The determinants of university dropouts: A bivariate probability model with sample selection

Abstract

In this paper, we study the determinants of university dropouts with a longitudinal data set on student enrolments at the Université de Montréal. With a bivariate probit model with selectivity bias, the variables explaining persistence and dropouts are related to the information gathered on the student about his or her interests and abilities. An environmental variable associated with the number of students in first-year compulsory courses is also a determining factor. These results are consistent with human capital and experimental models developed by economists, and psychosocioligical models pioneered by Tinto to explain dropout behavior. However, the different models offer different policy approaches to the problem of student attrition.

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Economics of Education Review 20 (2001) 475–484 www.elsevier.com/locate/econedurev
The determinants of university dropouts: a bivariate
probability model with sample selection
Claude Montmarquette
a,*
, Sophie Mahseredjian
a
, Rachel Houle
b
a
De
´partement de sciences e
´conomiques and Centre de recherche et de
´veloppement en e
´conomique (C.R.D.E.), Universite
´de
Montre
´al, C.P. 6128, succursale Centre-ville, Montre
´al, Que
´bec, Canada H3C 3J7 and CIRANO
b
Bureau de recherche institutionnelle, Universite
´de Montre
´al, C.P. 6128, succursale Centre-ville, Montre
´al, Que
´bec, Canada
H3C 3J7
Received 9 April 1996; accepted 14 April 2000
Abstract
In this paper, we study the determinants of university dropouts with a longitudinal data set on student enrolments
at the Universite
´de Montre
´al. With a bivariate probit model with selectivity bias, the variables explaining persistence
and dropouts are related to the information gathered on the student about his or her interests and abilities. An environ-
mental variable associated with the number of students in first-year compulsory courses is also a determining factor.
These results are consistent with human capital and experimental models developed by economists, and psychosociolig-
ical models pioneered by Tinto to explain dropout behavior. However, the different models offer different policy
approaches to the problem of student attrition. 2001 Elsevier Science Ltd. All rights reserved.
JEL classification: I20; C35
Keywords: University dropout; Economics and psychosociological models; Policy interventions; Bivariate probit model; Sample selec-
tion
1. Introduction
Postsecondary dropouts have become a major concern
in many countries over past years due to their increasing
frequency (see Tinto, 1993; Grubb, 1989; Oosterbeek,
1989; Hartog, Pfann, & Ridder, 1989, and references
therein). In North America and Western Europe, notably
in many European community member countries, a surge
in enrolment in the last decade has widened the gap
between the number of students who enter the university
system and the number who graduate. This has produced
tensions between selective “elite” schools and largely
* Corresponding author. Tel.: +1-514-343-2404; fax: +1-
514-343-5831.
E-mail address: montmar@crde.umontreal.ca (C.
Montmarquette).
0272-7757/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.
PII: S0272 -7757(00)00029-7
accessible public universities. It has also resulted in low
completion rates considered socially undesirable
(Pritchard, 1990; Neave & van Vught, 1991).
For many, the dropout problem is an important social
issue. American authors have suggested that society
would be better off if they were to be lowered (see, for
example, Fisher, 1987; James, 1988). In many Canadian
political and educational sectors (see Montmarquette,
1990), there is concern that higher graduation require-
ments will increase dropout rates. Furthermore, as
national economies are challenged by international com-
petition where education, not schooling, matters these
concerns are troublesome.
In a challenging article Manski (1989) suggested that
lowering dropout levels would not necessarily make
society better off. The decision to enrol is a decision to
initiate an experiment, a possible outcome of which is
dropout. Hartog et al. (1989) make a similar point, argu-

