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.
I like immigration, but it is a disaster for econometrics. People, would you please stand still while we measure you? You are probably right that most immigrants arrive into the lower deciles. A hundred or so wealthy EB-5 newcomers won't skew this measure much. But to be consistent, we should then assume that many of the fathers who started in the bottom 10% were themselves immigrants. I don't see any reason to think that future immigrants would be poorer than past immigrants, so if bottom-percenters of any background find themselves moving up the ladder, it is likely for the same reasons that natives advance, and not simply an artifact of poorer and poorer new arrivals. -- Hmm, it occurs to me that my argument is not so good in light of population growth. If immigrants are constantly increasing the number of people in the bottom deciles, it will tend to shift the goalposts so that most people's "place in line" improves even if their income number does not change. (On second second thought, this applies even if all the immigrants are equally poor. Also, a higher rate of reproduction among poorer deciles would contribute to this distortion.) So you are probably wise to account for some "decile inflation" given that U.S. and Canadian policy kinda sorta welcomes poor foreigners.