Global trends in numeracy 1820–1949 and its implications for long-term growth

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Abstract

This study is the first to explore long-run trends of numeracy for the period from 1820 to 1949 in 165 countries, and its contribution to growth. Estimates of the long-run numeracy development of most countries in Asia, the Middle East, Africa, America, and Europe are presented, using age-heaping techniques. Assessing the determinants of numeracy, we find school enrollment as well as Chinese instruments of number learning to have been particularly important. We also study the contribution of numeracy as measured by the age-heaping strategy for long-run economic growth using a pooled cross-section analysis. In a variety of ways, numeracy proved to be crucial for growth patterns around the globe.

Introduction

Human capital is at the heart of modern economic growth studies (Lucas, 1988, Romer, 1989, Mankiw et al., 1992 and Jones, 1996 among others). Growth economics has strongly emphasized the role of human capital formation and its persistence in nations over time. Also Unified Growth Theory has underlined the role of human capital in the transition from the Malthusian stagnation to the contemporary era of modern economic growth (Galor and Weil, 2000, Galor and Moav, 2002, Galor, 2005). Becker et al. (1990) placed investments in human capital at the center of their study, assuming that the return on growth-enhancing investments in human capital rises rather than declines as the stock of human capital increases. Their framework is characterized by multiple steady states that differ in regard to schooling decisions and opportunity costs of child care. Initial human capital stock and other major exogenous shocks play an important role in the determination of fertility, growth rates and the wealth of countries. However, their model was found to be inconsistent with the historical evidence which Mitch (1991) and Mokyr (1983) presented. They suggested that some countries’ growth paths did not fit into this demographic-educational pattern. For example, Britain experienced stagnating literacy between the mid-18th and mid-19th century, while France had an early fertility decline as early as 1800 without becoming a driving force of growth in 19th-century Europe. While education and a slowing population growth do not seem to explain the first Industrial Revolution satisfactorily, many economists who study long-term growth believe that these factors played a key role in the later transition to a regime of sustained economic growth (Boucekkine et al., 2003, Glaeser et al., 2004, Cervellati and Sunde, 2005 among others). Economic factors eventually altered the parental quality–quantity decision and stimulated human capital investments, reinforcing technological progress and economic growth.

Given that human capital accumulation is a crucial factor in long-run economic growth theory, efforts have been made to strengthen the available empirical evidence. O’Rourke and Williamson (1997), for example, were able to include schooling in European convergence regressions for 16 countries for the period between 1870 and 1913, concluding that globalization forces had, in fact, a greatly important influence on comparative development.2 When going further back in time to the early 19th century and beyond, schooling data, even for Europe, disappears, and literacy must generally be inferred from a proxy—the ability to sign one’s name on marriage certificates and legal documents (Reis, 2005; on advanced numeracy, see Baten and van Zanden, 2008). Leaving Europe, it becomes increasingly difficult to find systematic, comparable data. Crafts (1997) reports enrollment and literacy rates for 17 advanced economies since 1870 while Lindert (2004) provides school enrollment rates and teacher–student ratios on some 50 countries, substantially improving the Mitchell, 2003a, Mitchell, 2003b, Mitchell, 2003c data set. Benavot and Riddle (1988) have compiled additional schooling data for LDCs for the period between 1870 and 1940. Morrisson and Murtin (2007) have revised and extended Mitchell, 2003a, Mitchell, 2003b, Mitchell, 2003a, Mitchell, 2003a, Mitchell, 2003b, Mitchell, 2003a, Mitchell, 2003b, Mitchell, 2003c data set, using national census data to obtain an educational attainment data set for 1870–2000. Since census information was scarce for the developing world prior to the end of the 19th century, the authors had to assume enrollment rates of 1% or 0.1% for the LDC world in 1820.

Although these studies represent a clear improvement in our knowledge, about half of the existing 165 countries with populations above 500,000 are not yet documented for the late 19th century. As a result, existing samples of human capital data are biased towards today’s richer spectrum of countries, as those were the first to introduce schooling statistics. Studies on human capital development in the poorer half of the world would provide important insights into overall human development.

