The multi-state projection method is a well-established demographic tool developed in the 1970s. It is based on the standard cohort population projection (projecting the population by age group) which is used by the United Nations, the World Bank and for most national population projections. The modification in the multi-state projection is to divide the population into different groups that are projected in parallel education groups. Multi-state projection has been used to make international series of population by education attainment projections at the International Institute for Applied Systems Analysis/Vienna Institute for Demography and by the EPDC (both available in the EdStats Education Projections Query)ⁱ.

The starting point of the projection is the population pyramid by age, sex, and education. A graph of these data is shown for Egypt 2005 in Figure 1. Although the pyramid is shown in five-year age groups, the actual projections are done for single ages and single years. The projection is a simulation of how a real population changes through aging, deaths, births, and education transitions. In the calculation, for each new projection year, all the population in the pyramid "ages up" by one year. People who died in that year are subtracted from each age group; births are added to the bottom age group, and some people in the school-age groups (5 to 24) shift to a new education level. There is no migration assumed in these projections.

Deaths are calculated with age-specific mortality rates based on life expectancy projections. Births are added to the youngest age category. The new births are calculated by multiplying the number of women of childbearing age with the age-specific birth rates, based on the total fertility rate projections. Trends for both life expectancy and births are taken from the United Nations 2006 population projection.

Figure 1 – data used for multi-state projection of population by education attainment, based on the example of Egypt.
        

Top panel: the starting human capital pyramid for Egypt in 2005;

Middle panel: the trends 2005-2025 primary and secondary school entry that drive the projection of education attainment;

Bottom panel: ending human capital pyramid for 2025.

With regards to education, in each year, people who enter primary school transition from the category “No Schooling” to the education level “Primary”, and people who enter secondary school transfer from the education level “Primary” to “Secondary” (in addition to aging one year). The education transitions (primary and secondary school entry rates) can apply to people between the ages 5 and 24 for primary and between ages 10 and 24 for secondary. The education transitions are based on projections of primary and secondary school entry rates, shown for Egypt in the middle panel of the figure. Basically, these projections are extrapolations of trends from the past 15 years. The school entry projections are made by the EPDC and are updated in an ongoing fashion as new data becomes available.

The projected 2025 human capital pyramid is shown in the bottom panel. Note that the groups with no education have disappeared from the youth and younger adult age groups following the trend to universal primary (see trend graph in the middle) and there is near-universal secondary schooling among youth and young adults (also following the school trend).

  i. For a more technical explanation of the method, see Rogers (1975), Lutz, Goujon and Wils (2005) at www.epdc.org.

c. Levels of education attainment

 The projections provided to the EdStats Education Projection Query are made for three levels of education: no schooling, entered primary, and entered secondary and higher.

No schooling includes people who never entered any school, who have had only pre-primary education, non-formal, or “other” education.  Non-formal education can be superior to formal schoolingⁱ  and equivalent to primary, secondary, or even higher educationⁱⁱ.  It is problematic to include it in no schooling, but is placed there because of the uncertainty regarding its contents.  In practical terms, non-formal schooling is a small portion of education in most countries.

 “Entered primary” includes people who entered primary school and did or did not finish it.  “Entered secondary” includes all those who started secondary school as well as those who finished and went on to higher levels of education.

Some users will ask why “primary entry” was used instead of primary completion, which is one of the Education for All goals.  The practical reason is that primary entry captures the broadest range of educational experience in developing countries.   There are many countries where the portion of adults who have completed primary is low today and projected to remain low.  Many countries are making much progress at the lower education level of primary entry, but not as much yet on primary completion.  For those countries, it makes sense to differentiate at a lower education level.  On balance, using primary completion underestimates the number of people with some level of education, while using entry overestimates the number of people who likely have a functional education. We have erred on the positive side in choosing primary entry.

Secondary entry was deemed essential because of the increasing evidence that secondary education has much higher impacts on development than primary education.

i. J. De Stefano, A. Schuh Moore, D. Bawanz, and A. Hartwell. 2006  “Compilation: Reaching the Underserved: Complementary Models of Effective Schooling” Available www.equip123.net/  publications.

ii. EPDC (2008)  “The Extent and Impact of Non-formal Education in 28 Developing Countries.” Available at www.epdc.org/analysis