Gregory Clark has been studying (pdf) social mobility by looking at surname distributions among elites and underclasses. His question: How many generations does it take for elite or nonelite surnames to regress to the mean? Answer: centuries!
Clark compared England 1086-2011, Sweden, 1700-2011, the USA 1650-2011, India, 1870-2011, Japan, 1870-2011, and China and Taiwan 1700-2011.
Here are his preliminary results:
1 … Elites and underclasses all tend to mediocrity at a constant rate. And the rate of movement is constant across generations.
2. β is much higher than conventionally estimated, between 0.7 and 0.8. Social mobility is extremely slow. Complete regression to the mean typically takes 10-16 generations, 300-500 years.
3. β is constant across societies and social systems.
4. β is constant across measures of status – wealth, education, occupation – and across the entire distribution of status, being the same for the upper tail as for the lower tale.
5. Since β 2 = 0.5-0.6 the majority of social status is determined at conception.
6. We observe persistent elites and underclasses only in two cases. The first is an isolated elite with marital endogamy (as with the Copts in Egypt). The second is where an elite or an underclass is maintained by selective retention of members with the elite or underclass characteristics, and recruitment of outsiders with the characteristic.
7. Assortative mating is what makes β so high. Mating has become more assortative in the modern world, so mobility rates may decline further (Herrnstein-Murray claim).
8. Social status is likely mainly of genetic origin.
Worth emphasizing: Mobility rates may decline further owing to more assortative mating. If the elite marries the elite, and the nonelite marries the nonelite, enduring stratification ensues.
Reference: Gregory Clark, “Surnames and the Laws of Social Mobility” (pdf)