"Prestige is an accident that affects human beings. It comes into being and decays inevitably ... It reaches its end in a single family within four successive generations." Guglielmo Barone and Sauro Mocetti open their recent Bank of Italy working paper with that quote from the medieval Arab historian Ibn Khaldun, who, because he died in 1406, could not have known that comparing the tax records of Florence from 1427 and 2011 belies his assertion.

In "Intergenerational Mobility in the Very Long Run: Florence 1427–2011," published in April, Barone and Mocetti find that the richest and poorest families in Florence in 2011 were also some of the richest and poorest families, respectively, in 1427. Tantalizingly, they argue that Florence is unlikely to be a special case in this regard, meaning that the rest of Western Europe might display the same pattern.

The authors analyzed tax records to try to determine "intergeneration elasticity," the correlation between parents' and children's economic status. Higher elasticity means lower mobility. Italy's nationwide elasticity is about 0.5, according to Miles Corak's 2013 calculations; the UK's is about the same, while that of the U.S. is a hair lower. France's is closer to 0.4 and Canada's to 0.2. Famously equitable Finland, Norway and Denmark are even lower. Unsurprisingly, the measure is correlated to the Gini coefficient, a popular measure of income inequality. 

Barone and Mocetti found that the earnings elasticity for their sample was 0.04. In other words, as they wrote in a summary for VOX EU, "being the descendants of the Bernardi family (at the 90th percentile of earnings distribution in 1427) instead of the Grasso family (at the 10th percentile of the same distribution) would entail a 5% increase in earnings among current taxpayers (after adjusting for age and gender)." Of course, earning more over a few centuries is a good way to build up wealth, and the wealth disparity for the same families is over 10%. (For more, see also: How Monetary Policy Impacts Income Inequality.)

Surname Average euros (2011) Modal occupation (1427) Earnings percentile (1427) Wealth percentile (1427)
5 top earners in 2011:
A 146,489 Member of shoemakers' guild 97% 85%
B 94,159 Member of wool guild 67% 73%
C 77,647 Member of silk guild 93% 86%
D 73,185 Messer (lawyer) 93% 85%
E 64,228 Brick layer, sculptor, stone worker 54% 53%
5 bottom earners in 2011:
V 9,702 Worker in combing, carding and sorting wool 53% 45%
W 9,486 [Ditto] 41% 49%
X 9,281 Sewer of wool cloth 39% 19%
Y 7,398 Medical doctor 84% 38%
Z 5,945 Member of shoemaker's guild 55% 46%
Source: Tax records from the 1427 Census of Florence and from the Florence statistical office (fiscal year 2011); surnames are not reported for privacy reasons.

As the chart above—adapted form Barone and Mocetti's study—shows, the five highest-earning families in 2011 were all on the top half of the wealth distribution 584 years prior. The five lowest-earning families in this century were similarly in the bottom half in the 15th century. The same pattern does not hold for the earnings distribution, but to show that there is still a correlation, we created the graphs below (note that we only used the five highest and lowest earning families from the table above, so these charts aren't at all indicative of the whole data set):

How do the authors interpret these findings? They write that subsequent generation earning elasticity was very high for most of the intervening period—ranging from 0.8 to 1.0—meaning that society was more immobile than at present. Perhaps the effects of mass schooling and industrialization, which began to affect Italy in the 20th century, will begin to blur Florence's stubborn 15th-century wealth distribution. (For more, see also: A Brief History of Income Inequality in the United States.)

Also, where readers might expect to see a glass ceiling preventing the poor from scaling the economic ladder, the authors see "some evidence of the existence of a glass floor that protects the descendants of the upper class from falling down the economic ladder." 

In any case, Ibn Khaldun's assertion that four generations would erase a given family's wealth or poverty turned out not to be correct. Twenty-something generations later, Florentines still associate some of the same last names with wealth. And in case you think it's unfair to argue with a scholar who's been dead for 600 years, Gary Becker and Nigel Tomes were even more sanguine in 1986: "Almost all the earnings advantages or disadvantages of ancestors are wiped out in three generations."

At least in Florence, perhaps not. 

The original paper can be found here.

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