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EPDC Enrolment Rates Model

The series of trend projections for enrolment rates and gender parity indices for primary and secondary school levels were produced by the EPDC in 2007 and 2008 for the annual UNESCO Global Monitoring Report .   The projections to 2025 are made for net enrolment rates (NER) and gross enrolment rates (GER) for primary and secondary school, and gender parity indices (GPI) for each enrolment rate.  The projections for each indicator are based on historical trends from 1999-2006 using data from UNESCO Institute of Statistics (UIS). The projections are made using the ProjecTrends model developed by the EPDC. 

The projections help to distinguish those countries that are already on a path of adequate growth (say, to reach Education for All goals) from those where policy change is needed to accelerate growth. Table 1 shows the number of countries for which trends were projected in 2008.

The ProjecTrend model can be obtained from the EPDC by writing to Special requests can be made to make trends based on non-UIS data, such as national statistics, or sub-national statistics.

Table 1.  Number of countries covered by the EPDC 2008 global enrolment projections

 Projection NER and
 Total NER and
 GER and
 Primary level 144 142 175

 Secondary level

 119  168

  1. Methods and assumptions in the projections
  2. Projecting Net Enrollment Rates
  3. Projecting Gross Enrollment Rates
  4. Gender Parity Index

    Full Document 

a. Methods and assumptions in the projections

The projections are based on the continuation of historical trends meaning the extrapolation of past rates of NER, TNER, or GER.  The extrapolations are linear or logistic (approaching 100 or 1 in an s-shaped curve)i   depending on the indicator and data availability as described below.

The assumptions cannot take into account shifts in trends that might occur because of future changes in policy, or even recent changes in policy that have not yet manifested themselves in the data because of lags in the data availability, or lags in the time from policy decisions to implementation. The projections simply state: “If past trends continue, these are the outcomes.”   This said many countries do stay on a rather consistent path of enrolment growth for multiple decades. There are notable exceptions to this rule, where countries are able to accelerate growth after major education policy changes or capitalizing on post-conflict peace dividends; or where enrolment stagnates after a period of high growth and is disrupted due to civil violence.

i. For the linear extrapolation a straight line that best fits the data is calculated by using the "least squares" method, using the excel SLOPE function.  For the logistic extrapolation, a curved line approaching 100 is calculated using the excel SLOPE and LN functions: SLOPE (LN(1/trend data)-1, (years of data)).

b. Projecting Net Enrollment Rates

Observations of long-term growth of net enrolment rates have found that the pattern generally tends to follow an s-shaped curve that approaches 100%. If there are sufficient data pointsi, the trend projections for NER are therefore based on this kind of logistic curve (see case 1 below).   If there are not enough data points, either a linear extrapolation or no projection is made (second and third cases below).  The following are the rules for NER projections:

  1. IF more than 5 years of data are available AND the growth trend is positive, apply a logistic growth function to the data.
  2. IF between 2 and 5 years of data are available OR the growth trend is negative, apply a linear growth function to the data.
  3. IF none of the above applies, no projection is made.

i. Five or more years are required for the logistic projection.  This is based on trial and error.  An alternative method would be to use the logistic projection if the standard error for the trend through the data series is below a given cut-off value.

c. Projecting Gross Enrollment Rates

GER do not have a natural maximum at any particular level, such as 100%. In fact, many countries report many years of GER levels above 100% in the range of 120% or 130%. There are even some countries where GER can exceed 200% for a short period. Such high GER levels, while they signal high access and participation, are also indicators of inefficiency caused by high rates of repetition and/or high re-entry (where a child leaves school but re-enrolls in a later year). Over time, as school systems mature, the GER decline back down to 100%, approaching NER.

While not much is known about the timing of these trends, the EPDC has devised an estimation method based on the better-known path of NER and the relation of GER to NER, NER/GER.

In countries with fully mature primary school systems, the NER/GER ratio is close to 1; in other words, almost all children in school are of the official school age, and late school entry, repetition rates, and dropout rates are all very low. In countries with high levels of particularly late entry and high repetition rates, the NER/GER ratio is below 1 (it cannot exceed 1 by definition).

By matching years where NER and GER are available, the EPDC observed  that the NER/GER trend changes over time, in most countries rising, in others declining.  In countries where NER/GER is rising, the proportion of over- and under-age pupils is declining: the school system is becoming more efficient or regular.   As NER/GER approaches 1 it becomes more difficult to make the last improvements. The NER/GER curve is also logistic; assuming this logistic function produces more reasonable behavior in the projections, and it also seems empirically more likely.

There are also some countries where the ratio of NER/GER is declining – this implies that the growth of the over-age or under-age school population is more rapid than the on-time students. While not much is known about the NER/GER ratio, a likely cause for a declining NER/GER ratio is rapid enrolment growth where many under- and over-age children enter the system. For countries with a declining NER/GER ratio, a linear or logistic projection of that trend leads to the ratio approaching zero resulting in impossibly high GER ratios and division by zero errors. Because too little is known at present about the long-term behavior of the NER/GER ratio and to avoid impossible results, a constant NER/GER ratio is maintained for the projections in the case of a downward NER/GER trend.

The assumptions for NER/GER ratio projections are:

  1. IF the NER/GER trend is positive, project using a logistic curve.
  2. IF the NER/GER trend is negative, maintain constant at most recent value.
  3. IF only one year of NER/GER ratio is available, maintain this value in the projections.
  4. IF none of the above applies, no NER/GER projections are made.

These projections of the NER/GER ratio are used to project GER:

  1. IF NER and NER/GER projections exist, then the project GER is projected NER divided by the projected ratio of NER/GER For a number of countries, no NER projections could be made because there was not enough NER data.  In these cases:
  2. IF two or more years of GER data exist AND GER is increasing, a linear projection of GER is made, with a maximum value of 130.
  3. IF two or more years of GER data exist AND GER is declining AND GER is higher than 100, a linear projection is made to GER=100; thereafter GER is held constant.
  4. IF two or more years of GER data exist AND GER is declining AND GER is lower than 100, GER is assumed constant in the future (to avoid GER declines to zero).
  5. If none of the above applies, no projection is made.

d. Gender Parity Index

The gender parity index (GPI) is based on the ratio of male/female projections for NER or GER.

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