Master’s Thesis
The determinants of university choice in
Australia: Does cost matter?
Andrew O’Keefe
Student number: 10826297
Date of final version: August 12, 2015 Master’s programme: Econometrics
Specialisation: Econometrics
Supervisor: Dr. J.C.M. van Ophem Second reader: Dr. M.J.G. Bun
i Statement of Originality
This document is written by Andrew O’Keefe who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Contents
1 Introduction 1 2 Literature Review 4 3 The Model 12 3.1 Model Setup . . . 12 3.2 Estimation . . . 14 4 Data 18 5 Results 25 6 Conclusion 36 A Acknowledgements 38 Bibliography 39 iiChapter 1
Introduction
Current proposals to reform tertiary education funding in Australia advocate the removal of price regulation in the sector. Debate over the merits and consequences of removing price caps is complex but inarguably exposes university students to large increases in fees (Davis, 2015). The Australian reform proposals follow analogous actions by the governments of the Netherlands, the United Kingdom and the United States to change to the rate of public subsidies afforded to university students (Johnstone, 2004; Shin and Milton, 2006; UK, 2013; NUFFIC, 2013). An increase in the effective price of university faced by students can be expected to moderate demand for places. But it also has the potential to affect students from different socio-economic backgrounds in different ways. In a public university system built upon equal access and merit-based entry, we investigate whether the pursuit of a more market-driven pricing policy would disproportionately affect individuals from disadvantaged backgrounds.
The price students face for a university degree is entwined in the broader issue of how universities are funded. The norm in advanced economies is for governments to subsidise tertiary education owing to the positive externalities associated with its completion by members of society. The degree of subsidisation varies by country, but in Australia, over AUD 14 billion of the AUD 25 billion in tertiary education sector revenues came from public subsidies in 2012 (Department of Education and Training, 2013). In this era of general budgetary consolidation, continued growth in student demand for university places has created tension between the requirements for funding quality education services and the willingness of governments to fund them. Without changes to the funding mechanism, the expected growth in student demand over the five years from 2013/14 is projected to cost the Australian Government an additional AUD 7.6 billion (Department of Education, 2014). As of mid-2015, the Australian Government had signalled its unwillingness to meet these funding requirements through general taxation revenue. It follows that some combination of average increases in student tuition and decreases in expenditure per student – with consequent impact on educational quality – is a necessary policy response to bridge the university funding gap 1. Both university administrators and
1
University funding pressures have been offset to some degree by the influx of international students now attending Australian universities. A key regulatory feature that has seen the number of international students
CHAPTER 1. INTRODUCTION 2 government are agitating for an increase to student tuition as the preferred policy outcome (Davis, 2015).
Public policy changes that cause an increase in the financial imposition on students are invariably unpopular. For obvious reasons students oppose the changes. More generally, there exists broad public support for educational subsidies in Australia and community understanding of the spillover benefits of a more educated society is widespread (Davis, 2015). Despite the unpopularity, student subsidies have become the subject of fiscal savings measures not only in Australia, but in many other OECD countries over the past decade – most probably because tax rises to support higher education are even more unpopular and in some cases are regressive (Chapman et al., 2003). The UK government, for instance, trebled the tuition cap for public universities from GBP 3,290 to GBP 9,000 whilst decreasing public subsidies to the sector in 2012 (UK, 2013). Similarly, the Netherlands government introduced measures in 2014 that allowed some universities to experiment with increased tuition for honours courses. Eligible course may cost up to double the statutory rate of EUR 1,960 in 2015/16 that otherwise applies to students. Moreover, as of September 2015, Dutch students will no longer receive a basic grant to cover tuition costs and living expenses but will be eligible for a loan to cover these amounts in its stead (DUO, 2015). Such changes shift the balance of university funding from the taxpayer to the student.
A persistent challenge faced by governments when advocating for changes to the public-private funding balance is the paucity of evidence on the distributional consequences of shifts in funding policies. People from low socio-economic backgrounds constitute just 15 per cent of all university enrolments in Australia and are under-represented in the most prestigious universities, the courses with the most competitive entry requirements, and in postgraduate courses (James et al., 2008). Policies with the potential to exacerbate these differences are typically met with public opposition owing to popular belief that access to an university education should not be determined by wealth, ethnicity, or geographical location.
Equality of student access to education has long been a pillar of tertiary education policy in Australia. From 1973 to 1986 tertiary education in Australia was free for all students. The impetus for the policy at the time was that university should be accessible to all (Wran, 1988). However, over its duration, free tertiary education primarily saw relatively advantaged individuals accruing large private benefits at the expense of all taxpayers and so ultimately proved to be regressive policy. As such, it was reformed in the late 1980s when the Hawke government introduced universal fees for education and a system of income-contingent tuition loans called the Higher Education Contribution Scheme (HECS) (Chapman and Salvage, 1997).
grow by over 250 per cent in the decade to 2008 (Department of Education and Training, 2013) is that the fees universities charge to international students are uncapped. In 2014, one in five students in Australian universities was classed as international. The fees charged to international university students comprised 16.4 per cent of all university revenue in 2014, noting that there is not a direct correspondence between the proportion of students and contribution to university revenues owing to things like specific-purpose grants (Department of Education and Training, 2013).
CHAPTER 1. INTRODUCTION 3 The introduction of fees sought to rebalance the funding system so that university graduates materially contributed to the cost of their degrees whilst still recognising the broader benefits of a more educated society. The associated income-contingent tuition loans were designed so that individuals from all socio-economic backgrounds would have access to tertiary education as the repayment of the tuition loan was solely dependent on future earnings. The HECS funding model was subsequently found to have had a neutral impact on the proportion of students from low socio-economic families attending university (Chapman et al., 2003; Andrews, 1999). Australia was the first country to introduce a system of income-contingent tuition loans which has now been adopted by New Zealand, Chile, South Africa, the UK, and Thailand (Chapman and Ryan, 2005).
In the 25 years since the introduction of HECS, the tertiary education sector has become more complex. The rise of education as an export industry, increasing diversity among service providers, and further changes to public policy settings have all contributed to changing enrol-ment and funding patterns. The principle of accessibility, though, remains as important today as when the Whitlam government pronounced education would be free for all in 1973. It is paradoxical then that fundamental questions as to how different groups in society are affected by tuition increases remain poorly understood. In this paper, we contribute to the understand-ing of student-price responsiveness in Australia by developunderstand-ing a model to isolate the effect of tertiary education tuition on the probability of student enrolments.
Since 1997, the Australian tertiary education sector has had an atypical method for speci-fying tuition levels relative to comparable international regimes. The novel policy environment allows for identification of student price-responsiveness by income level and without the con-founding effects of cross-price elasticities. It is characterised by tuition levels that are common across universities – the norm in public university systems – but that vary across broad fields of study. Real tuition rates vary over time owing to regulatory changes including the intermittent reclassification of fields of study within the pricing strata. Using these data, we develop a nested logit model to identify the effect of tuition on the probability of enrolment at university.
We find that conditional on completing secondary school, the probability of individuals from low-income backgrounds enrolling in university under the prevailing regulatory arrangements is, in fact, less responsive to tuition fees than for individuals from middle and high income families, though the sensitivity in all three cases is small in absolute value. Enrolment at university is much more sensitive to the financial return to graduating from a course of study.
