Don't immigrants show that not only hard work (which they usually did) but other factors (like emigrating from a bad environment, which can be pretty risky) are needed for a better life?
I don't think it's the emigration part that's needed.
People are usually forced to emigrate somewhere else because of the conditions or their home country.
Those who are down to emigrate to a foreign country (especially if their original country is not a warzone or is not that bad - implying they're really trying hard to improve their life) probably have some other characteristics that can be useful for achieving success.
The debate then moves on how much of those characteristics are genetic and how much are due to the bad environment per se (or maybe the good environment their families where able to setup in a bad environment) - on which I think we don't yet have a scientific answer.
