Illegal immigrants may well be hard working, which is admirable, but are they also educating themselves to be more productive (i.e. able to generate more wealth

Illegal immigrants may well be hard working, which is admirable, but are they also educating themselves to be more productive (i.e. able to generate more wealth from the same number of hours worked?) If not, then they're not contributing towards growth in living standards/alleviation of poverty.