Measuring centuries of numerical literacy

Measuring the evolution of human capital in previous centuries is tricky business. The most common measure, years of schooling, is fraught with major mismeasurement even in modern times, as it does not take into account the quality of education. A better measurement is to look at various cognitive tests, but those are not available for more than a few decades. Some measure of literacy are available for the 19th century, based on the ability for individuals to sign their names.

Brian A'Hearn, Jörg Baten and Dorothee Crayen use a very subtle idea to get a better grip on the evolution of numerical literacy. Accuracy in age awareness is thought to be a reflection of people that are "calculating" and using numbers in everyday life. Inaccuracies translate into age heaping, for example reporting age in multiples of five. For recent data, it is known that age heaping is inversely correlated with human capital, so why not use it as a measure of human capital for older periods, as demographic data is not that bad.

This is what A'hearn, Baten and Crayen do, and they use it to compare different regions. They find that numerical literacy started to increase in Europe in the sixteenth century after a millennium of stagnation, and Russia waited two centuries to start improving.