I guess this eco-mobiilty all depends on the social structures and political environments. There is a Chinese proverb "富不過三代", or, fortune won't last three generations. The Chinese genealogy is relatively complete and you can actually trace Confucius' offspring to this date. But you'll be surprised to find big names today rarely also have some big name ancestors 500 years ago. One reason is that the Chinese social and political are constantly changing. In China the longest dynasty Ching lasted 268 yrs. Basically every 70-150 years there is a game-of-thrones type of revolutions going on, and the entire soc-pol systems flopped. Another reason is that a common used punishment by the emperor in the past is collective punishment, i.e. if someone is sentenced to death, all his/her relatives up to three upstream and three downstream, sometimes even all cousins, are also sentenced to death. If someone did escaped they would just change their surnames (and Chinese people change surnames relatively more frequently than we would think.) That's probably why a big-shot in the history book might have no offspring to be found nowadays.