3. Development and Persistence of Human Capital in Africa since the late 19th
4.2. Assessing human capital via the Age-Heaping Methodology
4.2.2. Age-Heaping as a Proxy for Basic Numeracy
To close the gap in this fragmentary evidence on human capital indicators for Asia in this period, we will employ a proxy approach in this study: the age-heaping method.
This method is based on the phenomenon that people in less educated societies tend to round their age if they are unable to recall or calculate their exact age when asked.
Typically, people choose ages on digits ending in multiples of five, i.e. they state their age as 30 if they are in fact, for example, 29 or 32 years old. Figure 4.3 displays the pronounced age-heaping of males and females in Afghanistan as reported in the 1979 census.
Figure 4.3: Age-heaping behaviour of males (left hand side) and females (right hand side) in Afghanistan according to the census of 1979
0100000200000300000male
20 40 60 80
age
0100000200000300000female
20 40 60 80
age
In contrast to most demographers who treat age-heaping as a mere statistical challenge, we interpret this phenomenon from a different point of view, namely as an indicator for a lack of numerical skills of the population. The usefulness of
age-heaping as a proxy for lack of basic numerical skill was first suggested by Bachi35 who found an inverse correlation between age-heaping and educational levels within and across countries. Mokyr36 pioneered its use in economic history. Crayen and Baten37 found that age-heaping tends to be more pronounced in population groups with lower incomes and/ or lower-status occupations.
To measure the extent of age-heaping within a certain population, the Whipple index was developed and became widely accepted (nx is the population of age x):38
100if WI 100;elseWI 100.) n ...
n n n ( 5 / 1
n n ...
n WI n
1
72 25
24 23
70 65 30
25
To spread the final digits of 0 and 5 more evenly across the age ranges, the age group intervals are defined 23-32, 33-42, and so forth. In demographic analyses this index is usually restricted to the age 23 to 72, as people older than 72 are prone to forget or overstate their age or might be positively selected due to a possible mortality bias.
People younger than 23 are not considered, as they often show a heaping pattern deviating from the typical multiples of 5; additionally, in the case of children, usually the parents state the age and not the children themselves. We follow the same restriction.
A’Hearn, Baten, and Crayen39 propose a linear transformation of the Whipple index, the so-called ABCC index, that is more intuitive for interpretation as this index ranges between 0 and 100: 0 indicates an age distribution with ages ending only on multiples of five whereas 100 implies no age-heaping at all:
35 Bachi, The tendency to round off age returns.
36 Mokyr, Why Ireland Starved.
37 Crayen and Baten, New evidence.
38 Whipple indices below 100 (ABCC indices above 100, respectively) in the 20th century rich countries are normally caused by random variation, hence those values are set to 100. Additionally, the adjustment
100 if WI 100; elseABCC 100 400) 100 WI 1 ( ABCC
2
We calculate the gender equality index in numeracy (GEnum) as the ratio of the difference between the Whipple index of females (WIf) and the Whipple index of males (WIm) to the Whipple index of males, multiplied by -100:
The higher the gender equality index, the more women who know their exact age in comparison to men. We expect the gender equality index to be negative;
negative gender equality indices imply better numerical discipline for men. Although our countries are rather characterised by gender inequality, we use a gender equality measure to make our results more easily comparable with the literature on female labour force participation by Goldin40 and Mammen and Paxson41 and to follow the methodology used by Manzel and Baten.42
Recently, several studies confirmed a positive correlation between this indicator and other human capital indicators. In their global study on age-heaping for the period 1880 to 1940, Crayen and Baten43 identified primary school enrolment as a main determinant of age-heaping: an increase of enrolment rates led to a significant decrease in the age-heaping level. This close correlation between schooling and basic numeracy is not only found among this global data set but is also confirmed by other studies for regional age-heaping sub-samples (e.g. Manzel et al.44 for Latin America around 1870 to 1930, Baten et al.45 for Chinese immigrants in the US, Prayon46 for