The remainder of this thesis is organized as follows. Chapter 2 provides an overview of the Australian tertiary education sector and reviews the literature on the price responsiveness of students to tuition fees. Chapter 3 develops the models for estimating the price-responsiveness of individuals to tertiary education tuition and the influence of university quality and prestige on student choices, and describes the estimation methodology employed for each. Chapter 4 summarises the unique data set constructed for the analyses and Chapter 5 presents the estimation results. Chapter 6 concludes.
Chapter 2
Literature Review
Owing to the unfamiliarity of most readers with the Australian policy context, we briefly sum-marise the tertiary education sector and the mechanism for determining student tuition contri-butions prior to addressing the state of the literature on student-price responsiveness and access.
A snapshot of tertiary education tuition policy in Australia
The tertiary education system in Australia consists of universities and other non-university higher education providers. There are 37 public and 3 private universities registered in Australia in 2015 and some 130 other higher education providers (Commonwealth of Australia, 2003) 1. The university sector has seen strong growth in student numbers over the past two decades, largely driven by domestic students enrolled in bachelor degree programmes. Indeed, the rate of university enrolments for individuals between 17 and 29 has more than doubled since 1982 (Norton, 2014). The influx in student numbers saw sector revenues rise to over $25 billion in 2012 (Department of Education and Training, 2013) making it an important contributor to national economy in addition to the vital educational services it provides. As illustrated in Figure 2.1, domestic students overwhelmingly study in courses that are subsidised by the federal government. The focus of this thesis is the public policies that drive the subsidised, domestic enrolments in the university sector.
The majority of domestic university students are admitted in the years immediately follow-ing the completion of secondary school. In 2012, 79 per cent of students commencfollow-ing bachelor degrees were aged 24 or under (Department of Education and Training, 2015a). While institu-tions may use a range of selection methods, depending on the course and on the educational background of the applicants, the first round of admission offers are made largely on the basis of Australian Tertiary Admission Rank (ATAR) scores. ATAR scores are awarded to students who complete secondary school and are essentially a weighted ranking of academic performance
1
Other higher education providers are colleges, institutes, and schools that are accredited by the Australian Tertiary Education Quality and Standards Agency to award some post-secondary school qualifications includ-ing various diplomas and certificates. Private universities have historically not received fundinclud-ing grants from the Federal government and so operate without the conditions attached to the public funding grants of public universities
CHAPTER 2. LITERATURE REVIEW 5 0 200 400 600 800 1,000 1,200 1,400 Num er o f stud en ts ( th o usan d s) Total students Doctorate Masters Bachelor 0 200 400 600 800 1,000 1,200 1,400 Num er o f stud en ts ( th o usan d s) Total students Full Fee Subsidized Domestic Foreign
Figure 2.1: Number of students enrolled at Australian universities, by broad level of study (i.e. Bachelor degree, Master Degree or PhD) (LHS), and by classification as domestic or international for public subsidisation purposes (RHS): 2003 to 2012
among students who graduated that year. For the remaining 21 per cent of mature age stu-dents, selection is mainly based on educational qualifications and experience (Department of Education and Training, 2015a).
Domestic students are typically subsidised by the federal government in what are known as Commonwealth-supported places. Commonwealth-supported places attract a significant public subsidy but also require the student to contribute an amount that depends on the units of study that they undertake 2. The student may pay their contribution amount directly to the university or may borrow the entire sum from the Commonwealth government who then pays the university on their behalf – an option taken by virtually all eligible students. Tuition loans of this type are indexed to inflation but do not attract a real interest charge and are only required to be repaid upon the student earning a moderate income – equal to AUD 53,345 in 2014/15 3 (Department of Education and Training, 2015b). Since tuition loans have no fixed repayment period and do not attract a real interest rate, the time taken for students take to repay their tuition loans is associated with an implicit subsidy proportionate to the difference between the indexation rate and the relevant market interest rate.
The breakdown of tuition fees between students and the government by main field of study is given in Table 2.1. There are four student contribution bands and eight government subsidy bands across the broad fields of study. Whilst loosely based on the costs of offering the units of study and the distribution of public and private benefits from graduating, in reality, the cost structure has been heavily influenced by historical practice and political compromises (Chapman and Ryan, 2005; Norton, 2014).
2
Students are often eligible to take subjects from outside of their primary field of study, but for most students, the units of study they undertake will attract the same fee rate applicable to their main field of study
CHAPTER 2. LITERATURE REVIEW 6
Subject areas Annual student
contribution Annual public subsidy Course length Total public subsidy Total student contribution Total course cost Law 10,266 1,961 4 7,844 41,064 48,908
Accounting, administration, economics,
and commerce 10,266 1,961 3 5,883 30,798 36,681
Humanities 6,152 5,447 3 16,341 18,456 34,797
Mathematics, statistics, computing,
and other health 8,768 9,637 3 28,911 26,304 55,215
Architecture 8,768 9,637 5 48,185 43,840 92,025
Behavioural science and social studies 6,152 9,637 3 28,911 18,456 47,367
Education 6,152 10,026 3 30,078 18,456 48,534
Clinical psychology, foreign languages,
and visual and performing arts 6,152 11,852 3 35,556 18,456 54,012
Allied health 8,768 11,852 4 47,408 35,072 82,480
Nursing 6,152 13,232 3 39,696 18,456 58,152
Science 8,768 16,850 3 50,550 26,304 76,854
Engineering and surveying 8,768 16,850 4 67,400 35,072 102,472
Dentistry, medicine, and
veterinary science 10,266 21,385 5 106,925 51,330 158,255
Agriculture 8,768 21,385 3 64,155 26,304 90,459
Average 8,155 11,551 4 41,275 29,169 70,444
Table 2.1: University course costs by student contribution and public subsidy rates.
Notes: Cost figures are from the 2015 academic year in Australian dollars (AUD). All costs are presented as full year amounts, given a student undertakes all units of study from the nominated main field of study.
In 2014, the Commonwealth government budget announced a substantial package of re-forms to the university sector. Following the removal of restrictions on the number of university places in 2012, the government announced its intention to remove price-regulation in the sector by the abolishing the legislated caps on student contribution amounts for university courses. Whilst the Minister for Education cited numerous reasons for the changes, the central motives for the reform appeared to be the wish to facilitate greater competition in the increasingly international sector, and to provide universities with more financial security without a com-mensurate increase on the public purse (Department of Education and Training, 2014). The reforms would have maintained the same government income-contingent loan system as previ-ously existed. Notwithstanding this, the proposals courted a high degree of controversy amid forecasts of large increases in university fees and the associated financial burden that university graduates would be subject to. At the time of writing, the reforms are yet to be passed by the Parliament of Australia (Hurst, 2014).
