General references

None of the Whipple estimates of the modestly sized literature entered

the data set unchanged, three general references which should be cited

(because they reflect most of the literature) are

Manzel Baten 2010: Manzel, Kerstin and Baten, Joerg (2010). “Gender

Equality and Inequality in Numeracy – the Case of Latin America and

the Caribbean, 1880-1949”, Revista de Historia Económica – Journal

of Latin American and Iberian Economic History 27-1 (2009), pp. 37-74.

Crayen and Baten 2010: Crayen, Dorothee, and Baten, Joerg (2010). Global

Trends in Numeracy 1820-1949 and its Implications for Long-Run Growth.

Explorations in Economic History, 47(1): 82-99.

Friesen, Prayon and Baten (2013): Friesen, Julia, Prayon, Valeria and

Baten, Joerg: “Women count. Gender (In-)Equalities in the Human

Capital Development in Asia, 1900-1960, Tübingen Working Papers in

Economics and Finance 29

But as the underlying age data comes from a variety of sources, here is

the complete list:

(we first reported authors and year; then author with first name;

finally title)

References

A’Hearn Baten Crayen 2009: Brian A’Hearn, Joerg Baten and Dorothee

Crayen: “Quantifying Quantitative Literacy: Age Heaping and the

History of Human Capital”. Journal of Economic History 69-3 (Sept

2009), pp.783-808.

Argentina 1869: Argentina, National census data of 1869, published in

Somoza, J., Lattes, A., 1967. Muestras de los dos primeros censos

nacionales de población, 1869 y 1895. Documento de Trabajo No 46,

Instituto T. Di Tella, CIS, Buenos Aires

Argentina 1895: National census data of 1869 and 1895, published in

Somoza, J., Lattes, A., 1967. Muestras de los dos primeros censos

nacionales de población, 1869 y 1895. Documento de Trabajo No 46,

Instituto T. Di Tella, CIS, Buenos Aires

Baten Sohn 2013: Baten, J and Kitae Sohn: “Back to the ‘Normal’

Level of Human-Capital Driven Growth? A Note on Early Numeracy in Korea,

China and Japan, 1550–1800”, University of Tübingen Working Papers

in economics and finance, No. 52

Baten Fourie 2013: Baten, J, and Johan Fourie “Numeracy in the 18th

Century Indian Ocean Region”): ERSA Working Paper No. 270 (2013)

Baten Ma Morgan Wang 2010: Baten, J., Debin Ma, Stephen Morgan and Qing

Wang (2010) “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: 347-359

Brazil 1970: VIII Recenseamento Geral do Brasil. Censo Demográfico de

1970.

Cairo 1848: see Ghanem 2012

Canada 1852 and 1881: Historical Censuses of Canada (Canada East, Canada

West, New Brunswick and Nova Scotia). Université de Montréal,

Montréal;

Costa Rica 1927: Censo 1927: “Censo de Población de 1927” (online)

Centro Centroamreicano de Población (CCP), HYPERLINK

"http://ccp.ucr.ac.cr/bvp/censos/1927/index.html"

http://ccp.ucr.ac.cr/bvp/censos/1927/index.html (assessed on

2012-05-29)

Crayen Baten 2010: Crayen, D., and Baten, J. (2010). Global Trends in

Numeracy 1820-1949 and its Implications for Long-Run Growth.

Explorations in Economic History, 47(1): 82-99.

DHS: Demographic and Health Surveys, various countries (abbreviated with

2-char ISO code) and years. HYPERLINK "http://www.measuredhs.com"

www.measuredhs.com last accessed 131226

Eberhardt 2010: Eberhart, Helmut et al. (2010), Preliminary dataset

“Albanische Volkszaehlung von 1918”, entstanden an der

Karl-Franzens-Universita¨t Graz unter Mitarbeit von Helmut Eberhart,

Karl Kaser, Siegfried Gruber, Gentiana Kera, Enriketa Papa-Pandelejmoni

und finanziert durch Mittel des Oesterreichischen Fonds zur Foerderung

der wissenschaftlichen Forschung; (FWF).

