The Journal of Economic History


Quantifying Quantitative Literacy: Age Heaping and the History of Human Capital

Brian A'Hearna1, Jörg Batena2 and Dorothee Crayena2

a1 Pembroke College, University of Oxford, Oxford OX1 1DW, United Kingdom. E-mail:

a2 Department of Economics, University of Tuebingen, Mohlstrasse 36, 72074 Tuebingen, Germany. E-mails: and


Age data frequently display excess frequencies at attractive numbers, such as multiples of five. We use this “age heaping” to measure cognitive ability in quantitative reasoning, or “numeracy.” We construct a database of age heaping estimates with exceptional geographic and temporal coverage, and demonstrate a robust correlation of literacy and numeracy, where both can be observed. Extending the temporal and geographic range of our knowledge of human capital, we show that Western Europe had already diverged from the east and reached high numeracy levels by 1600, long before the rise of mass schooling or the onset of industrialization.


A great many people helped us assemble the numeracy data set and refine our analysis, and we are indebted to them all. Special thanks to Bob Allen, Albert Carreras, Greg Clark, Kerstin Manzel, Jaime Reis, Vania Stavrakeva, Joachim Voth, Jan Luiten van Zanden, and seminar participants at Pompeu Fabra, EUI Florence, Tuebingen, LSE, and Oxford. Financial support was provided by the DFG (Crayen), EU-HIPOD, and ESF (GlobalEuroNet, Baten). Brian A'Hearn did the research for this article at Franklin and Marshall College, Jörg Baten and Dorothee Crayen partly at Universitat Pompeu Fabra.