Numeracy, Human-Capital and Economic Growth

Term Paper (Advanced seminar), 2005

24 Pages, Grade: 3




1. Numeracy

2. Human capital

3. Human capital indicator
3.1 Education indicators
3.1.1 Adult literacy rate
3.1.2 Combined gross enrolment ratio
3.1.3 Numeracy
3.1.4. Age heaping

4. Correlation between human capital and economic performance
4.1. Correlation between adult literacy rate and economic performance
4.2 Correlation between combined gross enrolment ratio and economic performance
4.3 Correlation between numeracy and economic performance
4.4 Age heaping as an numeracy indicator and its correlation with economic performance

5. Conclusion


Appendix 1
Appendix 2: India’s Age-Heaping and Literacy Rate
Appendix 3: Age heaping and GDP per capital of Botswana
Appendix4: Age Heaping and GDP per capital of China


Numeracy together with literacy is a basic element of human capital. Recently some international tests are conducted to make comparison of numeracy level among different countries.

Human capital is an long term economic grow factor. To quantify human capital, various indicators are composed: adult literacy rate, school enrolment rate, etc. These human capital indicators facilitate researchers to analyze the correlation between human capital quality and economic performance of a certain economy. Age heaping, a normally in demography used indicator to check the reliability of census, is an possible human capital indicator. It can reflect the numeracy level of the researched population. It is showed that for little educated populations, age heaping are a possible human capital indicator, which reflect the human capital level of the researched population.

1. Numeracy

The word “numeracy” is relative new in English vocabulary[1]. Oxford English Dictionary has in its 1976’s supplement defined it as “ability with or knowledge of numbers” and locates its origins in a 1959 report on English education that contrasted illiterate scientists with innumerate humanist. In some other languages, like in German, there is not equivalence of the word. Some call it “new literacy”, or “quantitative literacy”, or “mathematic literacy”, “mathematic literacy”.

The word was intended to be analogue of “literacy”. It reflected the late 1950s concern that the humanities and the sciences were diverging into two cultures; each unable to comprehend the other because of the extent to which knowledge had become esoteric. In this context, “illiterate” did not mean “unable to read, “, nor did “innumerate” mean “unable to add”; rather, the words referred to an unspecified degree of deficiency at high levels that hindered communication among scholars[2].

According to PISA[3] documentation, “mathematical literacy is defined as an individual’s capacity to identify and understand the role mathematics plays in the world, to make well-founded mathematical judgments and to engage in mathematics, in ways that meet the needs of that individual’s current and future life as constructive, concerned and reflective citizen”[4].

Especially now in commonwealth countries, including United Kingdom, Australian, New Zealand, as well as in the Untied states, numeracy has already been recognized together with literacy a core basic skill and it is often discussed and incorporated in primary education[5].

In today’s ever-computerized world, it is important to address the meaning of numeracy. As an important aspect of human capital, it has not so widely researched as on literacy. Numeracy as well as literacy is an important aspect of human capital, the following we will first to discuss the general conception of human capital.

2. Human capital

Human Capital is knowledge and skills that workers acquire through education, training, and experience. Human capital includes the skills accumulated in early childhood programs, grade school, high school, college, and on-the-job training for the adults in the labor force[6].

Already in eighteen century, the famous British economist, Adam Smith, in his “Wealth of Nation”, points out that the proficiency of workers as well as capabilities of all the people are the real source of economic growth. He wrote, “A man educated at the expense of much labor and time to any of those employments which require extraordinary dexterity and skill, may be compared to expensive machine. The work which he leans to perform, it must be expected, over and above the usual wages of common labor, will replace to him the whole expense of his education, with at least the ordinary profits of an equally valuable capital”. He also points out the positive external effect of human capital, “The acquisition of such talents, by the maintenance of the acquisition of such talents, by the maintenance of the acquirer during his education, study, or apprenticeship, always costs a real expense, which is a capital fixed and realized, as it were, in his person. Those talents, as they make a part of his fortune, so do they likewise of that of the society to which he belongs.[7]

And Alfred Marshall, in his “Principles of Economics”[8] has also written, “the most valuable of all capital is that invested in human beings.” The formal human capital theory was established in 1960s by Schultz (1961)[9], Weisbrod (1962)[10] and Denison (1962)[11]. Becker (1964) has analyzed both theoretically but also empirically the effects of investments in human capital of various forms: schooling, on-the-job training, medical care, migration, and searching for information about prices and incomes[12].

It is widely believed that human capital benefits not only the individual but also the society. So many government in the world are trying to build its human capital to make sure not to lose in today’s globalization era. However, human capital is not so easy to evaluate as the other forms of capital. In order to investigate the relationship between human capital and economic performance, it is necessary to measure human capital; in other words, we should find appropriate indicators for them.