Egypt 1848: Census of Cairo,

Egypt 1907: Census of Egypt: The Statistical Department of the Ministry

of Finance Egypt, 1907. Statistical yearbook of Egypt. 3rd census of

Egypt 1905. Cairo, The Government Press;

HYPERLINK "http://www.familysearch.org" www.familysearch.org :

Mortality registers of Sweden, last accessed 131226

Grether 2012: Grether, Kathrin (2012), Langfristige

Humankapitalentwicklung auf den Philippinen im international Vergleich.

Unpubl. BA Thesis Univ. Tuebingen

Gruber undated: Siegfried Gruber, Friendly communication, who collected

visitation data on a number of Serbian villages. Siegfried Gruber,

Karl-Franzens-Universität Graz, Centre for Southeast European History,

Project ‘‘Kinship and Social; Security”

Guettler 2011: Guettler, Sabine (2011), Verbreitung der

Bildungsinnovationen in Peru und Ecuador im 18. und 19. Jahrhundert,

Unpubl. Diploma Thesis Univ. Tuebingen

Habsburg 1880: Austro-Hungarian census of 1880, published as

Österreichische Statistik, Band 1, Heft 1–3, Band 2, Heft 1–2 and

Band 5, Heft 3, 1882–1884. The evidence covers Austria, Bosnia and

Herzegovina, Croatia, Czech Republic, Hungary, Slovakia and Slovenia. We

merged Austrian, Russian, and German regional statistics to obtain

weighed averages for the modern territories of Ukraine and Poland.

Hippe Baten 2012: Hippe, R. and Baten, J. (2012) “The Early Regional

Development of Human Capital in Europe, 1790 – 1880, Scandinavian

Economic History Review, 60, Number 3, 1 November 2012 , pp. 254-289

India 1881-1921: 1891-1921 (Census of India, 1891 (Bombay, Madras,

North-Western Provinces) Indian Empire Census of 1891, 1901, 1911 and

1921. The Superintendent of Government Printing India, Calcutta;

IPUMS: Ruggles Alexander Genadek Goeken Schroeder Sobek 2010: Ruggles,

S., Alexander, J.T., Genadek, K., Goeken, R., Schroeder, M.B., and

Sobek, M. (2010). Integrated Public Use Microdata Series: Version 5.0

[Machine-readable database]. Minneapolis: University of Minnesota.

Japan 1882: Ministry of Internal Affairs and Communications, 1882. First

Statistical Yearbook of the Japan Empire. Population statistics of the

Province of Kai 1879 (today’s Yamamashu Prefecture). Government

Publications, Tokyo;

Juif Baten 2013: Juif, D.-T., Baten, J. (2013). “On the Human Capital

of ‘Inca’ Indios before and after the Spanish Conquest. Was there a

“Pre-Colonial Legacy”?”,Explorations in Economic History 50-2

(2013), pp. 227-41. Older version: Tuebingen Working Papers in Economics

and Finance 27.

Manzel 2009: Kerstin Manzel 2009. Essays on Human Capital Development in

Latin America and Spain, Dissertation, Univ. Tuebingen

Manzel Baten and Stolz 2012: Manzel, K., Baten, J. and Stolz, Y. (2012)

“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. Detailed sources are listed in their

online appendix p.4/5

Manzel Baten 2009: Manzel, K. and Baten, J. (2009). Gender Equality and

Inequality in Numeracy: The Case of Latin America and the Caribbean,

1880-1949. Journal of Iberian and Latin American Economic History,

27(1): 37-74.

Matic 2010: Matic, E. (2010). Die Humankapitalentwicklung in Bulgarien

und Bosnien im 19./20. Jahrhundert. Unveröff. Bachelor-Arbeit

Universität Tübingen.

Meinzer 2013: Meinzer, Nicholas (2013) “The selectivity of migrants to

Australia: a new methodological approach”. Unpubl. Master thesis Univ.

Tuebingen.

Pertschy 2012: Pertschy, Robert (2012), Regionale Unterschiede der

langfristigen Humankapitalentwicklung in Chile im 19. Jahrhundert.

Unpubl. BA Thesis Univ. Tuebingen;

Rothenbacher 2002: Rothenbacher, F. (2002). The European Population

1850-1945. Basingstoke: Palgrave Macmillan.

Russia 1959 and 1970: Demoskop Weekly (2001). ėlektronnaja versija

bjulletenja Naselenie i obščestvo. Institut Demografii

Gosudarstvennogo Universiteta, Vysšej Školy Ėkonomiki, Moskva.