This study is a first step towards achieving almost global coverage of human capital estimates since the late 19th century. Moreover, quite a number of additional countries can be included in the period between 1820 and 1890. Another aim of this paper is to broaden the literature on human capital by constructing a numeracy index. We would argue that numeracy should be considered as a historical measure of human capital since knowledge about numbers and numeric discipline are even more crucial for economic growth than the ability to sign one’s name on a marriage certificate. Numeracy goes hand-in-hand with technological abilities, and it is a necessity for modern commercial economies. For Weber, Sombart, and Schumpeter, numeracy was at the very heart of modern rational capitalism. They traced the latter’s roots back to the invention of double-entry bookkeeping in late-medieval Italy. Carruthers and Espeland (1991) have described in some detail the process of abstraction and organization inherent in compiling a ledger, which made possible the development of concepts like capital, depreciation, and the rate of profit. It is no accident that the introduction of Arabic numerals to Europe and the earliest accounts of mathematical education stem from the same time and place. Hence, in this paper, we go beyond traditional literacy and enrollment indicators by presenting proxies for numeracy based on age-heaping.

What is age-heaping? Demographers normally use age data to describe a population’s age structure and to forecast population growth. In contrast, the idea behind this study is to use irregularities in the reporting of ages to estimate the level of education in an economy. Such irregularities appear in the form of heaped data, i.e. the age distribution does not run smoothly but rather exhibits sharp jumps and clustering at certain ages. This phenomenon is attributed to age-heaping, a term which describes the ignorance of one’s own age or the tendency to round ages. Age-heaping is a well-known phenomenon among demographers and applied statisticians. However, while both groups of scholars perceive age-heaping mainly as a data problem because it leads to biased vital rates on the one hand, and only the degree of heaping as a measure of data quality on the other hand, we use it as a proxy for non-numeracy.

A half-century ago, an influential study by Bachi (1951) and Myers (1954) investigated age-heaping and its correlation with education levels within and across countries. Thereby, Bachi (1951) was able to analyze the degree of age-heaping among Jewish immigrants to Israel in 1950 and among Muslims in Mandated Palestine in 1946, finding, amongst other things, that the increasing spread of education resulted in a better knowledge basis according to lower age-heaping. Myers (1976) found a negative correlation at the individual level between age-heaping and income. Another innovative example is the study by Herlihy and Klapisch-Zuber (1978) who used successive Florentine tax enumerations and found distinct heaping on multiples of five for adults, which declined substantially in the period from 1371 to 1470. Furthermore, they showed that age-heaping was more prevalent among both women in rural areas and small towns, and among the poor. Duncan-Jones (1990) employed this technique to study age data from Roman tombstones. Mokyr (1983) was the pioneer who established the age-heaping measure as an explicit numeracy indicator in economic history. He employed the degree of age-heaping to assess the labor-quality effect of emigration on the Irish home economy during the first half of the 19th century, as emigrants from pre-famine Ireland were less sophisticated than those who stayed behind. Thomas (1987) considered the slight but discernible improvement in the accuracy of age reporting as evidence that numerical skills in England had improved between the 16th and 18th century. Budd and Guinnane (1991) studied Irish age-misreporting in linked samples from the 1901 and 1911 censuses. They found considerable heaping on multiples of five in the 1901 census, which was also more frequent among the illiterate, poor, and aged. More recent research was conducted by Long, 2005, Long, 2006 who analyzed age data from the 1851 and 1881 British population censuses, identifying urban migrants in Victorian Britain as being educated beyond average. By exploiting repeated observations, he was able to show that individual age discrepancies (another measure of missing age awareness) had a significant negative impact on socio-economic status and wages. De Moor and van Zanden (2006) studied the relative numeracy of women during the Middle Ages, and Clark (2007) has recently reviewed the evidence.

From the literature cited above, we can conclude that demographic evidence exhibited significant age-heaping at least until the turn of the 20th century, and that the degree of heaping varied across individuals or groups in a way that makes age-heaping a plausible measure of human capital. The correlation of age-heaping and the prevalence of illiteracy among the population was explored in more detail by A’Hearn et al. (2006) who found in their analysis of 52 countries or 415 separate regions that the level of age-heaping is indeed correlated with illiteracy. The authors also concluded that the probability to report a rounded age increases significantly with regional and personal illiteracy.

