One analysis I read was that most migrants to the U.S. are essentially the rural poor from Mexico. Rural tends to equate to higher birth rates, while urban residents have fewer children. Thus the illegal immigrants were most likely to be those with the highest birth rate at home, and the disproportionate migration of that high fertility demographic here is why Mexico’s rate fell so fast.
That makes sense. I wonder if there’s a similar dynamic in the birthrates of Eastern Europeans living abroad, vs. those who remain their home country.