A wealthy family is supposed to lose its fortune over time, and the reason is pure math. Every generation splits the money among more children. Run that for 600 years and a single rich family from 1427 should have its wealth scattered across hundreds of thousands of descendants by now, each holding a sliver of nothing. That is how dynasties are supposed to die. Slowly, by division.
Florence is where it did not happen. The same surnames that sat at the top of the city's tax records in 1427 are still sitting at the top today. Two Bank of Italy economists proved it by lining up the 1427 census, a ledger the city only created because it was nearly bankrupt from a war with Milan, against Florence's 2011 tax records. Roughly 20 generations apart. The rich names never moved.
Then they measured how strong the pull was. Long-run earnings elasticity of 0.04. That sounds like nothing until you remember what standard models predict after 20 generations. Zero. An advantage was supposed to fade inside three generations. This one was still showing up after twenty.
Wealth held even tighter than income. Start at the bottom of the 1427 distribution versus the top, and the gap between them is still 12% today, six centuries later.
Here is the part that should bother you. When economists track mobility one generation at a time, they measure an elasticity around 0.3 to 0.5 and conclude advantages fade fast. But a single generation of income is noisy. A rich kid has a bad decade, a lazy heir, a plumber next door who gets lucky. Strip that noise out by following the same bloodline across centuries and the real number jumps to about 0.75. Gregory Clark found that same 0.75 in England, Sweden, China, and India. Different countries, different centuries, one stubborn constant.
At 0.75 per generation, an elite family does not return to average in three generations. It takes ten to fifteen. Three hundred years and up. The exponential math of the family tree should have buried these fortunes a dozen times over. It did not even dent them.
Barone and Mocetti gave the force a name. The glass floor. The children of the rich do not fall through it, and 600 years of tax records are the receipt.