Russian 1897: Russian Empire: First General Russian Empire Census of

1897.

Schneider 2011: Schneider, Christian (2011), Das Humankapital in den

Regionen Ecuadors, Unpubl. Diploma Thesis Univ. Tuebingen

Starbatty 2011: Starbatty, Peter (2011). Humankapitalentwicklung im

Osmanischen Reich 1760-1810. Regionale und ethnische Unterschiede.

Unpubl. BA Thesis Univ. Tuebingen.

Stolz Baten Botelho 2013: Stolz, Yvonne, Baten, J. and Botelho, T.

"Growth effects of 19th century mass migrations: “Fome Zero” for

Brazil?" European Review of Economic History 17-1 (2013), pp. 95-121.

Older version: Tuebingen Working Papers in Economics and Finance 20

Stolz Baten Reis 2013: Stolz, Yvonne, Baten, J. and Jaime Reis,

“Portuguese Living Standards 1720-1980 in European Comparison –

Heights, Income and Human Capital”, Economic History Review 66-2

(2013), pp. 545-578

United Kingdom 1851: Anderson, M. et al., 1979. National sample from the

1851 census of Great Britain [computer file]. Supplied by History Data

Service, UK Data Archive (SN: 1316). Colchester, Essex; Schuerer, K.,

Woollard, M., 2002.

United Kingdom 1881: National sample from the 1881 census of Great

Britain [computer file]. Supplied by History Data Service, UK Data

Archive (SN: 4375). Colchester, Essex;

UNDYB various years: United Nations, Department of International

Economic and Social Affairs, Statistical Office (various issues).

Demographic Yearbook. New York: United Nations.

United States 1850, 1860, 1870, 1880, 1900: Ruggles, S., Alexander,

J.T., Genadek, K., Goeken, R., Schroeder, M.B., and Sobek, M. (2010).

Integrated Public Use Microdata Series: Version 5.0 [Machine-readable

database]. Minneapolis: University of Minnesota

The titles cited above were used for the following countries and year:

Country From (or only birth decade) To Source (see above)

