Education Back Projections for 1970-2000

The Demography of Human Capital Formation

Reconstruction of Populations by Age, Sex and Level of Educational Attainment for 120 Countries for 1970-2000
Using Demographic Back-Projection Methods

IIASA World Population Program and
Vienna Institute of Demography (VID), Austrian Academy of Sciences

Wolfgang Lutz (lutz@iiasa.ac.at), Samir K.C. (kc@iiasa.ac.at), Anne Goujon (goujon@iiasa.ac.at), Warren Sanderson (wsanderson@notes.cc.sunysb.edu)

Correspondence and requests should be addressed to Anne Goujon or Samir K.C.

Publications

• Methodology

W Lutz, A Goujon, S K.C., W Sanderson. 2007. Reconstruction of population by age, sex and level of educational attainment of 120 countries for 1970-2000. Vienna Yearbook of Population Research, vol. 2007, pp 193-235.  Download PDF    

• Dataset

The full dataset can be downloaded here:

Absolute Population by Age, Sex and Education
Proportion of Population by Age, Sex and Education
Mean Years of Schooling by Age and Sex (Forthcoming)

• Comparison between the dataset and empirical data

F Riosmena, I Prommer, A Goujon, S KC. 2008. An Evaluation of the IIASA/VID Education-Specific Back Projections. IIASA Interim Report IR-08-019 [August 2008, 40 pp]. Download PDF
   

Purpose
Previous work
Our method
The basic principle of back-projection
Dealing with the open interval in highest age group
Age of transition to higher educational categories
Validation of results
Output tables
Analysis of results
References
   

Purpose

Assessments of the returns to investments in formal education at the aggregate (national) level require empirical information about the educational status of the adult population over some time period. This information needs to be consistent in terms of the definition of educational categories across countries and over time. Since the effects of educational attainment can be expected to differ by age (e.g., the education of 25-35 year olds is more important for economic growth than that of 65-75 year olds) as well as by sex, having full age details for men and women can be considered a great asset. In addition, only the explicit consideration of distinct levels of educational attainment allows for the analysis of the relative importance of primary versus secondary or tertiary education (and different mixes of the three) which should be key to all national and international education policy plans.

Previous Work

Because of the high importance of consistent international time series on the human capital of the adult population, several efforts have been made to construct such series. The problem is that the official data from censuses and reliable surveys, such as those collected by UNESCO, are only fragmentary and scattered over time and countries. In addition, these data suffer from various changes in definitions of educational categories over time and across countries which make them inappropriate for consistent time series analysis. Barro and Lee (1993, 1996, 2001) undertook the ambitious effort to complement these data with the somewhat more consistent time series of national school enrollment data at different levels using perpetual inventory methods which help transform accumulated education flows (enrollment) into human capital stocks. This resulted in a widely used data set that gives the mean years of schooling of the entire adult population (by sex but without age details) for 142 economies, of which 107 have completed information at five-year intervals from 1960 to 2000. Similar independent efforts have been made by Lau, Bhalla and Louat (1991), Lau, Jamison and Louat (1991), Nehru, Swanson and Dubey (1995), De la Fuente and Domenech (2002) and by Cohen and Soto (2001), which in many cases result in quite different estimates of mean years of schooling. Except for Cohen and Soto, none of these reconstruction efforts gives the desirable age details nor do many of them provide the distribution over different educational attainment categories. As far as we know, they also disregard in their calculations the well established fact that people with higher education have lower mortality rates, which can have quite significant effects on the educational composition of the older adult population.

Our Method

For this new reconstruction effort we do not refer to past school enrollment data using the (in this context) problematic perpetual inventory method, but choose a different approach which is derived from the demographic method of multi-state population projection which was developed at IIASA during the 1970s and is now a well accepted method among technical demographers. For this approach we need only one reliable data point for each country (typically around the year 2000) which gives the total population by sex, five-year age groups and the four attainment categories based on the ISCED: no education, primary, secondary and tertiary. Using this information we then back-project the full pattern (by age, sex and attainment categories) to 1970. This has the great advantage that the educational categories are by definition identical over time and therefore allow consistent trend analysis. This back-projection task is significantly simplified by the fact that the UN Population Division has estimated the population structures in five-year intervals for all countries of the world since 1950. Taking these estimates as a basis, our reconstruction effort is reduced to estimating the proportions in each of the four education categories for each five-year age group of men and women. This also means that (unlike in multi-state forecasting) we do not have to worry about educational fertility differentials, but only have to consider possible differentials in mortality and migration.

