# International Futures Help System

## Education Equations

### Overview

The IFs education model represent two types of educational stocks, stocks of pupils and stocks of adults with a certain level of educational attainment . These stocks are initialized with historical data. The simulation model then recalculates the stock each year from its level the previous year and the net annual change resulting from inflows and outflows.

The core dynamics of the model is in these flow rates . These flow rates are expressed as a percentage of age-appropriate population and thus have a theoretical range of zero to one hundred percent. Growing systems with a saturation point usually follow a sigmoid (S-shaped) trajectory with low growth rates at the two ends as the system begins to expand and as it approaches saturation. Maximum growth in such a system occurs at an inflection point, usually at the middle of the range or slightly above it, at which growth rate reverses direction. Some researchers (Clemens 2004; Wils and O’Connor 2003) have identified sigmoid trends in educational expansion by analyzing enrollment rates at elementary and secondary level. The IFs education model is not exactly a trend extrapolation; it is rather a forecast based on fundamental drivers, for example, income level. Educational rates in our model are driven by income level, a systemic shift algorithm and a budget impact resulting from the availability of public fund. However, there are growth rate parameters for most of the flows that allow model user to simulate desired growth that follows a sigmoid-trajectory. Another area that makes use of a sigmoid growth rate algorithm is the boost in flow rates as a result of budget surplus.

Intake (or transition), survival, enrollment and completion are some of the rates that IFs model forecast. Rate forecasts cover elementary , lower secondary, upper secondary and tertiary levels of education with separate equations for boys and girls for each of the rate variables. All of these rates are required to calculate pupil stocks while completion rate and dropout rate (reciprocal of survival rate) are used to determine educational attainment of adults.

On the financial side of education, IFs forecast cost per student for each level. These per student costs are multiplied with enrollments to calculate fund demand. Budget allocation calculated in IFs socio-political module is sent back to education model to calculate final enrollments and cost per student as a result of fund shortage or surplus.

The population module provides cohort population to the education model. The economic model provides per capita income and the socio-political model provides budget allocation. Educational attainment of adults calculated by the education module affects fertility and mortality in the population and health modules, affects productivity in the economic module and affects other socio-political outcomes like governance and democracy levels .

For help understanding the equations see Notation.