Isn't that generally the case income-wise? Immigrants are a self-selecting bunch. Picking up and moving to a different country is hard and you need to be fairly dedicated to cross that gulf and put up with all the differences in order to make it work. South Asian Indian-Americans are one of the highest earning ethnic groups in the US, earning about twice the median national household income. But the median income in India is awful.
That's a very interesting question, and the answer isn't straight-forward. On the one hand, obviously we should expect some selection effects. On the other hand, there is a relative status effect counter-acting it. Long story short, people prefer to be relatively rich in a poor country than relatively poor in a rich country, even if their absolute level of wealth would increase. Stark & Taylor (1991)[0] for example found that, at least when it comes to Mexico, the relative preference trumps the absolute preference: poorer households were more likely to migrate.