476 C. Montmarquette et al. / Economics of Education Review 20 (2001) 475–484
ing that “there is no fundamental distinction between
decisions on completed education and on partial edu-
cation”(p. l374). This argument is reflected in Ooster-
beek’s (1989) and Altonji’s (1993) models of sequential
decisions where the educational process is uncertain and
yields information to students so that they may revise
prior beliefs. A parallel may be drawn with the student
attrition model of Bean (1985) which emphasized atti-
tudes about the intent to persist. An alternative view on
attrition is the psychosociological models pioneered by
Tinto (1975) which are based on the idea of person–
environment fit, since if the students feel more connected
with the institution, it could change the nature of the
“students’experiment”in significant ways. It is funda-
mental for Tinto that institutions do a better job reaching
out to students and helping them, and where academics
and social systems appear as two-nested spheres (Tinto,
1997, p. 619). Vincens and Krupa (1994) have shown
that the explanation of successes and failures in the
French academic system combines individual variables
and the system’s organizational characteristics with
entrance selection and the continuing evaluation of stu-
dents. Specific programs and institutional policies
designed to enhance student retention must be evaluated
in this global context. Finally, we note that in the eco-
nomics of education literature, concerns were raised
about the design of better admissions rules (Anderson,
Benjamin, & Fuss, 1994) and the need to identify predic-
tors of persistence (Horvath, Beaudin, & Wright, 1992;
Adams & Becker, 1990).
In this paper, we study the determinants of university
dropouts with longitudinal data on student enrolments at
the Universite
´de Montre
´al. Section 2 presents the data.
The model and the econometric specification are dis-
cussed in Section 3. In Section 4, we report the empirical
results obtained from a bivariate probit model with sam-
ple selection. Section 5 concludes.
2. The data
The Universite
´de Montre
´al has developed a longitudi-
nal data bank, starting with the cohort of first-year stu-
dents registered in the fall semester of 1987. For each
successive term, we know if the student is still enrolled
in the initial program, if he or she dropped out, or if he
or she transferred to another program within the univer-
sity. The data used in the present study cover three sem-
esters (fall 1987, winter 1988 and fall 1988) beginning
with the entrance semester when the student is required
to select a specific (specialized) program at the Univers-
ite
´de Montre
´al.
1
The sample contains 3418 students
1
At the undergraduate level, the summer term is not treated
as a regular term.
enrolled in 43 programs, of which 91.2 percent returned
to their initial choice program for the second semester,
1.9 percent transferred to a new program and 6.9 percent
dropped out after the first semester. After the first aca-
demic year, dropouts represent 24.7 percent of the sam-
ple. “Dropping out”is a concept that is defined relative
to time. Students can leave school temporarily or perma-
nently. We observed that some students who leave a spe-
cialized program return to the same program or to
another program at the same university a few semesters
or even years later. However, the proportion of students
returning is low and the attrition occurs mostly during
the first or second semester of study in a program.
2
Thus,
ignoring the possibility of returning students seems justi-
fied.
In informational terms, the problem of persistence
may be viewed as an interaction between an experiment
in school and an experiment in the labor market. Both
experiments have opportunity costs that are important to
note. If the individuals decide to experiment with the
labor market, they forgo the benefits of a university edu-
cation. And if the university has a large number of Tinto-
type variables, it would raise one’s probability of con-
tinuing to degree completion. On the other hand, the time
used for experimenting with schooling represents for the
student the traditional opportunity cost of foregone earn-
ings. It corresponds to the expected income of a Que
´bec
high school graduate, or about $10,800 based on the
1991 Canadian census. As fees at the Universite
´de Mon-
tre
´al were low (and are still low, relative to the US or
the rest of Canada),
3
and undergraduates in Que
´bec
remained eligible for financial benefits even if they have
changed academic programs up to five times, we believe
to have a somewhat unique testing ground to examine
the “schooling-as-experimentation”model. However, if
these specific conditions create incentives to experiment
with schooling, unfortunately we do not have variables
that will unambiguously distinguish the “experimen-
tation”model from the human capital or psychosociolog-
ical models to explain dropout behavior.
Afull sample specification considers those students
who have changed programs within the university or
who are persistent. In the restricted sample specification,
students who have changed programs are excluded. This
sample consists of 2328 students enrolled in 27 pro-
grams. It is restricted to students enrolled in a program
2
In our sample, we observed that 15 students returned to
their initial program after dropping out and 15 more have reinte-
grated the university through another program. These categories
have too few observations to be taken into consideration in the
econometric model.
3
For almost 20 years, the tuition fees at the Universite
´de
Montre
´al (and across Que
´bec) have remained at $500 (Can.)
for the whole academic year. In European countries low tuition
fees and numerous student support programs are also prevalent.

