We have strong evidence that deeper cultural, everything from attitudes towards saving, government, and social trust, persists for generations after immigration: https://www.nas.org/academic-questions/36/2/rethinking-immig... (“The authors found that forty-six percent of home-country attitudes toward trust persist in second- and fourth-generation immigrants—in the adults whose parents, grandparents, and great-grandparents were immigrants. People from high-trust societies, like Sørensen, transmit about half of their high-trust attitudes to their descendants, and people from low-trust societies do the same with their low-trust attitudes.”).
You can see this just by going around the country. Scandinavia has much higher social trust than Italy. The upper midwest, where Scandinavian immigration dominated, has higher social trust than NJ/NY, which saw mass immigration from southern Italy.
These deep-seated cultural variations, in turn, have a strong impact on societal prosperity: https://news.harvard.edu/gazette/story/2020/09/joseph-henric... (“One of the points I want to make is a lot of the big institutions we think about, like Western law or representative government, actually flow, in part, from the way people think about the world.”).