The human capital model of educational attainment
Policy debates around university funding often highlight the effect of increases in tuition levels on the rate of university attendance. The standard economic framework for analysing these questions derives from the seminal work of Becker (1962, 1964) on human capital theory. The model posits that individuals rationally approach the question of whether or not to attend uni-versity by evaluating the costs and benefits to alternative courses of action. The substantive
CHAPTER 2. LITERATURE REVIEW 7 costs to an individual of attending tertiary education are the tuition fees and the indirect costs of foregone earnings while studying. The benefit is the wage premium and consequent increase in expected lifetime earnings from having completed a degree earned upon graduation, relative to the most profitable alternative choice in the labour market. Subsequent authors have ex-panded the work to investigate non-financial factors including the improved health outcomes from completing further education, the consumption-utility of tertiary education and the differ-ent cognitive costs among individuals of attending university (Long, 2007). In this way, tertiary education choices may be characterised as an investment decision with its costs and benefits captured by the internal rate of return to education (Borland, 2002).
The human capital accumulation model predicts that if tuition fees increase then the ag-gregate demand for tertiary education will fall as the marginal and infra-marginal individuals’ optimal choices change from attending to not attending university (Shin and Milton, 2008). The same dynamics hold for changes to the level of public subsidisation of university courses. If government decreases tuition subsidies – including implicit subsidies like loan repayment thresh-olds or indexation rates – then the net-tuition level faced by an individual increases causing knock-on reductions to the return to, and demand for, university places (Chapman et al., 2003). The model further predicts increases in aggregate demand for university places with increases in the utility of graduating. When graduate wage premiums go up, for example, the internal rate of return to education likewise increases and individuals’ optimal choices may change.
Returns to tertiary education
Studies of wages and salaries invariably find that university graduates earn more on average than non-graduates. The university graduate earnings-gap is partly explained by lower rates of unemployment among university graduates and partly by the fact that the graduate jobs are, on average, higher paying. The notion of a financial return to graduating university is fundamental to the human capital model. The return to university education may be captured by its Internal Rate of Return (IRR). The IRR is defined as that interest rate which equates the present value of the future flows of costs and benefits from enrolling in a course, as described in the previous section (Daly et al., 2015).
Simply attending university, of course, does not cause above average earnings. Individuals self-select into university and the likelihood of enrolment increases with the expected return to education (Willis and Rosen, 1978). Indeed, Venti and Wise (1983) showed that self-selection was the dominant factor in university enrolments. Self-selection induces ability bias when es-timating returns to education. Individuals that are admitted university tend to have strong levels of prior academic achievement, which is correlated with character traits including innate intelligence, work ethic and time management – all characteristics that are rewarded by employ-ers irrespective of whether or not an individual has graduated univemploy-ersity. Ignoring selectivity bias results in an over-estimation of the causal return to tertiary education (Card, 1999). Card (2000) provides an exposition of econometric solutions available to control for ability bias.
CHAPTER 2. LITERATURE REVIEW 8 Policies that affect equilibrium rates of return may change individual propensities to enrol in a course of study. It follows that the IRR may be used to estimate the causal impact of changes in tertiary education policy on university applications and enrolment. In the Australian con-text, Wei et al. (2010) calculate the IRR to university education at five yearly intervals from 1986 to 2006 using census data. They found that the IRR for men increased from 13.1 per cent to 19.6 per cent over the period to 2001 but then fell to 15.3 per cent in 2006. Over the same period, Wei et al. report that the IRR for women fluctuated within the 18.0 to 17.3 per cent range. Chapman and Ryan (2002) structured a similar temporal analysis around two major policy shifts in 1989 and 1996 4. Focussing on the policy consequences for the IRR to tertiary
education, the authors found little impact on magnitude of graduates’ average private benefits, which remained very high after the changes at around 14 per cent. Borland (2002) repeated the IRR exercise with an alternative data source and found evidence consistent with Chapman and Ryan (2002) of a reduction in university graduates rate of return of some 1.5 percentage points. Daly et al. (2015) extended the approach using more comprehensive data to estimate the financial returns to graduating from different academic majors. Their results demonstrated that while returns to education are on average positive and significant, there is great disparity between majors and by gender. The estimated rate of return to Medicine and Dentistry, for example, is predictably high, but the rate of return to some majors is quite low and in the case of performing arts, negative. The preceding studies raise important questions around just how many, and what are the average characteristics, of potential university students are at the margin of these average returns.
Tuition-price-responsiveness and university enrolment
A synopsis of vast literature on tuition-price-responsiveness is that students do not exhibit a great deal of sensitivity to tuition increases but that individuals from low-income families tend to be the most responsive (Neill, 2009). Where average returns to education are in excess of 14 per cent, this is perhaps not surprising for modest changes in tuition. Nonetheless, consistent with theory, applications to university should decrease when tuition increases and the magnitude of the price-response has been extensively researched – as has the characteristics of those individuals at the margin. Student sensitivity to university-education costs may be quantified by estimating the tuition elasticity of demand, though, by convention, is usually reported as a percentage change in enrolments per 1,000 dollar change in tuition.
Differentiation among education providers, particularly in the US college market, has led to numerous studies estimating the own and cross-price elasticities of demand. An early meta-analysis by Leslie and Brinkman (1987) using around 30 studies of the US college market from the 1970s and 1980s, found that a USD 1,000 (2001 dollars) increase in tuition was met with around a 4 percentage point decrease in the enrolment rate. Subsequent studies by Kane (1995),
4
The two policy changes were the introduction of HECS in 1989 and the package of policy changes in 1997 that included a 40 per cent increase to student HECS fees and a reduction in the income-contingent HECS loan repayment threshold
CHAPTER 2. LITERATURE REVIEW 9 Heller (1997) and Cameron and Heckman (2001) emphasise subtly different explanatory factors in their logistic models but find price responsiveness of broadly similar magnitudes of between 3 and 6 percentage points per USD 1,000 change – all quite inelastic responses. Long (2004) analysed whether price-responsiveness has changed over time using a conditional logit approach and found the role of price became significantly less important. In 1972, a USD 1,000 increase in tuition reduced college enrolment rates by 15 per cent whereas by 1992 price had ceased to play a significant role in explaining enrolment patterns.
Confounding the previous discussion is the stylised fact that as real tuition levels have in-creased in the preceding decades, so too have university enrolment rates. The notional anomaly is left unexplained in many studies as a consequence of using a partial equilibrium framework, or omitted variables in reduced-form model formulations (Shin and Milton, 2006). The human capital model calls for a general equilibrium framework that captures the complete rate of re-turn to education – not only its cost. However, estimates of price-responsiveness have tended to focus on tuition cost information, and competitors tuition costs, resulting in biased estimates. Shin and Milton (2006) includes the wage premium in a reduced form specification and find the dominant factors affecting enrolment patterns are the relative tuition levels among colleges and the wage premium to academic majors rather than absolute increases in tuition levels over the study period. Fu (2014) develops a comprehensive general equilibrium framework and estimates that a USD 1,000 (2003 dollars) increase would be associated with 1 per cent decrease in college enrolments, which is materially lower than previous studies. Though extenuating circumstances explain part of the difference reported in Fu, it nonetheless highlights the importance of em-ploying a holistic model.
