Time-varying Markov models of school enrolment

Abstract

This study uses Markov models to develop a general quantitative approach to aid the modelling of school enrolment. The performance of the stationary 1970s to limitations Markov project of the chain model, widely used during the 1960s and school enrolment, has thrown into relief traditional model. Only a few studies early the have thoroughly tested the model over a period of time to determine whether it is really valid for predictive purposes.
The present study starts by testing the stationary Markov model using data over a twelve year period for a subsystem of the Portuguese educational system, the model being applied to the whole country and to each district into which the country is administratively divided. Several least squares estimation procedures are performed to produce estimates of the transition probabilities. As expected this model proves to be inappropriate, generating biased and non-efficient estimates for the transition probabilities.
Assuming that the non-stationarity of the transition probabilities is due to causal factors, linear behavioural relationships are included in the model. An extended Markov model with time varying transition probabilities is developed and applied to the same Portuguese educational subsystem. Seventeen explanatory variables, divided into supply-side factors and demand-side factors, are used, and stepwise regression and pooled cross-section time-series regression are performed to produce estimates of the time-varying transition probabilities principal components analysis is also applied on supply factors and demand factors and new sets of explanatory variables are used.
The results show that the patterns of the time-varying transition probability estimates describe reasonably well the patterns of the corresponding observed point estimates. This suggests that it is appropriate to include a causal structure in the model. Having established the causal relationship influencing the time-varying transition probabilities, an analysis of these relationships suggests both policy implications of this work and areas for future research.