Rethinking Age Heaping: A Cautionary Tale from XIX Century Italy

June 22, 2021 | Blog
Home > Rethinking Age Heaping: A Cautionary Tale from XIX Century Italy

by Brian A’Hearn (Oxford University), Alexia Delfino (London School of Economics), and Alessandro Nuvolari (School of Advanced Studies, Pisa)

This blog post is based on an article recently published on open access on The Economic History Review, available at this link


A promising measure of human capital increasingly used by economic historians is age heaping: the overrepresentation of round numbers in an age distribution.  The idea behind this measure is intuitive.  If some individuals lack sufficient ‘numeracy’ to know their precise age, or are unable  to calculate it, they report a round number that is not implausible and has some salience for them. In a histogram, this results in observations being excessively ‘heaped’ on particular ages (Figure 1).

Figure 1. Frequencies of reported ages in the Italian census of population of 31 December 1881. Source:  MAIC, Censimento 1881

The interpretation of age heaping as a proxy for numeracy prevails in economic history.  However, other disciplines – such as political science and social history – view state capacity and culture as more relevant determinants of age heaping patterns.   We challenge the idea that age heaping in historical sources captures only numerical abilities through a case study of nineteenth century Italy, which, after 1861, was a new and developing state characterized by major geographic disparities in educational attainment and economic development.  This heterogeneity allows us to investigate the relative importance of different determinants of age heaping.


Age heaping and literacy

Age heaping in the early Italian censuses shows a number of patterns that are difficult to reconcile with a numeracy interpretation.  Figure 2 illustrates one of these anomalies. Each bar represents the Whipple index of age heaping among literates (the left/smaller value) and illiterates (the right/larger value) in one of Italy’s 69 provinces in 1871.  A Whipple index of 100 indicates no heaping and it increases with the extent of age heaping (Figure 2).

Figure 2. Whipple index values for literates (smaller/left value) and illiterates (larger/right value). Notes: Data refer to ages 23-72. Provinces are ranked 1-69 by age-heaping among literates. Source: as per article.

According to the interpretation of age heaping as a measure of human capital, we should expect people with a similar level of education to report their age with similar accuracy. Yet, more than 50 points separate the minimum and maximum W values for literates. Similarly, we find tremendous variation in age heaping among illiterates.  There is a gap of more than 100 points in the Whipple index between the minimum and maximum provincial values for illiterates.  This huge variation within the literate and illiterate groups dwarfs the variation between them, which is only 32 points on average.  Why do masses of illiterate peasant women in the North (W=130) report their ages just as accurately as the few educated men of the cities in the South (W=129)?

Further anomalies include variation by gender and marital status, and a sharp improvement in accuracy with the census of 1901 that is uncorrelated with any sharp improvement in educational attainment.  This latter observation suggests better census procedures (state capacity) rather than better numerical skills.


 Numbers in everyday life

Qualitative evidence on Italian social history during the nineteenth century also casts doubts on the assumption that individuals reporting heaped ages were severely innumerate.  Numbers were everywhere in the worlds of both peasants and city dwellers and included the ubiquitous game of morra, the objective of which is to quickly guess a sum (Figure 3).

From the late seventeenth century onward the state lottery (lotto) also ensured that all Neapolitans knew their numbers from 1 to 90.  A passion for the lotto was widespread. Printed lottery tickets specifying the numbers chosen by the bettor and the potential winnings presumed widespread recognition of written numbers.

Figure 3. A game of ‘Morra’ in Rome, 1816. Source:

Other matters required basic numeracy. Poor families developed rudimentary but effective strategies of cost-benefit analysis, which surely required a non-trivial amount of numerical skills, though not necessarily in forms familiar to us today. Written recordkeeping using nonstandard, ideographic systems of numeration has been documented for illiterate Umbrian peasants and Venetian fishermen in the late nineteenth century (Figure 4). This evidence reinforces the idea that, even among unskilled occupations, some basic numeracy was widespread.

Figure 4. Log books of Chioggia fishing boats. Note. Each entry represents the sum due an individual fisherman. The trapezoid at the beginning of each row is a sort of insignia adopted by the fisherman to identify himself. The marks that follow represent the sums due. In some cases, the owner of the boat also used Arabic numbers to indicate a total (e.g. 64 at the end of the first entry). The dots are used as a separation sign. Source: A.Ninni, Sui segni prealfabetici usati anche ora nella numerazione scritta dai pescatori clodiensi (Venice, 1889).


What’s left in age heaping for economic historians?

Education, and school-inculcated arithmetic skills, surely had a role  in age heaping patterns, but they cannot explain most of the variation in age heaping over time, between groups, and across Italian regions.  The decline of age heaping should be more properly seen as an outcome of modernization, a complex historical process featuring institutional change and cultural shifts alongside the spread of basic education.  A major implication of our findings is that age-heaping as a general indicator of numeracy is not warranted.


To contact the authors:

Brian A’Hearn,

Alexia Delfino,

Alessandro Nuvolari,