The notion of an American Dream can be boiled down to a simple concept: a meritocracy in which place of origin and social status do not preclude success for hard workers.

Talk of that dream fading has been present since the Great Recession sucked 9 million jobs out of the economy and knocked down already-depressed wages for millions.

Now, a study published by the Federal Reserve Bank of St. Louis has found a way to measure that decay. It does so by coming up with a simple, mathematical definition of the American Dream as represented by social mobility defined as "the probability that a child born to parents in the bottom fifth of the income distribution makes the leap all the way to the top fifth of the income distribution."

Calculated in this manner, the chances of achieving the American Dream are nearly twice as high in Canada as they are in the US.

In the US, children born to parents in the bottom fifth of the income distribution have a 7.5% chance of reaching the top fifth, according to Stanford's Raj Chetty, the paper's author.

For the UK, that figure is 9%, while Danish children at the lower rung of the income ladder have an 11.7% chance of climbing to the top. In Canada the figure goes as high as 13.5%.

While those differences might seem fairly small, Chetty explains why they are actually pretty huge.

"When some people initially see these numbers, they sometimes react by saying, 'Even in Canada, which has the highest rates of upward mobility, the rate of success doesn't look all that high. You only have a 13.5% chance of reaching the top if you start out at the bottom,'" Chetty writes.

"It is important to remember that, unfortunately, no matter what you do, you can't have more than 20% of people in the top 20%. As such, these differences are actually quite large."

Upward mobility also varies a great deal within the US, Chetty adds, as the map makes clear.