Access to tertiary education
A question that naturally follows inquiries into price elasticity is how the demographic com-position of the student body changes in response to increasing tuition levels. It is possible that increases in tuition may affect the socially or economically disadvantaged in ways that are different to other groups in society. Equality in access to higher education is an ongoing concern for policy makers owing to the under-representation in universities of individuals from low-income backgrounds, minority groups and otherwise disadvantaged members or regions in society. In Australia, individuals from the bottom income quartile make up just fifteen per cent of all university enrolments and are about one-third as likely to attend university as someone from the top income quartile (James et al., 2008). Exacerbation of this situation with policy changes is important owing to its effects on social mobility, but also for broader social issues encompassed by national and community development.
Studying tuition-related questions of access to tertiary education is quite nuanced as the factors that affect the propensity of an individual to graduate high-school, or to excel in academic studies may be the same as those that determine university enrolment. If there are long-standing reasons that explain student outcomes at secondary school, and these are correlated
CHAPTER 2. LITERATURE REVIEW 10 with income, then it is important not to erroneously attribute differences in enrolment rates by income level to course costs or contemporaneous credit constraints. Studying the influence of tuition conditional on university attendance, for example, will identify the price-elasticities at very a different margin to when individuals who chose not to study are included in an analysis. Access to tertiary education has been studied extensively in the US but with a focus on the relative importance on family background versus net tuition5. At the crux of the debate is whether or not individuals are able to finance the net, upfront costs of university through the credit market or there exist other factors that are inhibiting university attendance. Using longitudinal data and a form of conditional logistic model, Cameron and Heckman (2001) argue that differences in enrolment rates are explained by deeply embedded personal characteristics including family income and stability rather than short-term credit constraints. Black and Sufi (2002) investigate the trends in enrolment patterns over time with a multinomial logistic analysis and similarly conclude that the socio-economic status of individuals is much more important factor when predicting university enrolment than race, tuition costs and local labour market conditions. As detailed in earlier sections, the Australian system is markedly different as all domestic students are eligible for financial aid in the form of income-contingent loans. Moreover, low-income individuals are eligible for a stipend to cover living expenses so local credit constraints likely to play a smaller role than in the US-based studies. This intuition was tested by Cardak (2006) who found using a probit estimation that whilst students from disadvantaged backgrounds are under-represented at university, the reasons for the disparity may be found early in individuals’ lives.
Student access studies in Australia have tended to focus on the introduction of the HECS system. Moving from a free to tuition-based system could have affected individuals from low socio-economic status (SES) backgrounds in ways that are different other groups in society. Andrews (1999) investigated whether individuals from low-SES backgrounds were deterred from entering university by the introduction of HECS using aggregated wealth measures and looking at the trend in the proportion of commencing students from low-SES backgrounds over the decade to 1998. He found no evidence of tuition acting as a deterrent for low-SES individuals. Long et al. (1999) and Chapman and Salvage (1997) used four cohorts of 19 year-olds from the Youth in Transition longitudinal survey to analyse the responsiveness of low-SES individuals to HECS and found that wealth played a much more important role between cohorts relative to the tuition increase. Chapman and Ryan (2003) found that the main demographic shift in the student body following the introduction of HECS was a modest rise in the proportion of students from middle-income families.
We contribute to the literature on student access and student-price-responsiveness with a novel analysis of the joint choices of whether an individual attends university and their main field of study choice, conditional on attendance. Previous work has focussed on the use of a binary decision processes whereby individuals choice of whether or not to attend university. Our model
CHAPTER 2. LITERATURE REVIEW 11 departs from this approach by recognising that the choice to attend university is not strictly binary, but there are a many courses available to students and that, in Australia at least, they have different prices. We therefore employ a nested logit procedure to simultaneously model individuals’ decisions. The nested logit model models offers an improvement on the competing alternatives as they fail to properly account for the dependencies in the sequential decision-making process that students necessarily employ. In this respect, a key feature of our model is that the nesting structure allows for correlation among the errors of similar university courses.
Chapter 3
The Model
3.1
Model Setup
We assume that individual l has M courses of study to select from, including the option not to attend tertiary education at all. Recall that all universities in this study must charge the same tuition, so university-specific factors are not important in terms of price-consideration. Each course of study is associated with a vector of characteristics ylm, since it may vary over both
individuals and courses of study. The vector may include the net present value of its tuition costs, the average net present value to an individual from graduating a course of study, net of tuition, and the typical length of the degree. Course-of-study-specific variables may vary depending on the year an individual commences university. In our specification, we allocate the not-attend option zero tuition and zero net present value from graduating. By separating the tuition cost from the net present value, we are able to estimate its direct effect on the human capital accumulation decisions. Given their personal characteristics, individuals may trade-off the higher cost of some university courses against the returns from alternative, lower cost courses, or not studying at all. Using the average net present value (net of tuition costs) controls for the pull-factor of higher expected lifetime earnings from graduating (Shin and Milton, 2008). We construct a second vector, xl, of individual-specific characteristics. This includes typical
explanatory variables such as sex, age, household income, household wealth, and location of residence. It also includes measures of individual ability, secondary-school performance, par-ents highest level of education, and parpar-ents occupation. Following Cardak (2006), we capture the influence of the family stability on tertiary education choices with measures of parents em-ployment status, whether the individual comes from a broken home and the number of siblings. Given an individual’s characteristics, they may evaluate the lifetime value-added – as per the Becker model of human capital – from the M possible alternatives that include the M-1 courses of study, or not studying at all.
The utility of individual l from selecting alternative m, is given by Ulm. Utility is a function
of individual-specific vector xl and the course-specific vector ylm. In our model, utility may also
be dependent on interactions between individual and course-specific variables. The choice set
CHAPTER 3. THE MODEL 13 available to an individual is notionally unconstrained – since any individual is able to apply to any course of study – but the likelihood of admittance is strongly dependent on prior academic performance. All secondary-school graduates will not have achieved the ATAR score that per-mits them direct entry to study highly selective courses such as Bachelors of Medicine or Law, for example. We approximate this feature of university admittance by taking the difference between the average ATAR required for direct admittance to a course in the first round of offers and the approximated ATAR score of an individual. We assume that this variable takes the value zero for the not-attend option. We further allow for random elements in utility, reflecting innate differences in individual preferences, denoted lm, to enter linearly as per Equation 3.1.
Representing the non-random part of utility with ηlm, we get Equation 3.2.
Ulm= f (xl, ylm) + lm (3.1)
Ulm= ηlm+ lm (3.2)
If we now assume that the deterministic part of utility, ηlm is a linear combination of
individual and course-specific elements, we get Equation 3.3. Individual-specific variables are stored in a vector xlfor each decision-maker, l = 1, ..., L. A parameter vector γmfor each course
of study m = 1, ..., M captures the individual-specific effects on each of the possible choices. For individual-specific variables, only utility differences matter, so the estimates are relative to a base case which is normalised to allow for identification in the estimation procedure. As such, the parameter estimates represent the effect on the individual utility of the M alternatives, relative to the base case, of the decision-maker’s individual characteristics. Course-of-study-specific variables are collected in a vector ylm for each individual l=1, ..., L and for each for
each course of study m = 1, ..., M. We estimate the coefficients β to identify the effect of tuition costs on the probability of university enrolment. Lastly, alternative-specific constants αm for
all bar one of the alternatives enter the model (Heiss, 2002).