The basic principle of back-projection

The basic idea of back-projection in this context is very simple: Assuming that the educational attainment of a person remains invariant after a certain age, we can derive, e.g., the proportion of women without any formal education aged 50-55 in 1995 directly from the proportion of women without formal education aged 55-60 in 2000. Assuming that this proportion is constant along cohort lines, it directly gives us the proportion of women without education aged 25-30 in 1970. In a similar manner, the proportions for each educational category and each age group of men and women can simply be moved to the next younger five-year age group as one moves back in time in five-year steps. It is important to see that these are not arbitrary assumptions, but truisms under certain conditions. In the above example, the proportions of women without schooling aged 25-30 in 1970 and 55-60 in 2000 must be identical if nobody moves to the category with primary education after the age of 25 and if mortality and migration do not differ by level of education. This follows directly from the fact that the size of a birth cohort as it ages over time can only change through mortality and migration. In the following, we will discuss the assumptions reflected in the two “ifs” in the above statement.

Differential mortality and migration

Since the fact that mortality differs by level of education is well established and sensitivity analyses show that the effects on the educational composition of the elderly adult population are non-trivial, it is imperative to make adjustments for this factor. In order to assess the magnitude of these differentials in different settings, an exercise was carried out (as part of the Young Scientists Summer Program at IIASA in 2005) to estimate these differentials for as many countries as possible for which at least two sets of census data were available which had fully consistent educational definitions. This was complicated by the fact that the survival along cohort lines is also affected by migration and there is no empirical basis to separate these two factors. The results of this exercise showed sizable education differentials in survival, but also important variations of this across countries and over time. But some commonalities emerged from the pattern, such as the fact that the differentials between the no education and the primary education groups tend to be smaller than the differentials to the higher educational categories. Since no specific regional pattern appeared in this analysis, we chose to apply a uniform pattern to all countries. It is defined in terms of the life expectancy at age 15 (since differentials in child mortality largely depend on parents’ education rather than the education of the deceased). Taking secondary education as the reference category, we assume that life expectancy at age 15 is two years lower in the primary education category, three years lower in the no education category and two years higher in tertiary education category. In other words, life expectancy at age 15 is assumed to differ by five years between the lowest and the highest education category. The way it is defined, these differentials also cover educational differentials in migration for lack of more specific data on migration. In a few cases, however, where we know that migration has been disproportionately concentrated in the higher or lower education categories (such as Israel for highly educated immigrants and Mexico for poorly educated emigrants) we made additional adjustments.

Dealing with the open interval in highest age group

Another practical complication in applying the above described principle is the fact that national education data typically do not report the age structure of the population up to very high age groups. In many cases the highest age category is 65+, while in some cases it is higher and in other cases lower. But since the cohort aged 65+ in 2000 was 35+ in 1970 which is not sufficient age detail for the year 1970, one needs to make certain assumptions for the empirical information given for the highest open-ended age category. Further data points for these open-ended age groups were estimated by applying a linear regression to the logits of the educational attainment progression ratios (i.e., the probabilities of moving to a higher category) based on the empirical information of the younger age groups. It is, hence, based on the assumption of rather smooth trends in educational improvements for the age groups concerned and the logits make sure that the probabilities do not exceed unity or fall below zero.

Age of transition to higher educational categories

Since in this reconstruction effort we only go down to the 15-19 age group, transitions to higher education groups that happen on average before this age need not be of concern here. This is clearly the case for the transition from the category with no formal education to that with some primary, but more problematic for transitions to the completed junior secondary and completed tertiary categories. Here it is assumed that one-fourth of transitions to the secondary category (which is based on the completion of junior secondary school) happen in the 15-19 age group, while half of the transitions to the completed tertiary category are assumed to occur in the 20-24 age group. It is important to see that these specific assumptions only matter for the educational composition of the two youngest age groups. The reconstructed composition of all other age groups will be unaffected because we are backwards, from observed attainment to when the attainment was reached and, hence, have the ultimate cohortquantum (completed educational attainment distribution) as a given.

