I have a thought: how unlikely is it, a priori, for a bottom-tenth-son to be in the bottom decile in the "after" simply based on the intertia of new immigrants (to the US) replacing the bottom decile every generation? In other words, would they not have to actively go "backwards" in order to remain where they are and not be at least somewhat supplanted (in the bottom decile) by new immigrants? I haven't thought that out very far, but I will use it as the basis for my guess. Bottom: 5%
2nd: 15%
3rd: 20%
4th: 20%
5th: 10%
6th: 10%
7th: 10%
8th: 5%
9th: 5%
10th: trivial In other words, I'm guessing (with considerably less than 5 minutes of thought sadly) that it's reasonably easy to get somewhere above the bottom decile, but quite difficult to get past about the 7th. I'm probably comically wrong.