3. Human capital indicator

There are generally two groups of indicators: education indicators and health indictors. Education indicators are: literacy rate, primary education rate, secondary education rate, higher education rate, combined gross enrolment ratio, etc. These are readily available for the time since the middle of last century. Almost all the countries in the world have special institutions responsible for collecting the above mentioned human capital indicator data, and this make the research easy for economists, who are interested in the correlation between those human capital indicators and macro-economic variables. Health Indicators include infant mortality rates, morbidity rates, incidence of obesity, incidence of depression incidence of HIV/AIDS, etc[13].

3.1 Education indicators

There are various education indicators, which could be further divided into tow sub-categories: outcome indicators like adult literacy rate or average education years; input indicators like student teacher ratios and government education expenditure as percent of GDP etc.. Here the following we will discuss mainly the outcome indicators.

3.1.1 Adult literacy rate

Adult literacy rate is defined as the percentage of people aged 15 and above who can, with understanding, both read and write a short, simple statement on their everyday life.

Over the time, literacy level are improved substantially, especially in developed countries, where the literacy rate almost reach 100%, however most developing countries still have a relatively low literacy rate[14].

3.1.2 Combined gross enrolment ratio

Combined gross enrolment ratio for primary secondary and tertiary schools

The number of students enrolled in a level of education, regardless of age, as a percentage of the population of official school age for that level. The combined gross primary, secondary and tertiary enrolment ratio refers to the number of students at all these levels as a percentage of the population of official school age for these levels.

3.1.3 Numeracy

Numeracy as capital indicator is not so internationally developed as literacy. For the time being there are no standardized numeracy indicator worldwide, although one might count mathematic performance as numeracy.

As mentioned, in U.K., there is a strong belief in the importance of key stills of literacy and numeracy for economic performance of Britain’s economy and also the living standards of the individuals. Recently there are also some international tests for students (Please refer to appendix 1 for those studies) which can be used as numeracy indicators for econometric analysis.

3.1.4. Age heaping

For the time before the Second World War, there was very little data available regarding literacy and numeracy to make inter-regional or international comparison of human capital. As a second best solution, people used age heaping as proxy for human capital indicator.

There were even on census data, researchers were forced to other records available to them including prison records, school enrolment list, military enlistment records and archives, migration statistics. Those data do not contain explicit information on the education attainment of the people registered. To handle this difficulty, researchers found an alternative method to approximate the numeracy level[15].

As Crayen (2004) put it, “ the main line of this research of educational measures concentrates on data which record single year age data. Single year age data enables researchers to depict a population’s detailed age structure. The idea is to use irregularities in the reporting of age to estimate the people’s level of education. Such irregularities appear in the form of heaped data, i.e. the age distribution does not run smoothly but exhibits sharp jumps and clustering at certain ages[16] ”. This phenomenon is called age heaping or just heaping. Age heaping occurs because many people (particularly older people) tend not to give their exact age in a survey. Instead, they round their age up or down to the nearest number that ends in 0 or 5. When the ages are graphed, the distribution isn't smooth; instead, there are heaps over the ages ending in 0 and 5.


[1] As could seen in my electronic version of this paper, spelling checker of Microsoft Word does not recognize this word.

[2] S Cohen, Patricia (1982), „ A calculating people, the Spread of Numeracy in Early America“, University of Chicago Press

[3] Program for International Student Assessment (PISA)

[4] PISA web site,, accessed on 2005-08-16

[5] In the UK, there are following standard tests concerning: Certificate in Adult Numeracy level 1; Certificate in Adult Numeracy level 2

[6] Mankiw, (2004), Principles of economics, 3rd Edition, Dean Croushore

[7] Adam Smith, 1776, “An Inquiry into the nature and causes of the wealth of nations”, Methuen and Co., Ltd. Ed. Edwin Cannan, 1904. Fifth edition.

[8] Marshall Alfred, “Principles of Economics”, 8th Ed., Macmillan & Co., Ltd., London 1930

[9] Shultz, T W (1961), “Investment in human capital”, American Economic review, 51, 1-17

[10] Weisbrod, Burton A.(1962), “Education and Investment in Human Capital”, Journal of Political Economy, 70 (5): 106-123

[11] Denison, E. F. (1962), “the sources of Economic Growth in the United States and the alternatives before us”, New York: committee for economic development

[12] Becker, Human Capital, A theoretical and Empirical analysis, with special reference to education, 1964, The University of Chicago Press

[13] Discussion Paper on Health and Education Human Capital Indicators, February 2001, Center for the Study of Living standards

[14] See UNESCO on-line data-bank: assessed on 16.08.2005

[15] Crayen, 2004, page 3

[16] Crayen, 2004, Age Heaping – a Human Capital Indicator? An Econometric Analysis of Developing Countries

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Numeracy, Human-Capital and Economic Growth
University of Tubingen  (Wirtschaftgeschichte)
Hauptseminar "Humankapital und Wachstum in armen und reichen Ländern"
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human capital, numeracy, literacy
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Junzhai Ma (Author), 2005, Numeracy, Human-Capital and Economic Growth, Munich, GRIN Verlag,


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