Ulm = αm+ y0lmβ + x0lγm+ lm (3.3)
We assume that individuals evaluate each possible alternative in the choice set. That is, they determine expected lifetime utility for each course of study, and from not attending university. We further assume that individuals are rational and therefore select the option that yields the highest expected lifetime utility. In other words, the probability that an individual l selects course-of-study m is equal to the probability of alternative m being the largest of all Ul1, ..., UlM.
Denoting the choice of individual l by yl∈ {1, ..., M } gives:
Plm= P r(yl= m) (3.4)
= P r(Ulm> Ulz∀m 6= z) (3.5)
CHAPTER 3. THE MODEL 14
3.2
Estimation
We assume that the choice faced by an individual comprises two-parts. Individuals first choose if they will attend university, then conditional on attendance, choose in which course to enrol. We populate this decision-making structure with a nested logit model. The modelling approach is natural as the factors that influence the decision to attend university are likely to be different to those that explain the course of study ultimately chosen. Moreover, it allows us to use both individual-specific and alternative-specific explanatory variables. The latter is particularly important as the tuition varies across course of study and is imperative for our identification strategy.
Modelling unordered choices in this way offers clear methodological advantages over the competing alternatives of multinomial logit models and conditional logit models that are fre-quently employed to model tertiary education choices. The primary limitation of these models is the necessity to assume the Independence of Irrelevant Alternatives (IIA). The IIA property forces the odds ratio between two choices to be independent of the other alternatives. That is, the choice between any pair of available alternatives reduces to a binary choice model with i.i.d. Type 1 extreme-value distributed errors (Cameron and Trivedi, 2005). The IIA assumption is most important for the choice of course of study, where the conditional logit and multinomial logit models assume that unobserved shocks that affect an individual’s preference for one course has no effect on their preferences for the remaining courses – clearly a restrictive assumption. Given attendance at university, the high degree of substitutability among courses of study – as evidenced by the submitted preference orders of university applicants – suggests that correlation among the errors is highly likely. By way of example, suppose that the number of medicine places were exogenously doubled by the government. Relative demand for other health and science courses would fall as the more preferred course becomes more attainable to applicants with the increased supply. Assuming that IIA holds in this case would cause bias in the model estimates (Heiss, 2002).
Some authors, including Long (2004), have argued that the use of nested-logit models is inappropriate for modelling tertiary education choice. Whilst Long acknowledges that the choice is best approximated by a simultaneously-estimated two-step model, she opts for an alternative specification since the no-attend option is unable to be satisfactorily described in the US context, where the study takes place. Assuming the no-attend alternative has zero price, for example, has the potential to bias parameter estimates relating to the effect of course prices. Long therefore uses a logit model for the choice to attend university, followed by an independent, conditional-logit model for the choice of course, given enrolment at university. Two features of our model, however, attenuate this issue. First, we employ both tuition costs and course-specific net present value from graduation. Including both variables better captures the general effect of the return to education as the net present value of the no-attend option is assumed to be zero. Second, we only use course-specific variables to identify the effect of price on enrolment, so the more problematic university-specific variables – such as distance of the
CHAPTER 3. THE MODEL 15 University Choice Not attend Not
attend Not attend Attend
university
Course Group 1
Natural and Physical Sciences
Agriculture, Environmental and Related Studies Course
Group 2
Information Technology
Engineering and Related Technologies Architecture and Building
Course Group 3 Nursing Education Course Group 4 Medicine Other Health Course Group 5 Law Commerce Course Group 6
Society and Culture Visual Arts
Figure 3.1: Three-layer nesting structure used in the nested logit estimation of tertiary edu-cation choices
Notes: Courses of study are grouped at Layer 2 according to their similarity which is assumed to be a function of both place-scarcity and broad subject matter. Courses of study are allocated to a main field of study at Layer 3 according to the Undergraduate Australian Standard Classification of Education (ASCED).
no-attend option – are unnecessary assumptions.
Nesting of the decision-making process allows for a specification where errors are correlated across the alternatives but in a framework that remains consistent with additive, random-utility. Generalisation of the multinomial model in this way allows us to group courses of study for which unobserved shocks may be correlated. To estimate the nested logit model, we organise the data for each individual l as a series of choices among the M alternatives. The model therefore has M equations per individual with course-specific variables that vary across the M equations and individual-specific variables that are constant across the m equations. The binary dependent variable is equal to one for the alternative chosen and zero for the remaining alternatives.
We employ a three-layer nesting structure as illustrated in Figure 3.1. Individuals first choose whether or not to attend university. Conditional on attending university, individuals notionally choose from groups of similar courses, then select a specific course from within that group.
CHAPTER 3. THE MODEL 16 Courses of study are grouped according to their similarity which is assumed to be a function of both place-scarcity and broad subject matter. This structure does not imply that individuals actively choose a course group before making their ultimate decision, rather it merely allows for correlation among similar courses of study beyond that apparent in the attend/not-attend decision. Since choices must be consistent within the overall hierarchical framework, only those choices that are nested within all higher-level decisions are available at any given level.
Since we use a three-level nesting procedure, we recast Equation 3.3 in terms of the nesting layer. The first layer denotes the choice to attend university or not, and is accorded the index i. We use only individual-specific variables in the this layer for the estimation. Since the first layer contains only individual-specific variables, one choice – in our case the no-attend option, – must be normalized to zero. After normalisation of the no-attend option, we will have individual-specific parameter estimates for only the attend-university choice, relative to the no-attend option. We introduce an index, j, to denote the second nesting layer which identifies the grouping of the courses of study by similarity. In nesting layer 2 no explanatory variables are used so the dissimilarity parameters are the only parameter estimated here. The bottom layer captures the ultimate course of study choice among the M alternatives, indexed by k. The third layer includes only course-specific explanatory variables so we will estimate just one generic parameter for each variable at this layer. The modification gives us the general utility specification by nesting layer:
Uijk= ηijk+ ijk (3.7)
Within each nest, the distribution of the errors now includes a dissimilarity parameter τ – an additional parameter relative to other multinomial logit models. The dissimilarity parameter is a measure of the correlation between error terms of the alternatives within that nest, defined as √1 − ρ, where ρ is the correlation coefficient within the nest (Heiss, 2002) 1. Dissimilarity parameters are estimated at Layer 1 and Layer 2 of the model. Since the no-attend option contains only one choice at Layer 2 and Layer 3, the dissimilarity parameter is degenerate and is set to 1.
The random utility specification of the nested logit model assumes that the error term is distributed according to the multivariate version the extreme-value distribution given in Equation 3.8 (Kotz and Nadarajah, 2000).
F () = exp −X i∈I X j∈Si X k∈Rj exp(−ηtjk/τj) τj/vivj (3.8) Given the distributional assumption, we may now specify the form of the conditional prob-abilities. Let CU nirepresent the choice to attend university or not, CBand represent the
course-choice grouped by course similarity, and CCourse represent the ultimate course-choice, as
illus-1
Different authors have used other equivalent representations in the literature, McFadden (1981), for example, replaces τ with σ = 1 τ ,
CHAPTER 3. THE MODEL 17 trated in Figure 3.1. Then the set of conditional probabilities for the choices at each level is given by: P r(CCourse = k | CU ni= i, CBand= j) = exp(ηijk/τj) P l∈Rjexp(ηilk/τj) (3.9) P r(CBand= j | CU ni= i) = exp(ηijk/τj) τj/vi P l∈Si P l∈Rjexp(ηilk/τj) τl/vi (3.10) P r(CU ni= i) = exp(ηijk/τj) τj/vi vi P l∈I P l∈Si P l∈Rjexp(ηilk/τj) τl/vi vl (3.11)
Chapter 4
Data
Examination of individuals’ tertiary education choices through nested logit analysis permits the use of both individual-specific and course-of-study–specific variables. We use individual-specific data from a longitudinal survey of Australian households and alternative-specific data from three different sources to create a novel database for our investigation.
