Social Mobility is often measured as the chance of your children's income moving up/down from your income quintile compared to other people in the same nation.
Social mobility [...] refers to individuals or families, and their change in income (economic mobility). It also typically refers to vertical mobility—movement of individuals or groups up (or down) from one socio-economic level to another, often by changing jobs or marriage; [...] Social mobility can be the change in status between someone (or a group) and their parents/previous family generations ("inter-generational"); or over the change during one's lifetime ("intra-generational"). [...] "relative"—an estimation of the chance of upward (or downward) social mobility of a member of one social class in comparison with a member from another class. A higher level of intergenerational mobility is often considered a sign of greater fairness, or equality of opportunity, in a society.
While I have found some data regarding social mobility within a nation, I have been having difficulty in finding data regarding international social mobility. The wiki on Social Mobility notes that the USA has a lower level of social mobility than Sweden, but those studies (and others) are all measured relative to other people within the same nation.
The New York Times and the Wall Street Journal published a series of front-page articles on this issue in May 2005. Americans have often seen their country as a ‘land of opportunity’ where anyone can succeed despite his background. A study performed by economists at the Organization for Economic Cooperation and Development in 2009 found that Britain and the United States have the lowest levels of intergenerational mobility, or the highest levels of intergenerational persistence. The Nordic countries (Norway, Sweden, Denmark and Finland) and Canada tend to have high rates of social mobility. Norway proved to be the most mobile society.
To give you an example of why this matters, imagine a nation where nearly everyone makes $1 a day. Would people still consider that nation, the 'land of opportunity' because of a low level of intergenerational persistence? (i.e. If you were born into the top quintile making $2/day (or bottom quintile making $0.75/day), but your were equally likely to remain there or in one of the other quintiles (20% chance)).
For a real life example, I was able to find this income data for 2011. Table 10.1 shows Sweden and the USA Household Annual Disposable Income by Decile (pg 24)
Decile 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Sweden|22,167|30,875|36,170|40,873|45,634|50,926|57,384| 66,273| 81,348|146,487 USA | 8,223|20,431|31,872|43,895|57,260|72,886|92,292|118,632|160,864|300,367
What are the chances of a person born in Sweden moving from their USA income quintile/decile to another USA income quintile/decile over their lifetime? (is this more/less than the intergenerational social mobility of an American in the USA?)
(I.e. What are the chances of a Swede born into a family making $22,000 (Decile 2 USA) to end up making $160,000 (Decile 9))