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Assessing human capital formation with the age heaping indicator and other measures of human capital formation

The measure of the production factor “human capital” has never been simple, as advanced forms of skills are difficult to compare. Hence all economists have resorted to the use of proxy indicators, such as the share of people signing a marriage register. Grundlach (2001) notes that the empirical measurement of the human capital factor and the productivity of education in economic growth are still not completely satisfying in human capital research so far. A comparison of different proxy indicators might perhaps be the best possibility to obtain reliable insights. This is the rationale for using the age heaping methodology (as well as literacy and schooling in comparison, wherever this is available to us). We will explain the advantages and caveats in somewhat greater detail, as the application of the method in economic history is still relatively new. This approach employs the set of methods that developed around the phenomenon of “age heaping”, i.e. the tendency of poorly educated people to round their age erroneously – they answer more often “30”, if they are in fact 29 or 31, compared with people with a better endowment of human capital (Mokyr 1985). Crayen and Baten (2008) found that the relationship between illiteracy and age heaping for LDCs after 1950 is very close. They calculated age heaping and illiteracy for not less than 270,000 individuals that were organized by 416 regions, ranging from Latin America to Oceania. The correlation coefficient with illiteracy was as high as 0.7. A’Hearn, Baten, and Crayen (2009) used a large U.S. census sample to perform a very detailed analysis of this relationship. They subdivided by race, gender, high and low educational status and other criteria. In each case, they obtained a statistically significant relationship. Remarkable is also the fact that the coefficients are relatively stable between samples, i.e. a unit change in age heaping is associated with similar changes in literacy across the various tests. Those results are not only valid for the U.S.: In any country studied so far which had substantial age-heaping, the correlation was both statistically and economically significant.

In order to assess the robustness of those U.S. census results and the similar conclusions which could be drawn from late twentieth century Less Developed Countries, as mentioned in the introduction to this study, A’Hearn et al. (2009) also assessed age heaping and literacy in 16 different European countries between the Middle Ages and the early nineteenth century. Again, they found a positive correlation between age heaping and literacy, although the relationship was somewhat weaker than for the nineteenth or twentieth century data. It is likely that the unavoidable measurement error when using early modern data induced the lower statistical significance.

The possibly widest geographical sample studied so far has been created by Crayen and Baten (2010), who were able to include 70 countries for which both age heaping and schooling data (as well as other explanatory variables) were available. They found in a series of cross-sections between the 1880s and 1940s that primary schooling and age heaping were closely correlated, with R-squares between 0.55 and 0.76 (including other control variables, see below). Again, the coefficients were relatively stable over time. This large sample also allowed the examination of various other potential determinants of age heaping. To assess whether the degree of bureaucracy, birth registration, and government interaction with citizens is likely to influence the knowledge of one’s exact age, independently of personal education, Crayen and Baten used the number of censuses performed for each individual country up to the period under study as explanatory variable for their age heaping measure. Except for countries with a very long history of census taking, all variations of this variable turned out insignificant, which would suggest that such an independent bureaucracy effect was rather weak. In other words, it is the case that societies with a high number of censuses and early introduction of birth registers had a high age-awareness. But those societies were also early to introduce schooling, and this was the variable that had clearly more explanatory power than the independent bureaucracy effect. Crayen and Baten also tested whether the general standard of living had an influence on age heaping tendencies (using height as well as GDP per capita as welfare indicators) and found a varying influence: in some decades, there was a statistically significant correlation, in others there was none.