Demographic data on individuals
The individual-specific data is taken from the Household, Income and Labour Dynamics of Australia (HILDA) survey. The HILDA survey is a household-based, longitudinal survey that collects extensive economic and social information from respondents. It focuses on the family history, household income and other demographic variables. Beginning in 2001, the annual survey has collected data at the household and individual-levels from a sample of Australian households living in private dwellings (Summerfield et al., 2011). Whilst the HILDA survey is consistent from wave to wave in its basic formulation, it has a periodic focus on human capital and literacy making it ideal for the study of educational choices. The HILDA data were extracted using PanelWhiz software (Hahn and Haisken-DeNew, 2013).
The HILDA survey asks respondents if they are enrolled in a course of study for a trade certificate, diploma, degree or any other educational qualification during the applicable survey year. Respondents to this question in HILDA Wave 12 – with the focus on human capital and literacy – form the basis of the individual data for the analyses. In total, there are 2,857 relevant individuals in the longitudinal data set. The summary statistics for these individuals are presented in Table 4.1. The time-varying data are taken from the survey year prior to the year that the individual commenced study, or in the case of individuals who did not undertake study during the relevant period, the year when they were first asked if they were enrolled in a course of study. The rationale being that this was the year the individual conclusively decided to commence study or not and that the demographic information from this year, particularly the geographic information and local unemployment rate, is the most relevant from the sample for a cross-sectional analysis.
The effect of tuition rates on tertiary education choices may differ depending on the age
CHAPTER 4. DATA 19
Full sample 18-24 year olds
University education No university education University education No university education Mean/ Count Std. dev./ percentage Mean/ Count Std. dev./ percentage Mean/ Count Std. dev./ percentage Mean/ Count Std. dev./ percentage Sex Male 229 41.34% 429 42.86% 190 41.67% 207 46.21% Female 325 58.66% 571 57.04% 266 58.33% 240 53.57% Age 21.74 6.94 29.47 11.84 19.17 1.75 19.55 2.24 State ACT 17 3.07% 15 1.50% 13 2.85% 8 1.79% NSW 187 33.75% 300 29.97% 157 34.43% 134 29.91% NT 3 0.54% 7 0.70% 2 0.44% 2 0.45% QLD 94 16.97% 184 18.38% 75 16.45% 71 15.85% SA 45 8.12% 94 9.39% 37 8.11% 41 9.15% TAS 12 2.17% 30 3.00% 10 2.19% 18 4.02% VIC 158 28.52% 288 28.77% 134 29.39% 140 31.25% WA 38 6.86% 83 8.29% 28 6.14% 34 7.59%
Major city Yes 402 72.56% 689 68.83% 334 73.25% 295 65.85%
No 152 27.44% 312 31.17% 122 26.75% 153 34.15%
Unemployment rate 4.85 1.07 4.84 1.15 4.89 1.05 4.78 1.30
Mother’s education No tertiary 192 34.66% 525 52.45% 144 31.58% 200 44.64%
Non-university
tertiary 161 29.06% 297 29.67% 136 29.82% 137 30.58%
University 201 36.28% 179 17.88% 176 38.60% 111 24.78%
Father’s education No tertiary 160 28.88% 424 42.36% 123 26.97% 196 43.75%
Non-university
tertiary 181 32.67% 373 37.26% 146 32.02% 159 35.49%
University 213 38.45% 204 20.38% 187 41.01% 93 20.76%
Log household income 11.64 0.74 11.43 0.71 11.69 0.73 11.42 0.76
Secondary education Private school 0.50 0.50 0.33 0.47 0.53 0.50 0.33 0.47
Siblings Number 2.02 1.52 2.27 1.66 1.90 1.32 2.08 1.48 Ability: BDS 0.67 0.18 0.64 0.17 0.67 0.18 0.63 0.16 Ability: WPS 0.58 0.17 0.54 0.20 0.57 0.17 0.50 0.19 Ability: SDS 0.56 0.10 0.53 0.09 0.57 0.10 0.54 0.09 N 554 1001 456 448 N Total 1555 904
Table 4.1: Summary statistics for HILDA sample individuals by university attendance in 2012.
Notes: Full sample statistics are individuals that attended secondary school to at least 17 years of age but are not upper-bounded by age. School-leavers statistics are restricted to individuals aged 24 and under and that attended secondary school to at least 17 years of age. Major City is a binary indicator of the residence location of the individual according to the Australian Standard Geographical Classification (ASGC). Unemployment summarizes the unemployment rate if the Major Statistical Region of the individual’s location of residence. Ability: BDS represents the normalised Backwards Digit Span score, Ability: SDS represents the normalised Symbol Digits Modalities score, and Ability: WPS represents the normalised National Adult Reading Test score.
of the estimation sample. We consequently test this hypothesis by separately estimating the tuition-effect for secondary school leavers who comprise around 80 per cent of annual university enrolments. That is, for 18-24 year-olds who have completed secondary school, consistent with convention in the literature (Heller, 1997). Table 4.1 presents the summary statistics for both estimation samples.
repre-CHAPTER 4. DATA 20
Population Sample
Number of students Per cent Number of students Per cent Field of study
Natural and Physical Sciences 83,972 8.57% 43 7.75%
Information Technology 26,173 2.67% 17 3.06%
Engineering and Related Technologies 62,757 6.40% 42 7.57%
Architecture and Building 23,612 2.41% 14 2.52%
Agriculture, Environmental and Related
Studies 15,442 1.58% 10 1.8%
Health 161,117 16.43% 108 19.46%
Education 111,318 11.36% 76 13.69%
Management and Commerce 170,302 17.37% 96 17.3%
Society and Culture 252,145 25.72% 112 20.18%
Creative Arts 73,432 7.49% 37 6.67%
Total 980,332 100.0% 554 100.0%
State
New South Wales 279,623 32.2% 187 33.75%
Victoria 210,165 24.2% 158 28.52% Queensland 166,275 19.1% 94 16.97% Western Australia 96,201 11.1% 38 6.86% South Australia 61,070 7.0% 45 8.12% Tasmania 20,075 2.3% 12 2.17% Northern Territory 9,100 1.0% 3 0.54%
Australian Capital Territory 26,813 3.1% 17 3.07%
Total 869,322 100.0% 554 100.0%
University grouping
Group of Eight 333,898 26.2% 130 25.8%
Australian Technology Network
of Universities 215,930 17.0% 73 14.4%
Innovative Research
Universities 185,219 14.5% 90 17.9%
Regional Universities Network 101,982 8.0% 53 10.6%
Other universities 436,251 34.3% 158 31.3%
Total 1,273,280 100.0% 554 100.0%
Table 4.2: Sample descriptive statistics for the matched HILDA sample of students attending university in 2012 and the 2012 student population as measured by the Australian Department of Education and Training.