In sum, we would argue that age-heaping is a proxy for basic numerical skills. As such, it is an important component of human capital and a precondition for more advanced skills. A perfect human capital measure in our view would be a composite index of basic and advanced text-related skills, of basic and advanced numerical skills, of technological, social and organizational creativity, and perhaps other components. However, given that such perfect composite indexes are impossible to construct in most real world situations, scholars often use proxy indicators for more broad concepts. We would suggest that our basic numeracy indicator can also be a proxy for general human capital, especially if other indicators are not available (or point actually to similar values of human capital).

In the following section, we will first discuss important methodological aspects of age-heaping as a numeracy proxy. The third section examines the (non-interpolated) country level data especially for the Islamic world and the industrialized countries. The next section will attempt to make a first estimate of the global development of numeracy for eight world regions from 1820 to 1949. This section will use interpolation. Section 5 will discuss the potential determinants of numeracy. Finally, Section 6 tests the implications for economic growth, and the seventh part provides a conclusion.

Section snippets

The age-heaping technique

The age-heaping technique can be applied to many sources of age data such as census returns, military enrollment lists, legal or hospital records, and tax data. However, care must be taken as to by and to whom the age question was posed, how it was formulated, and whether self-reported ages were compared to birth registers. Double-checked age information does not normally reflect any age-heaping besides minor, random fluctuations and therefore cannot be used. If the enumerator asked for both

A first glance at country level data

For the industrialized countries, the coverage of our data set is very good (Fig. 1 and Appendix B: Data sources appendix). Most of these countries conducted several censuses during the 19th and 20th centuries, and our cohort analysis covers the majority of the Western world (incl. Japan). However, given that many of these countries had already experienced the peak of their decline before 1820, the observations mainly cluster together between 100 and 120 for the early-to-mid 19th century, and

World region estimates

We will also present a very preliminary estimate of numeracy trends for the different world regions (Fig. 3). For the industrialized countries and East Asia, we obtained many of the necessary country-birth decade observations, whereas for the Middle East and North Africa, documentation was much scarcer, in particular for the pre-1880 period. For East and Southeast Asia, we were able to produce estimates for the period from the 1840s onwards, while values for sub-Saharan Africa and Latin America

Determinants of age-heaping

Age-heaping mainly originates either from a respondent’s ignorance of his or her exact age, or missing numeric discipline. Nowadays, we can assume that most people living in industrialized countries know their exact age or their year of birth, and otherwise they can check this information in registries, passports etc. if necessary. By contrast, people living in developing countries will more often have only a vague idea about their age or the year when they were born (this even applies to

Implications for empirical growth economics

What are the implications of our new estimates for empirical growth economics? Can age-heaping based on numeracy explain growth capabilities in a large number of countries? To test this subject matter, we employed all available GDP growth figures between 1820 and 1870, as well as between 1870 and 1913 (Maddison, 2001), and combined them with our numeracy estimates of the respective periods. In total, we could identify a set of 62 GDP growth figures for those two crucial periods in the 19th

Conclusion

In this paper, we presented age-heaping as an indicator of human capital, which of course has its limitations. However, this is the nature of all human capital indicators. The limitations of signature ability as a measure of functional literacy are obvious, but can also be raised with respect to the self-reported “ability to read.” School enrollment as an input measure is conceptually problematic, since we do not know about the quality of schooling and the concept and educational methods of the

Acknowledgments

We thank Robert Allen, Steve Broadberry, Greg Clark, Joel Mokyr, Sevket Pamuk, Leandro Prados de la Escosura, and Joachim Voth for their important comments on earlier versions, as well as participants of the EHES Conference in Lund 2007, the World Clio Congress 2008 near Edinburgh, and of seminars in Oxford and Tuebingen. Deborah Rice and Christian Dick provided able research assistance. Financial support from the ESF GlobalEuroNet program, EU HIPOD project and the German Science Foundation

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