Abstract
In this article, we provide comprehensive insights into the implementation and the use of the age-heaping method. Age heaping can be applied to approximate basic numerical skills and hence basic education. We discuss the advantages and potential issues of different indicators, and we show the relationship of those indicators with literacy and schooling. The application of age-heaping-based indicators enables us to explore various topics on basic education such as the gender gap and the divergence of countries in the very long run. This well-established technique has been used by a great variety of authors who also show that numeracy has a large impact on growth.
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Notes
- 1.
Brain drain means that highly educated people emigrate from their country of origin to another. Brain gain means the opposite effect.
- 2.
However, we have to keep in mind that there are individuals still living today, predominantly in the least developed countries, which are not aware of their true age when they are asked for it (Juif and Baten 2013).
- 3.
De Moor and Van Zanden (2010) even report a preference for multiples of 12 in different medieval and early modern sources, among them a census from Tuscany in 1427 and another from Reims in 1422. This phenomenon could be the result of religious orientations and the underlying usage of the number 12 as a holy number. Interestingly, this heaping pattern was more often adopted by women than by men, especially during early modern times in the South Netherlands. This could be due to a stricter adherence of religious practices or beliefs by women than by men, though this is not scientifically proven so far.
Another pattern might also occur if a certain share of the population was surveyed and the results were written down in year t, whereas the rest of the data collection was performed in the following year t + 1. After the census was finished, the census official compiled the results in a clean and comprehensive list in year t + 1. Because he or she was aware of the age statements that had been reported in year t, he added 1 year to those ages. As a result, we find heaping on the terminal digits one and six in these lists. If this pattern can be identified without reasonable doubt, the additional year should be subtracted from all of the affected age statements.
In a similar way, the authors of some studies have found that numeracy estimates based on age statements of marriage lists tend to be upwardly biased (which is partly due to the fact that marriage was restricted to those who earned a living and could nourish a family in many historical societies). Death registers on the other hand tend to yield downwardly biased estimates. This type of bias could happen if the deceased person did not have any relatives or close friends whom the recorder could ask for an age statement. Consequently, he or she estimated the age by himself. Adjustment factors for these types of sources are available from the authors.
- 4.
Self-reporting is, of course, not an option if we consider tombstones or death registers. The ages provided in these sources reflect the heaping pattern of the individual who reported the age in place of the respective person. But even in such cases, there are gender- or social group-specific differences observable (Duncan-Jones 1990, p. 83). It is most likely that the persons providing the ages for the tombstones were related to the deceased person or at least of similar social or educational status.
- 5.
They found information on censuses from which it becomes clear that the authorities required the census takers of surveying each person individually.
- 6.
Please see A’Hearn et al. (2006, pp. 11–21) for a more detailed discussion on the properties.
- 7.
The Mokyr index we refer to in this section is also called the Lambda index (A’Hearn et al. 2006).
- 8.
The digit “0” includes all ages ending in zero, hence 30, 40, 50, etc. The digit “1” includes all ages ending in one, hence 31, 41, 51, and so on.
- 9.
Myers criticizes that starting the aggregation at a certain age, for example, 20, increases the share of people with a digit ending in zero because “… the ‘leading’ digits naturally occur more frequently among the persons counted than the ‘following’ ones.” (Myers 1954, p. 826).
- 10.
For a more detailed description of the “blended” method, see Myers (1954).
- 11.
Statistical scale dependency means that the assumed mathematical scale independency can change when applying an indicator to random samples of different sizes. For more information on this topic, see A’Hearn et al. (2006, pp. 11–21).
- 12.
If the Whipple indicator is larger than 100, they suggest adding 0.2 units to the value of the age group 33–42 for every Whipple unit above 100. The resulting value is aggregated to the value of the age group 23–32, which delivers the new estimate for this group. For example, if the value of the age group 23–32 is 150 and that of the age group 33–42 is 160, then the digit above 100 has to be multiplied by 0.2 (60 * 0.2 = 12). The result is added to the original value of those aged 23–32 (150 + 12). Consequently, the new estimate for the youngest age group is 162 (Crayen and Baten 2010a, Appendix A, pp. 95–96).
- 13.
The name of the index is constructed by the initials of the last names of the three authors plus Gregory Clark’s.
- 14.
Height is employed as a proxy indicator for infant malnutrition because the smaller a person is, the more likely it is that he or she did not have access to protein-rich nutrition which also hinders the development of numerical skills. State antiquity approximates the quality of institutions.
- 15.
De Moor and Van Zanden (2010) use the Whipple index for their calculations. We translated the numbers into ABCC values for convenience.
- 16.
The occupations in brackets are only examples. In total, there are hundreds of occupations in the dataset that were arranged according to the Armstrong scheme.
- 17.
Germany is an exceptional case because the values of the intermediate, skilled, partly skilled, and unskilled groups differ only slightly.
- 18.
The coefficients are subsequently multiplied by 125 to correct for the 20 % of the people who state a multiple of 5 correctly. For further information, please see Appendix B in Tollnek and Baten (2013).
- 19.
The data are arranged in age groups and then transferred into birth half centuries. Hence, the value of the respective age group is subtracted from the census year. The resulting values are rounded to 50-year-intervals. For example, if the census year was 1740, then the age group 23–32 was born in the half century 1700.
- 20.
The values for Argentina and Mexico are estimates based on regression results. They are controlled for capital effects and male share. For further information, please see Manzel et al. (2012). The data of all of the countries are arranged in birth decades. Hence, the value of the age group is subtracted from the census year, and the resulting values are rounded to 10-year intervals. For example, if the census year was 1940, then the age group 23–32 was born in the decade 1910.
- 21.
Crayen and Baten (2010a) use the Whipple index for all of their calculations. We translated all of the numbers into ABCC values for convenience.
- 22.
East Asia is dominated by Chinese data, since Japan is considered part of the industrialized countries.
- 23.
He subtracts the 20 % of the people who report a multiple of 5 correctly from the total number of people who state a rounded age. Hence, the reported percentage share contains those who incorrectly state a rounded age.
- 24.
De Moor and Van Zanden (2010) use the Whipple index. We translate the results from the Whipple index into ABCC levels for convenience.
- 25.
The women, however, represent higher values at the “dozen index” that detects rounding behavior on multiples of 12. This is likely due to religious practices among Catholics (De Moor and Van Zanden 2010).
- 26.
The data are arranged in birth decades.
- 27.
The low inequality of non-Hispanic countries might be due to the institutional framework created by slavery. As both men and women were torn away from their home countries and had to work equally, the “traditional” gender roles did not evolve as they did in other countries. Besides, Caribbean women tended to work outside the household more often than Latin American women (Manzel and Baten 2009).
- 28.
Included countries are Afghanistan, Bangladesh, India, Iran, Sri Lanka, Nepal, Pakistan, Hong Kong, Indonesia, Cambodia, Federation of Malaya, Sarawak, the Philippines, and Thailand.
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Tollnek, F., Baten, J. (2014). Age-Heaping-Based Human Capital Estimates. In: Diebolt, C., Haupert, M. (eds) Handbook of Cliometrics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40458-0_24-1
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Age-Heaping Based Human Capital Estimates- Published:
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DOI: https://doi.org/10.1007/978-3-642-40458-0_24-2
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Age-Heaping-Based Human Capital Estimates- Published:
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DOI: https://doi.org/10.1007/978-3-642-40458-0_24-1