The evidence shows that immigrant groups tend to retain the social status that they arrive with, Gregory Clark points out:
The same goes with more recent immigrants to the United States. Due to visa restrictions, certain immigrant groups were permitted entry to the United States only if they could prove they had skills that were needed in the U.S. labor market. For example, the Africans, Chinese, Christian Arabs, Filipinos, Indians, Iranians, and Koreans who did gain entry into the United States were from the upper echelons of their home societies. And, in the United States, they enjoy significantly higher than average social status (as measured, again, by the number of doctors per 1,000 members of the group). Groups who, for various reasons, did not face the same restrictions — including the Hmong, Latinos, and Maya — entered the United States with low social status and have struggled to achieve upward mobility since. Immigration to the United States, in other words, rarely changes one’s social status.
The same pattern is echoed in Europe. In the 1960s and 1970s, Austria, Belgium, Denmark, Germany, and Switzerland created guest worker programs to recruit unskilled workers for basic factory jobs, often from Turkey’s poor, rural areas. Today, the children of those Turkish immigrants all perform worse on language and mathematics tests than domestic populations, which is a reliable indicator of lower social status. The lower status of their parents was thus reproduced in their new home countries.
By the same token, countries that selected elite immigrants to begin with now have high-performing immigrant classes. For example, the United Kingdom selects immigrants based more on education and skills. As a result, African, Chinese, and Indian immigrants outperform their British counterparts; although children of white British parents born between 1963 and 1975 attained on average 12.6 years of education, children of African migrants stayed in school for 15.2 years, those of Indian migrants for 14.2 years, and those of Chinese migrants for 15.1 years.