A lot has changed in the Italian city of Florence in the roughly 700 years since the 1427 census, but a striking new paper from Guglielmo Barone and Sauro Mocetti shows that one thing has changed less than you might think — the genealogical composition of who is rich and who is not.

Conventional studies of economic mobility generally look at the change across one generation — typically comparing the incomes of fathers and their sons. These studies show that mobility varies significantly from country to country, with a relatively low 0.2 percent elasticity of income in the Nordic countries and a relatively high 0.5 percent elasticity of income in places like the UK, the US, and Italy. An elasticity of 1 would mean that income status is perfectly inherited between father and son, whereas an elasticity of 0 would mean no inheritance.

The important thing is that even a relatively high elasticity implies a great deal of mobility in the long run. An elasticity of 0.5 in one generation implies 0.25 in two generations and 0.125 in three generations. As Gary Becker and Nigel Tomes concluded back in 1986, "Almost all the earnings advantages or disadvantages of ancestors are wiped out in three generations."

Barone and Mocetti show that, empirically, this is not the case, and there is meaningful income persistence across seven centuries in Florence. Their paper adds to earlier work by UC Davis economic historian Gregory Clark, which reached a similar conclusion with regard to Sweden going back to the 17th century. The implication is that there's much less economic mobility over the long run than short-term figures would lead you to believe — even in the countries where short-term mobility is very high.

Today's rich Florentines had rich ancestors

Studying ancestry over the very long term is difficult, but Barone and Mocetti took advantage of a surprisingly detailed set of tax records left behind by the city of Florence in 1427 and the fact that in Western societies surnames tend to pass lineally from father to son.

The table below shows some of their most striking findings. They looked at 2011 income data to identity the five highest-earning surnames in present-day Florence. They then looked back at 1427 data to find information about the earnings and occupations with those same five surnames 700 years ago. For privacy reasons, they then replaced those surnames with the letters A, B, C, D, and E.

They show here that the four highest-earning surnames of 2011 were all above-average surnames back in 1427. Indeed, three of the four were in the top 10 percent.

This is much greater intergenerational income persistence than could possibly be accounted for by even Italy's relatively high 0.5 percent elasticity. It's also remarkable considering the massive political and social upheavals that have occurred in the city during this time — including several episodes of foreign conquest and domestic revolution.

The situation in Sweden seems to be similar

One might, of course, see this as merely a curious fact about Florence. But Gregory Clark conducted a similar study of Sweden and had a broadly similar finding.

He did not have access to historical income data, so instead he exploited the fact that when surnames were introduced in 17th-century Sweden they had strong class implications. A defined group of noble families had surnames based on the names of their noble houses. A larger group of middle-class craftspeople adopted a name based on their profession. Peasants usually adopted a name based on the first name of their father — a name like Andersson for a guy whose dad was named Anders.

What he showed was that hundreds of years later in 2008, people with surnames indicating great-great-great-great-great-great-great-great-grandparents who were members of the nobility were drastically more likely to be in the Swedish financial elite than people with the surname Andersson.

On the one hand, this is less surprising than the Florentine case, since Sweden has had less political upheaval than Italy and the 17th century is much more recent than the 15th. On the other hand, it's more surprising, since Sweden has had much more explicit income redistribution than Italy and has a much greater level of measured economic mobility.

What's going on here?

The most plausible explanation of this data is that simply projecting one generation of mobility out across three or four or 30 generations is misleading. Income and occupational social status are linked, but only imperfectly so.

It's not unusual for the child of an economically successful professional to attend an elite educational institution and then move into an artistic or academic or nonprofit career or political career that might still involve traveling in elite circles but at a much lower salary level than his father's. If the professional's grandson then also attended an elite college and moved into a high-paying career in business and law, statistics would show a great deal of economic mobility while common sense would indicate three generations' worth of a high-status family.

Shared family access to real estate assets, social connections, a common gene pool, and elite educational institutions could allow for a great deal of long-term entrenchment even as a close-up view appeared to show instability as people shift in and out of different fields.

The truth, however, is that we don't really know what's going on. Short-term mobility is much easier to study than long-term mobility, since the records are much more precise and complete. The important thing to know is that as best as we can tell, short-term mobility does not translate into long-term mobility — even in countries like Sweden where short-term mobility is very high.

So on the one hand, Becker's reassurance that we don't need to worry about inequality because long-term mobility is high seems wrong. On the other hand, the notion that Sweden-style policies are good because they promote long-term mobility also seems wrong. Perhaps mobility itself is an inherently misguided social goal.

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