Researchers at the Bank of Italy have used surnames (which are relatively region-specific) as a proxy to inspect the fortunes of Florentine families since the 1427 census. They found the top-five earning surnames in 2011 were also the elites six centuries ago, when they were lawyers or members of the wool, silk and shoemaker guilds. The researchers found evidence of dynasties in some elite professions, such as banking and law.
That is not to say there was no mobility. Lower-class people had a fairly good chance of rising to a higher position, but there seemed to be a “glass floor” that stopped the upper classes from sliding to the bottom.
Florence is not unique. Studies (often using rare surnames to track families through generations) have found similar stories in countries as varied as Sweden and China. In the UK, the effect seems to last about six generations before finally petering out.