Austria 1810 1880 Rothenbacher 2002

Belgium 1810 1870 Rothenbacher 2002

France 1810 1890 Rothenbacher 2002

France 1920 1960 1990 UNDYB

Germany 1830 1900 Rothenbacher 2002

Luxembourg 1810 1870 Rothenbacher 2002

Netherlands 1820 1880 Rothenbacher 2002

Switzerland 1810 1870 Rothenbacher 2002

Switzerland 1920 1960 1990 UNDYB

Denmark 1830 1890 Rothenbacher 2002

Estonia 1880 1930 Russia 1959 1970

Estonia 1820 1860 Russia 1897

Finland 1910 1950 1985 UNDYB

Finland 1810 1890 Rothenbacher 2002

Iceland 1820 1900 Rothenbacher 2002

Ireland 1900 1950 1979 UNDYB

Ireland 1960

1991 UNDYB

Ireland 1840 1890 Rothenbacher 2002

Latvia 1880 1940 Russia 1959 1970

Latvia 1820 1860 Russia 1897

Lithuania 1880 1930 Russia 1959 1970

Lithuania 1960

1989 UNDYB

Lithuania 1820 1860 Russia 1897

Norway 1960

1990 UNDYB

Norway 1900 1940 1980 UNDYB

Norway 1810 1870 Norway 1861-1900

Sweden 1810 1900 Rothenbacher 2002

Sweden 1920 1960 1991 UNDYB

United Kingdom of Great Britain and Northern Ireland 1910 1920 1951

UNDYB

United Kingdom of Great Britain and Northern Ireland 1810 1820 United

Kingdom 1851

United Kingdom of Great Britain and Northern Ireland 1830 1900

Rothenbacher 2002

United Kingdom of Great Britain and Northern Ireland 1930 1960 1991

UNDYB

United Kingdom of Great Britain and Northern Ireland 1840 1850 United

Kingdom 1881

Bosnia and Herzegovina 1910 1960 1991 UNDYB

Croatia 1850

Habsburg 1880

Greece 1870 1920 UNDYB

Italy 1810 1900 Rothenbacher 2002

Malta 1880 1920 UNDYB

Portugal 1860 1910 Rothenbacher 2002

Slovenia 1810 1850 Habsburg 1880

Slovenia 1920 1960 1989 UNDYB

Spain 1830 1940 Crayen and Baten 2010

The former Yugoslav Republic of Macedonia 1920 1950 1994 UNDYB

Belarus 1880 1940 Russia 1959 1970

Belarus 1820 1860 Russia 1897

Bulgaria 1890 1930 1970 UNDYB

Czech Republic 1810 1830 Habsburg 1880

Czech Republic 1840 1900 Rothenbacher 2002

Czechoslovakia (until 1993) 1810 1830 Habsburg 1880

Hungary 1880 1910 Rothenbacher 2002

Hungary 1930 1950 1990 UNDYB

Hungary 1810 1840 Habsburg 1880

Poland 1820 1860 Russia 1897, Hippe and Baten 2012

Poland 1870 1890 Rothenbacher 2002

Poland 1900 1950 1978 UNDYB

Republic of Moldova 1820 1860 Russia 1897

Republic of Moldova 1880 1940 Russia 1959 1970

Republic of Moldova 1950 1960 1989 UNDYB

Romania 1810 1840 Habsburg 1880

Romania 1890 1920 1966 UNDYB

Russian Federation 1820 1860 Russia 1897

Russian Federation 1960

1989 UNDYB

Russian Federation 1880 1930 Russia 1959 1970

Slovakia 1810 1840 Habsburg 1880

Ukraine 1880 1940 Russia 1959 1970

Ukraine 1820 1860 Russia 1897

Ukraine 1810

Habsburg 1880

Bermuda 1870 1920 1950 UNDYB

Bermuda 1960

1991 UNDYB

Bermuda 1930

1970 UNDYB

Canada 1960

1991 UNDYB

Canada 1810 1850 Canada 1852 and 1881

Canada 1890

1976 UNDYB

Canada 1900 1930 1971 UNDYB

Greenland 1880 1920 1951 UNDYB

Greenland 1930

1965 UNDYB

United States of America 1960

1990 UNDYB

United States of America 1890 1920 1950 UNDYB

United States of America 1930 1950 1980 UNDYB

United States of America 1810 1880 IPUMS

Aruba 1910 1960 1991 UNDYB

Bahamas 1910 1960 1990 UNDYB

Barbados 1860 1910 UNDYB

British Virgin Islands 1910 1950 1991 UNDYB

Cayman Islands 1920 1970 1998 UNDYB

Cuba 1900 1950 1981 UNDYB

Dominican Republic 1870 1920 1950 UNDYB

Dominican Republic 1930 1940 Manzel Baten 2009