In conclusion, the correlation between age heaping and other human capital indicators is quite well established, and the ‘bureaucratic’ factor is not invalidating this relationship. A caveat relates to other forms of heaping (apart from the heaping on multiples of five), such as heaping on multiples of two, which is quite widespread among children and teenagers and to a lesser extent among young adults in their twenties. This shows that most individuals knew their age as teenagers, but only in well-educated societies they are able to remember or calculate again their exact age later in life. At higher ages, this heaping pattern is mostly negligible, but interestingly somewhat stronger among populations who are numerate enough not to round on multiples of five. We will exclude those below age 23 and above 72 since a number of possible distortions affect those specific age groups, leading to age reporting behaviour, different to the one featured by the adult group in between. Many young males and females married in their early twenties or late teens, when they also had to register as voters, military conscripts etc. At such occasions, they were sometimes subject to minimum age requirements, a condition which gave rise to increased age awareness. Moreover, individuals physically grow during this age group, which makes it easier to determine their age with a relatively high accuracy. All these factors tend to deflate age heaping levels for children and young adults, compared with the age reporting of the same individuals at higher ages. The age heaping pattern of very old individuals is subject to upward as well as downward bias for the following reasons, and hence the very old should also be excluded. There remains some uncertainty about whether age heaping in the sources contains information about the numeracy of the responding individual, or rather about the diligence of the reporting personnel who wrote down the statements. A potential bias always exists if more than one person is involved in the creation of a historical source. For example, if literacy is measured by analysing the share of signatures in marriage contracts, there might have been priests who were more or less interested in obtaining real signatures, as opposed to just crosses or other symbols. We find it reinforcing that previous studies always estimated generally much more age heaping (and less numeracy) for the lower social strata, and among the half of the sample population which had lower anthropometric values (Baten and Mumme 2010). Moreover, the regional differences of age-heaping are similar to regional differences in illiteracy. It can be concluded that the method of age heaping is a useful and innovative tool to assess human capital.

Calculating the Heaping Index

How is the heaping index calculated? The ratio between the preferred ages and the others can be measured by several indices, one of them being the Whipple Index. To calculate the Whipple index of age heaping, the number of persons reporting a rounded age ending with 0 or 5 is divided by the total number of people, and this is subsequently multiplied by 500. Thus, the index measures the proportion of people who state an age ending in a five or zero, assuming that each terminal digit should appear with the same frequency in the ‘true’ age distribution. (1) For an easier interpretation, A’Hearn, Baten, and Crayen (2009) suggested another index, which we call the ABCC index. It is a simple linear transformation of the Whipple index and yields an estimate of the share of individuals who correctly report their age: (2) The share of persons able to report an exact age turns out to be highly correlated with other measures of human capital, like literacy and schooling, both across countries, individuals, and over time (Mokyr, 1983; A’Hearn et al., 2009; Crayen and Baten, 2010).

