Tuition Fees and University Enrolment: A Meta‐Regression Analysis
| Date | 01 December 2018 |
| Author | Zuzana Irsova,Olesia Zeynalova,Tomas Havranek |
| Published date | 01 December 2018 |
| DOI | http://doi.org/10.1111/obes.12240 |
1145
©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 80, 6 (2018) 0305–9049
doi: 10.1111/obes.12240
Tuition Fees and University Enrolment:A
Meta-Regression Analysis*
Tomas Havranek,†,‡ Zuzana Irsova,‡ and Olesia Zeynalova‡
†Research Department, Czech National Bank, Prague, Czech Republic
(e-mails: tomas.havranek@ies-prague.org, zuzana.irsova@ies-prague.org,
lesya.fox89@gmail.com)
‡Institute of Economic Studies, Faculty of Social Sciences, Charles University, Prague,
Czech Republic
Abstract
One of the most frequently examined relationships in education economics is the corre-
lation between tuition fee increases and the demand for higher education. We provide a
quantitative synthesis of 443 estimates of this effect reported in 43 studies. While large
negative estimates dominate the literature, we show that researchers report positive and
insignificant estimates less often than they should. After correcting for this publication
bias, we find that the literature is consistent with the mean tuition–enrolment elasticity be-
ing close to zero. Nevertheless, we identify substantial heterogeneity among the reported
effects: for example, male students and students at private universities display larger elas-
ticities. The results are robust to controlling for model uncertainty, using both Bayesian
and frequentist methods of model averaging.
I. Introduction
The relationship between the demand for higher education and changes in tuition fees1
constitutes a key parameter not only for deans but also for policymakers. It is therefore not
surprising that dozens of researchers have attempted to estimate this relationship. While the
relationship (often, but not always, presented in the form of an elasticity) can be expected
to vary somewhat across different groups of students and types of universities, there has
JEL Classification numbers: I23, I28, C52.
*Data and code are availablein an online appendix at http://meta-analysis.cz/education. Havranek
acknowledges support from the Czech Science Foundationgrant #18-02513S, and Irsova acknowledges support from
the Czech Science Foundation grant #16-00027S. This project has also receivedfunding from the European Union’s
Horizon 2020 Research and InnovationStaff Exchange program under the Marie Sklodowska-Curie grant agreement
#681228 and Charles University project PRIMUS/17/HUM/16. We thank the editor and four anonymous referees
of the Oxford Bulletin of Economics and Statistics for useful comments. We are also grateful to Craig Gallet for
providing us with the data set used in his meta-analysis.The views expressed here are ours and not necessarily those
of the Czech National Bank.
1For parsimony,in this paper, we usually omit ‘fee’ and use the word ‘tuition’in its North American sense, ‘a sum
of money charged for teaching by a college or university’.
1146 Bulletin
-1 -.5 0.5
Effect of tuition on enrollment (partial correl. coefficient)
1970 1980 1990 2000 2010 2020
Publication year
Figure 1. No clear message in 50 years of research
Notes: The figure depicts a common metric (partial correlation coefficient) of the reported effect of tuition fees
on enrolment in higher education institutions. The time trend is not statistically significant.
been no consensus even on the mean effect, as many literature surveys demonstrate (see,
for example, Jackson and Weathersby, 1975; Leslie and Brinkman, 1987; Heller, 1997):
the estimates often differ by an order of magnitude, as we also show in Figure 1.
The academic discussion concerning the correlation between tuition fees and demand
for higher education dates back at least to Ostheimer (1953). Even though large price
elasticities do occasionally appear in the empirical literature (see, among others, Agar-
wal and Winkler, 1985; Allen and Shen, 1999; Buss, Parker and Rivenburg, 2004), the
majority of the evidence corroborates the notion of a rather price-inelastic demand for
higher education across many contexts. Researchers offer numerous explanations for the
observed lack of large elasticities: for example, the effect of financial aid compensating
tuition changes (Canton and de Jong, 2002), increasing earnings of graduates relative to
those of non-graduates (Heller, 1997), historically small tuition fee increases in real terms
and the impact of aggressive marketing (Leslie and Brinkman, 1987), larger student will-
ingness to pay for quality (McDuff, 2007), expansion of the student pool with female and
minority participants, and the fact that many university students come from higher-income
families (Canton and de Jong, 2002). Even the very first literature review by Jackson and
Weathersby (1975) put forward the case for the correlation between tuition and enrolment,
while significant and negative, to be rather small in magnitude.