40 Goldin, The U-Shaped Female Labour Force Function.
41 Mammen and Paxson, Women’s Work.
42 Manzel and Baten, Gender Equality and Inequality in Numeracy.
43 Crayen and Baten, Global trends. For each decade in the period under investigation the relationship between age-heaping and schooling is remarkably stable and has almost the same coefficient in each
100WI WI GE WI
3
m m f
num
early 20th-century Africa). A’Hearn, Baten, and Crayen47 examined the U.S. censuses of 1850, 1870, and 1900 and found for the overall sample, as well as for sub-samples, a positive and statistically-significant relationship between literacy and basic numeracy. They also found that this relationship varies by census, ethnic group, and birth region. For early modern Europe they could confirm a positive correlation of signature ability as a proxy for literacy and age-heaping as a proxy for numeracy.
Hippe48 examined systematically the relationship of numeracy and literacy on a regional basis for seven European countries in the 19th century. He found for each individual country a high correlation between the two indicators. In the same way, we collected literacy data for the Asian region to check whether we could find the same positive relationship between basic numeracy and literacy. We took literacy data from the United Nations Demographic Yearbooks (UNDYB) and assigned age groups to the corresponding birth decades.49 Comparing the two human capital indicators on the basis of these birth cohorts we find indeed a strong positive correlation (with a Pearson’s correlation coefficient of 0.85). Unfortunately, due to limited data availability, only nine countries with overlapping data are left for this analysis (Figure 4.4).
Based on the results of these studies it can be concluded that the correlation between numeracy and other education indicators can be regarded as well-established and age-heaping can be interpreted as a proxy for (lacking) basic numerical skills.
46 Prayon, Development and persistence of human capital in Africa.
47 A’Hearn, Baten, and Crayen, Quantifying quantitative literacy.
48 Hippe, How to measure human capital?
49 We took the literacy data from the same UNDYB sources as for the ABCCs (see census list in the Appendix). As for the ABCCs, we assigned the literacy rates of the different age groups to the corresponding birth decades and took the mean of the birth decades 1900s-1960s. Figure A.2 in the Appendix displays the relationship of gender equality in numeracy and gender equality in literacy with the same data set, disaggregated by birth decade. We observe a positive correlation between the two
Figure 4.4: Relationship of literacy and the ABCC-index in Asia
ABCC-index mean of birth cohorts 1900s-60s (males+females)
0 20 40 60 80
literacy in %
mean of birth cohorts 1900s-60s (males+females)
Note: hk=Hong Kong, id=Indonesia, in=India, ir=iran, lk=Sri Lanka, myfm=Federation of Malaya, mysa=Sarawak, ph=Philippines, th=Thailand
Indeed, the age-heaping method possesses advantages that literacy and enrolment evidence lack. Due to its consistent calculation, age-heaping results might be easier to compare across countries, whereas comparisons of literacy and enrolment rates might be misleading due to significant measurement differences (especially due to different definitions of literacy) and different school systems. Further, owing to the typical high drop-out rates in developing countries and heterogeneous teacher quality, it can be argued that enrolment rates are less conclusive for our goal as enrolment ratios are an input measure of human capital. Although a country might have high enrolment ratios, these ratios do not permit conclusions about the quality of education.
Age-heaping on the other hand is - like literacy - an output measure of human capital.
Another convenient advantage of the method is that it can applied to a wide range of sources, for instance census data, passenger lists, or any other kind of individual age recording. This way we can trace basic numerical skills of populations from periods and areas for which no other human capital indicators exist yet. This applies especially
to this study: We do not have another human capital indicator disaggregated by gender that covers so many Asian countries for the period 1900-1960.
Like other proxies, the age-heaping measure has its limitations. It only captures age-heaping on multiples of five, although people in their late teens and early 20s tend to round on multiples of two. In addition, some cultures have specific number preferences, for example the 8 or the dragon year in China.50 Similarly, if individuals were asked for their date of birth instead for the age at their last birthday, a birth year-heaping pattern could arise. In both cases the age-year-heaping method does not return unbiased estimates, so the age-heaping patterns should be checked carefully. Further, due to its upper boundary and therefore lacking variation, we do not get meaningful results in populations where no or only marginal age-heaping exist.51