Notes: Law students are included in Society and Culture measure as per statistical conventions of the Australian Department of Education and Training. The total number of students in the population varies according to the exclusion of certain B-class tertiary education providers and the exclusion of Other category labels.
sentative of the Australian population, though there is a materially higher proportion of women – 58 per cent – in the sample than in the general population. In the HILDA sample, individuals enrolled in tertiary education are on average 7.73 years younger than their non-enrolled coun-terparts in the full sample though, naturally, this difference disappears for the age-restricted
CHAPTER 4. DATA 21 sample. University attendees are more likely to live in a major Australian city in both samples. The parents of students enrolled in universities are on average more highly educated than those of non-university-enrolled individuals. The difference is more pronounced for the 18-24 year old sample where around 40 per cent of the parents of university-attendees are university educated relative to just 25 per cent of mothers and 20 per cent fathers of the non-university-enrolled individuals. 1. Household regular income of university-attendees is on average higher and family size smaller than non-university attendees.
In 2012, the HILDA survey collected supplemental information on the cognitive abilities of respondents. Three measures were included: Backwards Digit Span, Symbol Digits Modalities, and modified version of the (Australian) National Adult Reading Test (Wooden, 2013). The Backwards Digit Span is a measure of memory recall, the Symbol Digits Modalities is a general test of attention, visual scanning and motor speed (Strauss et al., 2006), and the National Adult Reading Test is used to provide an estimate of pre-morbid intelligence (Wooden, 2013). The results of the three cognitive ability measures are presented in Table 4.1, normalised to be between zero and 1. Students enrolled at university perform marginally better on all three tests in both samples with the largest differential occurring in the National Adult Reading Test where university students on average outperform other individuals by around 10 per cent.
Table 4.2 presents a comparison of the HILDA sample with population level statistics from the Department of Education and Training. It shows that the HILDA sample is broadly repre-sentative of the population of students enrolled in Australian universities.
Course-of-study data
We use alternative-specific variables to investigate the influence of tuition of tertiary education choices. By regulation, course tuition is constant across Australian public universities, so the study of student-price-responsiveness requires course-of-study-specific variables.
For the course-of-study-specific variables, we use data on course costs from the Australian Government, Department of Education and Training (DET). The DET maintains a database containing annualised course costs for Commonwealth-Supported students by main field of study. The policy principles that underpin the specification of course costs are detailed in Chapter 2 and are not repeated here. As illustrated in Figure 4.1, the real annual costs of the four pricing bands have remained relatively stable since policy changes introduced in 2005. The real cost to students of Band 3 courses has remained at approximately AUD 9,500 per year in comparison to the lowest cost National Priority pricing band courses that have attracted real annual fees of approximately AUD 4,500. Fields of study are occasionally reallocated among the four pricing bands according to national educational priorities and changes in underlying costs of administrating courses, among other things (Norton, 2014).
An important feature of our analysis is an explicit recognition that tuition is just one input 1
The average level of education in the Australian population has increased over time so it is possible that the higher average age of individuals not enrolled in tertiary education is influencing average education differential, notwithstanding the previous qualifier on the calculation of respondents age
CHAPTER 4. DATA 22 $4,000 $5,000 $6,000 $7,000 $8,000 $9,000 $10,000 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Science IT Medicine Nursing Commerce Society & Culture Band 3
Band 2
Band 1
National Priorities
Figure 4.1: Selected university course costs by main field of study: Annualised costs 2003 to 2012
Notes: Data is in 2012 Australian dollars. Courses of study are annually allocated to one of four student contribution bands. The national priority band was intriduced in 2005, prior to this there were three student contribution bands.
to the overall return to education. This feature distinguishes our analysis from many others that concentrate only on tuition costs (Shin and Milton, 2008). To capture the general effect of the return to education, we take estimates of the private rate of return to education by main field of study and gender from Daly et al. (2015). In their paper, Daly et al. estimate the expected net present value (NPV) to an 18 year old secondary school graduate from attending university over a 46 year working life. We recognise that the HILDA sample contains mature-age individuals who may not have 46 years of working life remaining, so we test the sensitivity of our results to the inclusion of mature-age individuals. The NPV by main field of study and gender are presented in Table 4.3. We can see that the lifetime returns to studying Medicine, Law and Commerce are very high whereas the lifetime returns to Science, Education and Nursing are more modest. The lifetime returns to studying Visual Arts is estimated to be negative. For estimation purposes, we net out the course costs from the NPV values used by Daly et al. to enable both tuition and course-specific NPV (net of tuition) to be separately included as explanatory variables. For illustrative purposes, Table 4.3 also contains the NPV of tuition cost by main field of study in 2012. In terms of total course costs, long Band 3 courses such as Medicine and Law are the most expensive whereas short, National Priority band courses such as
CHAPTER 4. DATA 23
Course of Study NPV of graduating course of study: male
NPV of graduating course of study:
female NPV of course cost
Science $250,952 $199,998 $13,296 Information technology $431,425 $344,135 $23,680 Engineering $473,393 $183,586 $31,265 Architecture $314,063 $131,613 $38,702 Agriculture $250,952 $199,998 $23,680 Medicine $797,304 $692,482 $45,313 Nursing $243,668 $170,059 $16,614 Health sciences $510,529 $372,782 $45,399 Teaching $232,499 $205,992 $21,936 Commerce $497,256 $255,859 $27,724 Law $716,044 $521,913 $36,606 Social Science $277,534 $195,463 $16,614 Arts -$20,256 -$9,558 $16,614 Average $382,720 $266,486 $27,496
Table 4.3: Net present value estimates by main field of study and gender from Daly et al. (2015)
Notes: NPV Estimates are the expected NPV to an 18 year old secondary school graduate from attending university over a 46 year working life using a 2 per cent discount rate. Course cost NPV is presented as the negative of the true NPV value, again using a 2 per cent discount rate, and are from 2012 only.
Science are the least expensive. The tuition cost NPVs are included as positive values – rather than as the negative values that would have been used in NPV calculations – so, a priori, we expect a negative coefficient estimate.
The final course-specific variable we require relates to the university admission process. As described in Chapter 3, an integral part of admission to university in Australia is the Australian Tertiary Admission Rank (ATAR). Where university courses are oversubscribed, as is routinely the case, universities use ATAR scores as the primary differentiator among applicants. Whilst the HILDA survey does not collect information on individual ATAR scores2, the DET and state-based University Admission bodies publish the minimum ATAR score required to gain entry to a course of study at each university. Using this information, and the main field of study and institution information collected in the HILDA survey, we proxied for the ATAR scores of each individual using the cut-off ATAR required for course entry. Since highly selective courses are not always available to individuals given their ATAR score, we use the difference between an individual’s ATAR score and the course-average ATAR cut-off score by course to capture this effect (Long, 2004).
