in sewing. My 55-year-old dad tried to find work. But at 15, I was the only one with a job – after school, for minimum wage. Thank God for the food stamps," she told the Charlotte gathering.

From the famous to the unknown, everyone got in on the act. Hollywood star Scarlett Johansson was not to be denied. "My father barely made enough to get by. We moved every year, and we finally settled in a housing development for lower middle-income families," she said, though that hardly sounds too Dickensian. But Michelle Obama could make up for that. "My father was a pump operator at the city water plant, and he was diagnosed with multiple sclerosis when my brother and I were young," she reminisced.

It is important to say there is no doubt these stories are true. They are also moving, showing the brave struggles and sacrifices that one generation can make for another, or the sheer obstacles that some individuals have overcome to achieve high office. But in the context of the propaganda jamborees that are modern conventions, they are being used to make a political point: the American Dream came true for me and it can for you, too. Increasingly, however, evidence for the truth of that sentiment is seriously wanting.

Despite the heartwarming tales emerging from both sides of the political aisle, social mobility in America is under serious threat. In many ways, if you are to be born poor, you would be better-off being born somewhere else in the developed world than in the United States of America. Your chances of improving your social lot are likely to be better. As Columbia University Professor Howard Steven Friedman writes, about the work of the Economic Mobility Project, the prospects of bettering oneself in the US can be worse than in many other developed countries, even class-ridden Britain. Friedman points out that an American male's income is nearly twice as reliant on his father's background as a Canadian's. Another study showed some 42% of American sons of fathers born in the poorest fifth of society ended up in that fifth themselves. That compares to 30% in the UK, and a range of 25-28% in Denmark, Sweden, Finland and Norway.

A separate report, by University of Ottawa Professor Miles Corak in 2006, reviewed 50 mobility studies of nine countries. He, too, ranked the Scandinavian nations and Canada as the most likely to be socially mobile, with the US and the UK bringing up the rear. But just in case you had any doubts, the Nobel Prize-winning economist Joseph Stiglitz has also got in on the argument. In his recent book, The Price of Inequality, he writes that America's growing gap between the rich and the rest of us has decreased social mobility:

"America has the least equality of opportunity of any of the advanced industrial economies."

Many believe the nub of America's problem is with the very poor, skewing the figures for the country as a whole. As the first graph in this Business Insider story shows the real difference between a socially mobile country, like Denmark, and a less mobile one like the US is with the bottom fifth of society. Elsewhere on the spectrum, countries are much more comparable. Which makes the "poverty arm's race" on display in Tampa and Charlotte all the more misleading: if you are really born on the "wrong side of the tracks" in today's America, you are much more likely to stay there than end up testifying to a national convention about your remarkable rise out of deprivation.

As America's politicians outdid each other to try and show how far they had come, the reality on the ground now is making those journeys longer and far more difficult. Unlike the Monty Python sketch, that is not funny.