Grenada 1860 1910 UNDYB

Guadeloupe 1890 1930 1967 UNDYB

Haiti 1930 1940 UNDYB

Haiti 1870 1920 1950 UNDYB

Jamaica 1910 1960 1991 UNDYB

Martinique 1940 1960 1990 UNDYB

Martinique 1890 1930 1967 UNDYB

Netherlands Antilles (until 2010) 1910 1960 1992 UNDYB

Puerto Rico 1930 1960 1990 UNDYB

Puerto Rico 1870 1920 1950 UNDYB

Saint Lucia 1910 1960 1991 UNDYB

Trinidad and Tobago 1860 1910 1946 UNDYB

Belize 1860 1910 1950 UNDYB

Costa Rica 1940

UNDYB

Costa Rica 1900 1930 1963 UNDYB

Costa Rica 1840 1890 CostaRica 1927

El Salvador 1930 1940 Manzel Baten 2009

El Salvador 1870 1920 1950 UNDYB

Guatemala 1870 1920 1950 UNDYB

Honduras 1890 1940 1974 UNDYB

Mexico 1870 1900 Manzel, Baten and Stolz 2012

Mexico 1910 1960 1990 UNDYB

Nicaragua 1930

1963 UNDYB

Nicaragua 1870 1920 1950 UNDYB

Nicaragua 1940

UNDYB

Panama 1950

1980 UNDYB

Panama 1960

1990 UNDYB

Panama 1870 1920 1950 UNDYB

Panama 1930

1960 UNDYB

Argentina 1810 1860 Manzel, Baten and Stolz 2012

Argentina 1900 1950 1980 UNDYB

Bolivia (Plurinational State of) 1890 1940 1976 UNDYB

Bolivia (Plurinational State of) 1950 1960 1992 UNDYB

Bolivia (Plurinational State of) 1870 1880 UNDYB

Brazil 1810 1820 Manzel, Baten and Stolz 2012

Brazil 1900 1920 UNDYB

Chile 1890 1940 UNDYB

Colombia 1940 1950 1985 UNDYB

Colombia 1880 1930 1964 UNDYB

Colombia 1810 1840 Manzel, Baten and Stolz 2012

Ecuador 1870 1880 UNDYB

Ecuador 1810 1840 Manzel Baten Stolz 2012

Ecuador 1950 1960 1990 UNDYB

Ecuador 1890 1940 1974 UNDYB

French Guiana 1880 1930 1967 UNDYB

Guyana 1860 1910 UNDYB

Paraguay 1880 1930 UNDYB

Peru 1860 1910 Manzel, Baten and Stolz 2012

Suriname 1880 1930 1964 UNDYB

Uruguay 1880 1930 1963 UNDYB

Uruguay 1950

1985 UNDYB

Uruguay 1940

1975 UNDYB

Uruguay 1810 1840 Manzel, Baten and Stolz 2012

Venezuela (Bolivarian Republic of) 1930 1940 Manzel Baten 2009

Venezuela (Bolivarian Republic of) 1870 1920 1950 UNDYB

Australia 1860 1910 1947 UNDYB

Australia 1920 1960 1991 UNDYB

New Zealand 1950

1986 UNDYB

New Zealand 1860 1910 1945 UNDYB

New Zealand 1920 1930 1961 UNDYB

Fiji 1940 1950 1986 UNDYB

Fiji 1920 1930 1966 UNDYB

Fiji 1860 1910 1946 UNDYB

Vanuatu 1910 1960 1989 UNDYB

Guam 1920 1970 2000 UNDYB

Marshall Islands 1920 1950 1988 UNDYB

Cook Islands 1910 1950 1996 UNDYB

French Polynesia 1910 1940 1986 UNDYB

Tonga 1900 1950 1986 UNDYB

Afghanistan 1900 1950 1979 UNDYB

Bangladesh 1900 1940 1974 UNDYB

Bangladesh 1830 1890 India 1881-1921

India 1830 1890 India 1881-1921

India 1900 1940 UNDYB

Iran (Islamic Republic of) 1880 1930 UNDYB

Maldives 1880 1930 1967 UNDYB

Maldives 1940 1950 1985 UNDYB

Nepal 1900 1950 UNDYB

Pakistan 1830 1890 India 1881-1921

Pakistan 1900 1940 Pakistan 1973

Sri Lanka 1860 1950 UNDYB

China 1910 1950 1990 UNDYB

China, Hong Kong Special Administrative Region 1950

1986 UNDYB

China, Hong Kong Special Administrative Region 1960

1991 UNDYB

China, Macao Special Administrative Region 1910 1950 1991 UNDYB

Japan 1890

UNDYB

Japan 1960

1990 UNDYB

Japan 1860 1880 Japan 1882

Japan 1900 1950 1985 UNDYB

Mongolia 1950 1960 1990 UNDYB

Republic of Korea 1950

1980 UNDYB

Republic of Korea 1960

1990 UNDYB

Republic of Korea 1930

1960 UNDYB

Brunei Darussalam 1930

1971 UNDYB

Brunei Darussalam 1950

1981 UNDYB

Cyprus 1920 1930 1992 UNDYB

