The Economist reports about research that exploits variation in the frequency of surnames over time to infer the degree of social mobility over centuries.
As late as 2011 aristocratic surnames appear among the ranks of lawyers, considered for this purpose a high-status position, at a frequency almost six times that of their occurrence in the population as a whole. Mr Clark reckons that even in famously mobile Sweden, some 70-80% of a family’s social status is transmitted from generation to generation across a span of centuries. Other economists use similar techniques to reveal comparable immobility in societies from 19th-century Spain to post-Qing-dynasty China.
The article quotes several papers on the topic.