The report outlines the development of a model to study the movement of students in, through and out of higher education in Australia. It provides a means for projecting the number of students, graduates and dropouts by age, gender and broad field of study. The model also provides estimates of the probability of a student completing a course, the average time a student takes to complete a course and the average time a student stays in the system.
Despite the collection and maintenance of a large and extensive database on higher education by the Department of Employment, Education, Training and Youth Affairs (DEETYA), little model building or analysis of the higher education system has been done in Australia. Prior to March 1996 DEETYA was the Department of Employment, Education and Training (DEET). The recent studies which have looked at the system in varying degrees of detail are Sloan et al. (1990) and Cullen and Smart (1992), both of which will be briefly reviewed later. The Finn Report (1991) includes projections of student numbers prepared with a DEET model designed largely for projecting total Equivalent Full-time Student Units (EFTSU).
The model developed in this study is an input-output model. Markov processes of probability theory provide a theoretical underpinning for the models. Input-output models, or Markov chain models are commonly used in economics, marketing, manpower planning, health and demographic accounting.
Most of the literature on the application of input-output models in education appeared in the sixties and seventies. Gani (1963) used this type of model to project enrolment for, and award of, bachelor degrees in Australian universities. Pollard (1970a; 1970b) also used a version of this model to look at the higher education in Australia. Stone (1971; 1972a) has written extensively on their use in economics, health and education planning. He also applied the model to accounting of pollution; see Stone (1972b). The input-output model was used to study the supply of secondary school teachers in Victoria by Burke (1976).
There are several reasons for modeling the higher education sector using an input-output model. The model provides a consistent method of accounting for all students found in the various stages of the higher education system at the beginning and end of a given period, and the numbers flowing into, through and out of the system during that time. It allows projections to be made based in part on the demographic changes and in part on the assumed form for the structure of the system. The assumed form can be the continuation of the present structure or the structure to be expected if certain policy changes were to be implemented. Thus, the supply of graduates coming into the labour market by age, gender and field of study can be estimated.
The model can be used to answer what if questions. For example, it allows us to investigate the effect of a change in government policy regarding the number of school leavers who are admitted into higher education. The model also provides useful statistics on such things as the average and the standard deviation of the time a student spends doing a course. It provides the same statistics for the time a student takes to complete a course. Moreover, estimates of the probability of a student completing or dropping out of a course can be derived from the analysis of an input-output model.
There appear to be few recent applications of this form of model. The reason seems to lie in the lack of data on student flows on which to base the estimates for the model's parameters. The main data on which the current study is based are discussed in Chapter 3. These data are stock data at a particular point in time and not flow data which ideally are needed to estimate an input-output model. However, as discussed in Chapter 3 the data are so detailed that it is possible with a reasonable degree of accuracy to infer the flows for the major course levels and for a number of fields of study. This work on inferring flows from stock data represents the main contribution of this study to modelling student flows through the higher education system.
A model providing information on the projections of graduates in different fields of study, and by age and gender, can be linked to a similar model for demand projections of skilled labour and a model for the projection of migrant skilled labour to identify future bottlenecks in the labour requirements of the economy. The model developed in this report will form part of the study: Medium Term Supply and Demand Projections for Major Australian Professions. This study is funded by a large ARC grant and the research for it is jointly undertaken with the Centre for Policy Studies and the Centre for Population and Urban Research, both of Monash University.
1.2 Higher Education Enrolment and Completions, 1989 to 1994
The five years between 1989 and 1994 have been a period of rapid expansion and structural change in higher education in Australia. Data published in DEET (1995a) show total student numbers grew by just under 33 percent from 1989 to 1994, with overseas student numbers increasing by over 82 percent in this period. By 1994 the latter group made up about 8 percent of all students.
Higher degree by research numbers increased by over 110 percent in the five years to 1994, while Higher degree by coursework and Other postgraduate numbers saw growth of about 133 and 24 percent, respectively. The postgraduate students made up about 20 percent of all students in 1994. In comparison undergraduates, who in 1994 comprised 80 percent of all students, have seen their numbers grow by only about 26 percent between 1989 and 1994.
The growth in student numbers has not been uniform across all fields of study during this period. It varied from about 82 percent for Law and Legal Studies to a slight decline for Education. Apart from Veterinary Science, numbers in all other fields of study increased by between 30 and 50 percent.
Undergraduate completions increased by just under 42 percent in the years 1989 to 1993. Research degree completions rose by over 50 percent and Coursework higher degree completions increased by over 180 percent over this period.
Further details of the changes in enrolment and completions between 1989 and 1994 are given in Appendix B. The model developed in this study will help in describing the type of changes recently experienced in more detail, and particularly the likely changes in the next few years. The next section briefly reviews three studies that considered projections of student numbers in higher education in Australia recently.