The existing narrative literature surveys, including Jackson and Weathersby (1975),
McPherson (1978), Chisholm and Cohen (1982), Leslie and Brinkman (1987), and Heller
(1997), place the tuition–enrollment relationship below a 1.5 percentage-point change per
$100 tuition increase. The first quantitative review on this topic, Gallet (2007), puts the
mean tuition elasticity of demand for higher education at −0.6. However, every single
review acknowledges that the mean estimate could be somehow biased and driven by the
vast differences in the design of studies, namely, methodological (Quigley and Rubinfeld,
1993), country-level (Elliott and Soo, 2013), institution-level(Hight, 1975), and qualitative
differences. Our goal in this paper is to exploit the voluminouswork of previous researchers
on this topic, assign a pattern to the differences in results, and derive a mean effect that
©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
Tuition fees and university enrolment 1147
could be used as ‘the best estimate for public policy purposes’ that the literature has sought
to identify (Leslie and Brinkman, 1987, p. 189).
Achieving our twogoals involves collecting the reported estimates of the effect of tuition
fees on enrolment and regressing them on the characteristics of students, universities, and
other aspects of the data and methods employedin the original studies. Such a meta-analysis
approach is complicated by two problems that have yet to be addressed in the literature on
tuition and enrolment: publication selection and model uncertainty. Publication selection
arises from the common preference of authors, editors, and referees for results that are
intuitive and statistically significant. In the context of the tuition–enrolment nexus, one
might well treat positive estimates with suspicion as few economists consider education to
be Giffen good. Nevertheless,sufficient imprecision in estimation can easily yield a positive
estimate, just as it can yield a very large negative estimate. The zero boundary provides
a useful rule of thumb for model specification, but the lack of symmetry in the selection
rule will typically lead to an exaggeration of the mean reported effect (Doucouliagos and
Stanley, 2013).
The second problem, model uncertainty, arises frequently in meta-analysis because
many factors may influence the reported coefficients. Nevertheless, absent clear guidance
that would specify which variables (out of the many dozen potentially useful ones) must
be included in and which must be excluded from the model, researchers face a dilemma
between model parsimony and potential omitted variable bias. The easiest solution is to
employ stepwise regression, but this approach is not appropriate because important vari-
ables can be excluded by accident in sequential t-tests (this problem is inevitable, to some
extent, also with more sophisticated methods of model selection – every time we need to
choose which variables to exclude).2In contrast, we employ model averaging techniques
that are commonly used in growth regressions: Bayesian model averaging and frequentist
model averaging, which are well described and compared by Amini and Parmeter (2012).
The essence of model averaging is to estimate (nearly) all models with the possible com-
binations of explanatory variables and weight them by statistics related to goodness of fit
and parsimony.3
Our results suggest that the mean reported relation between tuition and enrolment is
significantly downward biased because of publication selection (in other words, positive
and insignificant estimates of the relationship are discriminated against). After correcting
for publication selection, wefind no evidence of a tuition–enrolment nexus on average. This
result holds when we construct a synthetic study with ideal parameters (such as a large data
set, control for endogeneity, etc.) and compute the implied ‘best-practice estimate’: this
estimate is also close to zero. Nevertheless, we find evidence of substantial and systematic
heterogeneity in the reported estimates. Most prominently, our results suggest that male
students and students at private universities display substantial tuition elasticities.
2Campos, Ericsson and Hendry (2005) provide a useful review of general-to-specific modelling.
3Model averaging allows us to take into account the model uncertainty associated with our meta-analysismodel.
Nevertheless, this approach does not address the model uncertainty in estimating the tuition–enrolment nexus in
primary studies: this second source of model uncertainty is the reason for conducting a meta-analysis in the first
place (Stanley and Jarrell, 1989; Stanley and Doucouliagos, 2012). A technical treatment of these two sources of
model uncertainty with relation to Bayesian model averaging is available in appendix B of Havranek, Rusnak and
Sokolova (2017).
©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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