Whilst we are able to match the data from the different sources according to the main field of study, the classification system employed in the HILDA survey and by Daly et al. (2015), and 2The HILDA data and the Longitudinal Survey of Australian Youth are the foremost two Australian data sets
that may be used for this type of analysis. The LSAY contains information on the ATAR score of an individual and more extensive education-related information but has poorer information on demographic and household variables. Since the latter is very important in our analysis, we chose to use the HILDA data and proxy for the individual ATAR scores
CHAPTER 4. DATA 24 the DET approach used to allocate units of study to funding clusters and student contribution bands, differ in small but material ways. HILDA respondents enrolled in a university course were asked to identify the main field of study of the course that they undertook according to the Undergraduate Australian Standard Classification of Education (ASCED). We use these data to match the individual-specific data to the institution-specific and course-cost data. The ASCED is not used by the DET to aggregate fields of study to course-cost bands. Most responses correspond directly with the DET data, however, non-medicine, health-related courses and the study of economics are not able to be precisely matched. Economics courses in the HILDA data set are classified as social sciences, along with political sciences, languages, psychology etc. Whereas in the DET databases, they are classified alongside business and commerce courses. Similarly, the Other Health response in the HILDA survey contains Pharmacy, Dental studies, Veterinary studies which is an aggregation of multiple classes of courses in the DET database3. The consequence is that the matching of data for these individuals, and the attribution of ATAR scores, is less precise than for other courses which is a limitation of our methodology.
3Allied Health contains some variation within. Out of the seven sub-fields of study identified in this category,
four fields require four years to complete (Radiography, Rehabilitation Therapies, Complementary Therapies, and Pharmaceutical), two fields take three years to complete (Public Health and Other Health) and one field of study takes five years to complete (Optical Science).
Chapter 5
Results
Table 5.1 presents individual choices by the nesting structure used in the preferred estimation specification. The preferred specification contains only those individuals who completed sec-ondary school, and only those university attendees enrolled in undergraduate courses of study. It includes both school-leavers and mature-age individuals. Of the sample of 1,555, there are 1,001 individuals who did not attend university and 554 who did attend university.
Prior to presenting the estimation results, we first examine the Independence of Irrelevant Alternatives for the estimation sample. Given the nesting structure detailed in Table 5.1, we are able to test whether the odds ratio between two nests is independent of the other alternatives
Layer 1 N Layer 2 N Layer 3 N
No University 1001 No University 1001 No University 1001 University 554 Course Group 1 48 Natural and Physical Sciences 43
Agriculture, Environmental and Related Studies
10
Course Group 2 73 Information Technology 17 Engineering and Related
Technologies
42
Architecture and Building 14 Course Group 3 108 Nursing 32
Education 76
Course Group 4 76 Medicine 15
Other Health 61
Course Group 5 128 Law 32
Commerce 96
Course Group 6 116 Society and Culture 79
Visual Arts 37
Total 1555
Table 5.1: Three-layer nesting structure used in the principal analysis.
Notes: N denotes the count of individuals within the nest at each nesting layer.
CHAPTER 5. RESULTS 26
Course group included in the restricted estimation Test statistic Prob > χ2
Course group 2 124.95 0.0000 Course group 3 19574.71 0.0000 Course group 4 2101.32 0.0000 Course group 5 7071.68 0.0000 Course group 6 366.82 0.0000 Course group 7 418.41 0.0000
Table 5.2: Hausman test results for the Independence of Irrelevance Alternatives in the full estimation sample
Notes: Hausman unrestricted estimation on the full alternative set, and the estimation on the restricted alternative set, exclude the no attend option Hausman and McFadden (1984). P-values are calculated using a χ2(16) distribution.
using a Hausman specification test. Hausman and McFadden (1984) explained that if the IIA holds, then the exclusion of a subset of alternatives from the conditional logit model will give consistent results. Hence, the IIA may be tested using a conditional logit model of the data which is easily created (Maddala, 1983). We first estimate a conditional logit model on the full set of alternatives, then estimate restricted conditional logit models for each nest by excluding all other alternatives from the estimation. The results of the Hausman tests are presented in Table 5.2. They provide clear evidence that the odds ratios are not independent since the null hypothesis that the differences are not systematic is strongly rejected in each case, hence, a nested logit model is appropriate.
Estimation results for the full sample model are given in Table 5.3, though the year dummies and constant terms are suppressed. The standard errors for the analysis are calculated using the Huber-White sandwich estimator. For the course-of-study-specific explanatory variables, the results reveal that course cost is an insignificant factor in individuals’ decisions in the final layer of the nesting structure, that is, the course-of-study-choice level. The return to graduating from the course does, however, have a significant, positive effect on an individual’s choice of course. As expected, the ATAR differential has a positive and significant effect on an individual’s choice of course. We had no strong a priori expectation for the course length parameter sign, and the coefficient estimate is positive, suggesting that there longer courses are more preferred. For the individual-specific explanatory variables (used in Layer 1 of the estimation), the results are normalised using the no-attend option as the base-case. We see that females are more likely to be enrolled at university as are individuals from a high-income background and those with high ability as measured by the National Adult Reading Test. Somewhat surprisingly, having a primary residence in a major city makes an individual significantly less likely to attend university relative. The prior study dummy variable captures individuals who have either previously completed a course-of-study at university or who have attended university but not completed a course. As expected, if an individual falls into this category then it significantly
CHAPTER 5. RESULTS 27
Coefficient Std. Err.
Layer 3 : Course-specific variables
NPV of total course cost -0.4812 0.8642
NPV of graduating course (net of course cost) 1.6937 *** 0.4876
Course ATAR Differential 0.1384 *** 0.0123
Course length 0.8102 ** 0.3608
Layer 1: Individual-specific variables Base Case (Not attend university)
Sex -0.8491 *** 0.2182
Age -0.0018 0.0130
Ability: Symbol modalities score 0.8323 0.8566
Ability: Word pronunciation score 1.0164 ** 0.4732
Ability: Backwards digits score -0.5949 0.4620
Attended private high school 0.5762 *** 0.1534
Lives in a major city -0.6934 *** 0.1764
Previously enrolled in course of study -1.8476 *** 0.2273
Unemployment rate in MSR 0.0955 0.0664
Household income 0.2986 *** 0.1036
Father years of education 0.0415 0.0405
Mother years of education 0.0276 0.0418
Dissimilarity parameters τ Layer 1 University 1.9816 * 1.0814 Layer 2 Course Group 1 0.2427 0.3369 Course Group 2 1.2168 *** 0.3372 Course Group 3 2.4342 ** 1.1210 Course Group 4 1.1954 ** 0.4821 Course Group 5 3.5853 *** 0.8323 Course Group 6 5.8520 *** 1.7950 Observations 21770 Cases 1555
Alternatives per case 14
Log likelihood -1918.33
LR test for IIA (τ all = 1, p-value) 0.000
Table 5.3: Estimation results for the nested logit model
Notes: The specification contains only individuals who have completed secondary school, and university attendees enrolled in undergraduate courses of study. The estimation contains dummies for the study commencement year and constant terms, though these are not presented. *** denotes significance at the 1 % level, ** significance at the 5 % level and * significance at the 10 % level. Cases is the number of individuals in the sample whereas the Observations is the number of alternatives per individual, multiplied by the number of individuals.
decreases their probability of university attendance. We test the sensitivity of the results to the inclusion of these individuals later in the chapter.
