Here is some new work by Gregory Clark (pdf):
What is the true rate of social mobility? Modern one-generation studies suggest considerable regression to the mean for all measures of status – wealth, income, occupation and education across a variety of societies. The β that links status across generations is in the order of 0.2-0.5. In that case inherited surnames will quickly lose any information about social status. Using surnames this paper looks at social mobility rates across many generations in England 1086-2011, Sweden, 1700-2011, the USA 1650-2011, India, 1870-2011, Japan, 1870-2011, and China and Taiwan 1700-2011. The underlying β for long-run social mobility is around 0.75, and is remarkably similar across societies and epochs. This implies that compete regression to the mean for elites takes 15 or more generations.
Here is NPR coverage:
“If I just know that you share a rare surname with someone who was wealthy in 1800, I can predict now that you’re nine times more likely to attend Oxford or Cambridge. You’re going to live two years longer than an average person in England. You’re going to have more wealth. You’re more likely to be a doctor. You’re more likely to be an attorney,” Clark says.
Dylan Matthews offers some charts. For the pointer I thank Fred Rossoff.