Cyprus 1860 1910 1946 UNDYB

Cambodia 1880 1930 1962 UNDYB

Indonesia (until 1999) 1900 1950 UNDYB

Malaysia 1870 1930 Crayen and Baten 2010

Myanmar 1840 1870 India 1881-1921

Philippines 1870 1920 1948 UNDYB

Singapore 1920 1960 2000 UNDYB

Thailand 1920 1930 UNDYB

Thailand 1860 1910 1947 UNDYB

Viet Nam 1960

1989 UNDYB

Armenia 1820 1860 Russia 1897

Armenia 1880 1930 Russia 1959 1970

Azerbaijan 1820 1860 Russia 1897

Azerbaijan 1880 1940 Russia 1959 1970

Bahrain 1890 1940 1971 UNDYB

Bahrain 1950

1981 UNDYB

Georgia 1880 1940 Russia 1959 1970

Georgia 1820 1860 Russia 1897

Iraq 1880 1930 UNDYB

Israel 1870 1920 UNDYB

Kuwait 1880 1930 1970 UNDYB

Occupied Palestinian Territory 1910 1960 1991 UNDYB

Qatar 1900

1986 UNDYB

Syrian Arab Republic 1890 1940 UNDYB

Turkey 1820 1860 Russia 1897

Turkey 1870 1920 1950 UNDYB

Turkey 1950 1960 1990 UNDYB

Turkey 1930

1965 UNDYB

Kazakhstan 1820 1860 Russia 1897

Kazakhstan 1960

1989 UNDYB

Kazakhstan 1880 1930 Russia 1959 1970

Kyrgyzstan 1880 1930 Russia 1959 1970

Kyrgyzstan 1960

1989 UNDYB

Kyrgyzstan 1820 1860 Russia 1897

Tajikistan 1880 1940 Russia 1959 1970

Tajikistan 1820 1860 Russia 1897

Turkmenistan 1880 1930 Russia 1959 1970

Turkmenistan 1820 1860 Russia 1897

Uzbekistan 1820 1860 Russia 1897

Uzbekistan 1880 1940 Russia 1959 1970

Algeria 1890 1930 1966 UNDYB

Egypt 1870 1910 1947 UNDYB

Egypt 1830 1860 Egypt 1907

Libya 1890 1940 UNDYB

Morocco 1880 1930 1960 UNDYB

Tunisia 1880 1930 1966 UNDYB

Benin 1900 1950 1979 UNDYB

Burkina Faso 1900 1950 1985 UNDYB

Cape Verde 1910 1960 1990 UNDYB

Cote d'Ivoire 1910 1960 1988 UNDYB

Gambia 1890 1940 UNDYB

Ghana 1880 1940 UNDYB

Guinea-Bissau 1870 1920 UNDYB

Liberia 1940

1974 UNDYB

Liberia 1890 1930 1962 UNDYB

Mali 1890 1940 1976 UNDYB

Nigeria 1880 1930 1963 UNDYB

Saint Helena 1900 1950 1987 UNDYB

Togo 1880 1940 UNDYB

Cameroon 1890 1940 1976 UNDYB

Central African Republic 1900 1940 1975 UNDYB

Democratic Republic of the Congo 1910 1950 1985 UNDYB

Botswana 1940 1960 1991 UNDYB

Botswana 1880 1930 1964 UNDYB

South Africa 1920 1950 1980 UNDYB

South Africa 1860 1910 1950 UNDYB

Swaziland 1940 1950 1986 UNDYB

Swaziland 1880 1930 1966 UNDYB

Burundi 1910 1960 1990 UNDYB

Kenya 1960

1989 UNDYB

Kenya 1940 1950 1979 UNDYB

Kenya 1880 1930 1962 UNDYB

Madagascar 1890 1940 UNDYB

Mauritius 1890 1940 1970 UNDYB

Réunion 1910 1960 1988 UNDYB

Uganda 1950 1960 1991 UNDYB

Uganda 1890 1940 1969 UNDYB

United Republic of Tanzania 1880 1930 1967 UNDYB

Zambia 1890 1940 UNDYB

This following is an excerpt of the paper Manzel and Baten (2010). For

the citation see above.

Age heaping has been used a number of times recently to measure

education levels (Mokyr 1983, Crayen and Baten 2008a and 2008b,

A’Hearn, Baten and Crayen 2009, de Moor and van Zanden 2008, Clark

2007, Manzel 2007, Baten, Crayen and Manzel 2008, see also the

applications in Cinnirella 2008, Mironov 2006, O’Grada 2006). It

describes the phenomenon that people tend to round up or down their age,

mostly in multiples of five, when asked how old they are. The main

reasons for this are lack of knowledge about their real age or lack of

numerical discipline. Consequently, estimating the degree of age heaping

gives us information about the educational system as well as about

institutions in a society.