1.3 A Brief Review of Previous Studies
DEET Model
The DEET model (unpublished) used in the early 1990s was primarily designed for projecting total EFTSU for budget purposes. It assumed an increase in school leaver entry from about 24 percent of the age cohort in 1990 to nearly 30 percent by the year 2001. This was based on the assumption that school retention rates would reach 80 percent, and that nearly 40 percent of those students undertaking the final year of secondary schools would transfer to higher education.
In this model constant age-entry rates were assumed for non-school leaver entrants, who form the majority of all entrants. They made up about 55 percent of all students commencing undergraduate courses in 1994. Total student numbers are estimated by a pipeline assumption, which is:
This implies that on average a student remains in the system for 2.734 years.
DEET made projections of the student intake and the total number of students in the system for each state and territory. They did not make projections of the number of students dropping out or those completing courses. They did not make projections by field of study, age or gender.
Sloan et al. (1990)
In their study of the academic labour market, Sloan et al. (1990) developed a model for projecting national student undergraduate and postgraduate numbers by field of study. Their model divides the commencing undergraduate student intake into three categories to be projected separately:
The school leavers intake was estimated as a proportion of the previous year's Year 12 student population. Various scenarios were considered for this transfer rate, as well as that for the retention rate from the first year of secondary school to Year 12. The mature age intake assumed a constant age-entry. This means that the mature age student intake is a constant proportion of the population aged between 19 and 39 years. High and a low growth rate scenarios were envisaged for the overseas student intake.
Sloan et al (1990) projected the numbers dropping out of courses by applying an aggregate exit rate in each field of study. In their model the exit rate is the total number of students who exit the system (before completion) in a year expressed as a percentage of the total stock of undergraduate students in that year. They also use a completion rate which is the proportion of the student stock completing their course at the end of a year. Note that this rate is applied to the total stock of students and not to students in the final year of their course. These exit and completion rates will be affected by changes in the composition of the stock of students. For example a sharp increase in the number of first year students, who have a relatively high dropout rate, will tend to push up the measured exit rate and reduce the completion rate. They estimated the average undergraduate exit rate of 14.7 percent and a completion rate of 19.3 percent.
The commencing postgraduate student numbers were also assumed to be in three categories:
For all postgraduate courses an average exit rate of 13.8 percent and a completion rate of 32.8 percent was estimated. The corresponding rates for just higher degrees were 10.1 and 19.3 percent.
Sloan et al. (1990) used the student number projections to derive Equivalent Full-time Student Unit (EFTSU) projections by field of study. From this projections were made of EFTSU by Academic Organisation Unit (AOU) which were then used to estimate the supply and demand of academic staff in universities. Their study does not consider projections by age or gender.
Cullen and Smart (1992)
Cullen and Smart (1992) set access targets for school leavers, the under 30 age group, the over 30 age group and those entering with credits from other post-secondary awards. They linked research degree intakes to undergraduate completions. Intakes to other postgraduate courses were linked to the stock of graduates in the community. The analysis was entirely done in terms of EFTSUs.
They made separate assumptions to estimate the average time a student spends doing a course and the average completion rate for it. Their completion rate is the proportion of a cohort who commences a course that eventually completes it. This is similar to the probability of completion which we consider later in this study. Note that this is not the same as the definition used by Sloan et al. whose completion rate was the number of students completing a course in say 1994 expressed as a percentage of all students enrolled in that course in 1994. On the basis of these estimates they then estimated the cost per completion of a course. According to Cullen and Smart (1992), the average time spent doing a degree program by an undergraduate student who commenced as a school-leaver was 2.72 years. The average time a student spent doing a postgraduate research degree was 3.58 years and that for doing Master's coursework the figure was 2.16 years. The completion rate for each of the three level of courses was estimated to be 66 percent. Cullen and Smart (1992) do not report the methodology used to obtain the results.
In Chapter 2 we describe in matrix notation an input-output model for the higher education sector and a model for projecting student intake into the system. This chapter also contains a discussion on the data requirements for estimating these models. Chapter3 contains the initial analysis of enrolment and completions data used for estimating the input-output models. The age profiles and the gender balance of students in various fields of study and levels of course are considered. Furthermore, the distribution of time in the system and time to completion are also analysed by field of study and level of course. At the end of this chapter the school enrolment data and the population projections by age and sex are discussed.
The results from fitting and estimating the input-output models are presented and discussed in Chapter 4. Separate models are fitted for all persons, males and females. Undergraduate and postgraduate students are considered separately. The analysis for undergraduates provides estimates for total students as well as estimates disaggregated by broad field of study. The postgraduate data is disaggregated at level of course: Research degree, Master's by Coursework and Other Postgraduate courses. At the end of this chapter the estimated models are evaluated for stability over time by considering their prediction accuracy retrospectively. Finally, in Chapter 5 we draw some conclusions and discuss directions for future work in this area.