Bibliography


 * A’Hearn, Brian, Baten, Joerg, and Crayen, Dorothee and “Quantifying Quantitative Literacy: Age Heaping and the History of Human Capital” Journal of Economic History 69-3 (Sept 2009), pp.783-808.
 * Bachi, Roberto (1951): “The Tendency to Round off Age Returns: Measurement and Correction”, Bulletin of the International Statistical Institute 33, pp. 195-221.
 * Baten, Joerg and Christina Mumme: “Globalization and Educational Inequality in Long-Run Development during the 17th to 20th Centuries: Latin America and other Developing World Regions”, Journal of Iberian and Latin American Economic History 28-2 (2010), 279 -305. doi:10.1017/S021261091000008X.
 * Baten, Joerg, Debin Ma, Stephen Morgan and Qing Wang, “Evolution of Living Standards and Human Capital in China in the 18-20th Centuries: Evidences from Real Wages, Age-heaping, and Anthropometrics” Explorations in Economic History 47-3 (2010): 347-359. http://dx.doi.org/10.1016/ j.eeh.2009.09.003; This article in Chinese in Qishi Rencong (Review of Qing History) 2011, pp. 326-345. Older Version: LSE Economic History Working Paper No. 27870
 * Baten, Jörg, Dorothee Crayen and Hans-Joachim Voth, “Numeracy and the Impact of High Food Prices in Industrializing Britain, 1780-1850”, Review of Economics and Statistics (forthcoming). Older Version: Universidad Pompeu Fabra Economic Working Paper No. 1120
 * Baten, Joerg and Jan Luiten van Zanden (2008): “Book Production and the Onset of Early Modern Growth”, Journal of Economic Growth 13-3, pp. 217-235,
 * Clark, Gregory (2007): A Farewell to Alms: A Brief Economic History of the World, Princeton: Princeton University Press.
 * Crayen, Dorothee and Baten, Joerg "New Evidence and New Methods to Measure Human Capital Inequality before and during the Industrial Revolution: France and the U.S. in the 17th to 19th Centuries " Economic History Review 53-2 (2010), pp. 452-478.
 * Crayen, Dorothee and Baten, Joerg “Global Trends in Numeracy 1820-1949 and its Implications for Long-Run Growth”, with Dorothee Crayen, Explorations in Economic History 47-1 (2010), pp. 82-99 doi:10.1016/j.eeh.2009.05.004 Older version is available as CESifo Working Paper 2218.
 * De Moor, Tine, and Van Zanden, J.-L., ’Uit fouten kun je leren. Een kritische benadering van de mogelijkheden van 'leeftijdstapelen' voor sociaal-economisch historisch onderzoek naar gecijferdheid in het pre-industriële Vlaanderen en Nederland’, Tijdschrift voor Economische en Sociale Geschiedenis, 5 (2008), pp. 55-86.
 * Hippe, Ralph and Joerg Baten, “The Early Regional Development of Human Capital in Europe, 1790 – 1880, Scandinavian Economic History Review (2012), 60, Number 3, 1 November 2012, pp. 254-289 [this article did win a best-article prize of the SEHR] Older Version: AFC Working Papers 11-07
 * Humphries, Jane and Leunig, Tim “Cities, Market Integration and Going to Sea: Stunting and the Standard of Living in Early Nineteenth-Century England and Wales”, Discussion Papers in Economic and Social History 66, Oxford: University of Oxford.
 * Juif, Dácil-Tania and Joerg Baten“On the Human Capital of ‘Inca’ Indios before and after the Spanish Conquest. Was there a “Pre-Colonial Legacy”?”, Explorations in Economic History (2013, forthcoming). Older version: Tübingen Working Papers in Economics and Finance 27
 * Kayser, Daniel and Peyton Engel. “Time- and Age-Awareness in Early Modern Russia.” Comparative Studies in Society and History 35, no. 4 (1993): 824–39.
 * Manzel, Kerstin, Stolz,Yvonne, Baten, Jörg “Convergence and Divergence of Numeracy: The Development of Age Heaping in Latin America, 17th to 20th Century”, Economic History Review 65, 3 (2012), pp. 932–960.
 * Manzel, Kerstin Joerg Baten and Yvonne Stolz, “Convergence and Divergence of Numeracy: The Development of Age Heaping in Latin America, 17th to 20th Century”, Economic History Review 65, 3 (2012), pp. 932–960. Older Version: CEPR Working Paper
 * Mironov, Boris N., ‘Novaya Istoricheskaya Demografia Imperskoy Rossii: Analycheski obsor Corremennoy Istoriografii’, Vestnik Sankt-Peterbursgskovo Universiteta, 4 (2006), pp. 62-90.
 * Mokyr, Joel (1983): Why Ireland Starved: A Quantitative and Analytical History of the Irish Economy, 1800-1850, George Allen & Unwin: London.
 * Myers, Robert J. (1954): “Accuracy of Age Reporting in the 1950 United States Census”, Journal of the American Statistical Association 49 (268), pp. 826-831.
 * Tollnek, Franziska and Joerg Baten “The Farmer’s U: Which Occupational Group Inherited Human Capital in Early Modern Europe and Latin America?” Working Paper ANU
 * Yvonne Stolz and Joerg Baten, “Brain Drain, Numeracy and Skill Premia during the Era of Mass Migration: Reassessing the Roy-Borjas Model”,, Explorations in Economic History 49 (2012), pp. 205-20. Older Version: CESifo Working Paper No. 3705.
 * Yvonne Stolz, Joerg Baten and Jaime Reis “Portuguese Living Standards 1720-1980 in European Comparison – Heights, Income and Human Capital”, Economic History Review (forthcoming 2013)
 * Yvonne Stolz, Joerg Baten and Tarcisio Botelho "Growth effects of 19th century mass migrations: “Fome Zero” for Brazil?" European Review of Economic History (forthcoming 2013). Older version: Tübingen Working Papers in Economics and Finance 20