As early as the 1950s Bachi (1951) and Myers (1954) found a correlation

between the degree of age heaping and literacy. Mokyr (1983) was the

first to apply age heaping as a proxy variable for the educational level

of a population in order to investigate whether there was a brain drain

from pre-famine Ireland. Studies find a strong negative correlation

between age heaping and literacy or schooling, such as Crayen and Baten

(2008b) for the 19th and 20th centuries, A’Hearn, Baten and Crayen

(2009) for the 19th century U.S. states and the countries of Europe

during the early modern period, Manzel and Baten (2008) for Argentina

during the 19th century, and Nagi, Stockwell and Snavley (1973) for

African countries of the mid-20th century. To measure the degree of age

heaping, various indices can be used. A’Hearn, Baten and Crayen (2009)

show that the Whipple Index is most appropriate for this purpose. It

determines the tendency of age heaping on the digits 5 and 0 and is

calculated by taking the ratio of the sum of people reporting an age

ending on multiples of five and the total sum of people in a certain age

range. This ratio is then multiplied by 500. Meaningful interpretations

of the index vary between 100 and 500. In the case of 100, no age

heaping on multiples of five is present, in the case of 500, the age

data contain only digits ending in multiples of five (Hobbs 2004).

Hence, the Whipple Index (Wh) gives us information about numeracy skills

or numerical discipline and can be used as a proxy for an important

component of the educational level of a population. The calculation of

the Whipple Index requires single age data for ten successive years, so

that each terminal digit appears once. Mortality will have the effect

that fewer people are alive at age 44 than at age 40, and at age 49 than

at age 45, which could bias the Whipple Index downwards (Crayen and

Baten 2008a). Therefore we choose the age groups 23-32, 33-42 etc. to

overcome this problem. We exclude age data for under 23-year olds,

because many young males and females married in their early twenties or

late teens and had to register as voters, military conscripts etc. On

such occasions, they were sometimes subject to age requirements, a

condition which gave rise to increased age awareness. Moreover,

individuals grow physically during this period, which makes it easier to

determine their age with a relatively high accuracy. Age information for

over 72-year olds is not included as age statements of older people

involve several problems: age exaggeration, survivor bias, higher

mortality of males (Del Popolo 2000) and other household members who

report the ages of older persons play a more pronounced role than at

younger ages.

The Whipple Index is defined inversely, i.e. it represents lack of

numeracy rather than numeracy. For an easier interpretation, A’Hearn,

Baten and Crayen (2009) suggested another index, the ABCC index. It

transforms the Whipple Index and yields an estimate of the share of

individuals who correctly report their age:

.

The method of approximating educational levels with age heaping

behaviour certainly has its deficiencies in measuring human capital, as

misreporting of ages may also have political or cultural reasons. The

degree to which age heaping is influenced by schooling and the effect of

other institutional factors is not easy to disentangle, although Crayen

and Baten (2008b) assessed this and found that schooling was more

important than other factors such as bureaucracy and previous

census-taking. We conclude that -- at least in the absence of other

indicators – age heaping is a valuable instrument to approximate the

development of human capital.

Gender equality

To measure educational equality between the sexes, we define a measure

of “gender equality” (GE) as

where whf and whm are the Whipple Indices of females and males,

respectively. Thus, the higher our measure of gender equality, the lower

the share of women rounding up or down their age in comparison to men

rounding up or down in a certain country. A positive (negative) gender

equality index implies a female (male) numeracy advantage. Most of the

time, the index will be negative. We formulate this as gender equality

in order to make it more easily comparable with the literature on female

labor force participation rates (Goldin 1995, Mammen and Paxson 2000).

Of course, this does not imply that our countries were characterized by

gender “equality” between 1880 and 1949.

A Whipple Index of 0 is theoretically possible and would mean an

avoidance of ages ending in 5 and 0. However, values below 95-100 are

uncommon.

A 17-year-old might round up/down to 18 or 16, but not to 15 or 20.

Moreover, children were excluded because of a high likelihood that the

parents rather than the child himself answered the question.

†

‡

ˆ

š

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ˆ

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effect becomes visible from the age of 70 onwards, in others only from

the age of 80. In order to obtain reliable results, we exclude those

older than 72 from our analysis.

The name comes from the initials of the authors’ last names plus that

of Greg Clark, who suggested this in a comment on their paper.

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