Validation of results

The method as outlined above resulted in a first set of reconstructions which for each country and each year (1970, 1975, …, 2000) gives a full matrix of proportions in the four different education categories by the ten individual age groups (15-19, 20-24, …, 60-64) and 65+. These results have then been checked against empirical data from the countries concerned wherever they exist in usable form for earlier points in time. Wherever the discrepancy between the reconstructed and the empirical data was higher than a specific tolerance limit, a special look into the matter was started. Here the emphasis was to look for changes in definitions of educational categories and to study whether the diverging pattern could have been produced by certain special events such as strong education-specific migration flows. Whenever such sources of divergence were identified, appropriate adjustments were made to the data. In another validation step, the data was converted into mean years of schooling and compared to the Barro and Lee and other previous reconstruction efforts. A detailed comparison to these other data is given in a separate paper.

(Fernando Riosmena, Isolde Prommer, and Vegard Skirbekk)

Output tables

A set of pyramids and standard output tables will be produced for 120 countries. The pyramids will represen the UN’s age-sex distribution (15-64) of the population for each year that is stratified by our estimates of proportions in four educational attainment levels. These stratified pyramids serve as a comprehensive visual summary of the educational attainment for each country, according to the population distributed by age and sex during the period 1970-2000. In the remaining three pages per country, three sets of tables with absolute numbers and proportions are presented. The first set will consists of seven tables, one for each year with two blocks for males and females. Each table will give the number of population distributed by age and educational attainment. The last line of the block gives the same for the aggregate adult (15+) population. In the last column, mean years of schooling for people in corresponding age groups are presented. This has been done in order to make the data comparable to Barro and Lee and other reconstructions, and to accommodate for the fact that some analysts do not want to consider the full attainment distribution, but would rather summarize it in an aggregate indicator. To translate the distribution into mean years of schooling, certain assumptions need to be made about the mean years that people with a certain attainment have spent in school. The second set of tables will contain the same data, but in terms of proportions. On the last page, data for both sexes will be combined.

Analysis of results

Some first regressions, using the new data and following some of the models as used by Barro and Lee and others, showed that indeed these new data result in much more consistent significant positive effects of human capital on economic growth.

References

Barro, R.J. and J.W. Lee. 1993. International comparisons of educational attainment. Journal of Monetary Economics 32(3): 363-394.

Barro, R.J. and J.W. Lee. 1996. International measures of schooling years and schooling quality. American Economic Review 86(2): 218-223.

Barro, R.J. and J.W. Lee. 2001. International data on educational attainment: Updates and implications. Oxford Economic Papers 53(3): 541-563.

Cohen, D. and M. Soto. 2001. Growth and Human Capital: Good Data, Good Results. CEPR Discussion Paper No. 3025. London: The Centre for Economic Policy Research.

De la Fuente, A. and R. Domenech. 2002. Human Capital in Growth Regressions: How Much Difference Does Data Quality Make? An Update and Further Results. CEPR Discussion Paper No. 3587. London: The Centre for Economic Policy Research.

Lau, L.J., S. Bhalla, and L.J. Louat. 1991. Human and Physical Capital Stock in Developing Countries: Construction of Data and Trends. Draft Mimeo, World Development Report. Washington, D.C.: The World Bank.

Lau, L.J., D.T. Jamison, and F. Louat. 1991. Education and Productivity in Developing Countries: An Aggregate Production Function Approach. PRE Working Paper Series No. 612. Washington, D.C.: The World Bank.

Nehru, V., E. Swanson, and A. Dubey. 1995. A new database on human capital stock in developing and industrial countries: Sources, methodology, and results. Journal of Development Economics 46: 379-401.

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Last updated: 26 Mar 2010