477C. Montmarquette et al. / Economics of Education Review 20 (2001) 475–484
Table 1
“The determinants of university dropouts”: descriptive statistics of independent variables
Symbol Definition Mean (standard deviation)
Full sample Restricted sample
Personal characteristics
GENDER Gender of student (1=female) 0.608 0.656
AGE Age of student 20.671 (2.434) 20.612 (2.410)
ZSCORE The student’s relative academic performance in college 50.362 (0.651) 50.481 (0.633)
(including estimates ZSCORE)
UGPA1 University grade point average after the first semester 2.660 (1.281) 2.894 (1.124)
PUBLIC Attendance of public or private college (1=public) 0.865 0.867
FLTIME Admission status at the university (1=full-time) 0.965 0.977
PROGQ Characteristic of the program enrolled in at the university 0.771 –
(1=quota of admissions)
Socioeconomic factors
MTONG Mother tongue of the student (1=French) 0.922 0.931
REGION Region of origin of the student (1=Montre
´al) 0.752 0.754
Environmental variables
GMEAN Average number of students in first-year compulsory courses in 66.077 (29.987) 64.462 (28.637)
each academic program
GMEAN2 Square of GMEAN 5265.140 (4315.686) 4974.978 (3992.302)
Average number of students in first-year compulsory courses in each academic program
GR1 Groups with less than 41 students 0.167 0.159
GR2 Groups with 41–100 students 0.676 0.718
GR3 Groups with more than 100 students 0.158 0.123
Sample size 3418 2328
with an entrance quota and to students whose academic
CEGEP performance variable, ZSCORE, is available. In
Que
´bec, students finish high school after 11 years then
go on to an institution known as “CEGEP”before start-
ing university or a job. CEGEPs offer two types of train-
ing: a preuniversity education, which is a prerequisite for
university, and a vocational education leading directly to
the job market. The ZSCORE variable is a key element
to gain access to a university program with an entrance
quota (see below for a full description of this variable).
Table 1 presents the independent variables of the
model and descriptive statistics of each variable. For
each student, information is available for certain personal
characteristics and socioeconomic background. Some of
these explanatory variables reflect an ex-ante student
demand to experiment with schooling. The individual
characteristics variables include gender (GENDER), age
(AGE), performance at CEGEP (ZSCORE), attendance
to public or private CEGEP (PUBLIC), university grade
point average after the first semester (UGPA1), admis-
sion status at the university (FLTIME), and character-
istics of the program chosen at university, for example,
programs with an entrance quota (PROGQ).
4
The
4
To avoid confusion, note that within a single department
some programs offered can be submitted to entrance quota but
not others. In most cases, however, all programs offered within
a specific department are with or without an entrance quota.
ZSCORE is a standardized measure of the performance
of students at the CEGEP level
5
and is used in the admis-
sion of students to programs with quotas. These pro-
grams concern more than 77 percent of the students in
the sample (see PROGQ in Table 1). If the quality of
education varies from one institution to the other, the
ZSCORE does not consider this diversity.
6
The variable
ZSCORE was missing for 7.9 percent of students in the
sample, mainly for those who came from outside the
Que
´bec education system. For the full sample, we have
obtained estimates for the missing collegial academic
performance variable, ZSCORE through a set of instru-
mental variables.
7
The means and the standard deviations
of the ZSCORE variables are comparable for the two
5
Z⫺score=(X⫺M)/S, where Xis the student’s grade; Mis
the average grade of students having taken the same course,
during the same term, and in the same group; Sis the standard
deviation. Once the Z-score for each course has been computed,
the average of all Z-scores for one student is determined. It
varies between ⫺3.00 and 3.00. So as not to deal with negative
values, the constant 50.00 is added. Therefore, ZSCORE has a
maximum of 53.00 and a minimum of 47.00.
6
Z-scores have only been officially corrected by the “per-
ceived”quality of the CEGEP since 1989.
7
Missing elements of the ZSCORE variable were estimated
by OLS with the independent variables GENDER, AGE,
MTONG, REGION and PUBLIC.

478 C. Montmarquette et al. / Economics of Education Review 20 (2001) 475–484
samples. However, as expected, the mean of UGPA1 for
the restricted sample is greater and has a lower standard
deviation than for the full sample.
The socioeconomic variables are the student’s mother
tongue (MTONG), citizenship status (CITIZEN) and
regional home base (REGION). There are obvious limi-
tations concerning these variables, since parental income
and education are not available.
We expect those differences in personal characteristics
and socioeconomic variables observed among students
will reflect differences in quality and information. It
therefore should be the case that the less qualified and
the less-informed students drop out more frequently.
Finally, we include intervention or environmental
variables. GMEAN represents the average class size of
all first-year compulsory courses in each academic
department. It is widely recognized that in the first sem-
ester of the first year of university that the persistence
of students is most tenuous and that classrooms are cen-
tral in the process of retention during that critical period
(Tinto, 1993, pp. 201, 219). Class size in first-year com-
pulsory courses is a key element in eliciting student
interest and involvement in learning. As we expect a
nonlinear effect of the class-size variable on persistence,
we introduce the average number of students in first-year
compulsory courses, GMEAN, and its square,
GMEAN2. An alternative specification in terms of class
size groups (GR1, GR2, GR3) is also considered in the
regressions.
3. The model and econometric specification
Academic success and sustained interest in the stud-
ent’s initial choice of discipline are important “a priori”
determinants of his or her persistence. The student might
question his or her initial choice and drop out if he or
she encounters academic difficulties or disillusion due to
information gleaned from experimentation. They may
also have made an investment decision based on inad-
equate information in advance. The students must con-
sider several options when experimenting with school-
ing: retention or persistence transfer to a new program,
and dropout. Over time, these decisions are discrete
sequential choices made by the student and can be ana-
lyzed empirically.
Consider an individual iin a two-period model who
must choose between two alternatives: persistence or
dropout. For a given individual i,i=1, …,N, the total
utility of each alternative j,j=1, 2 at time tcan be
expressed as a sum of two components:
U
ijt
⫽b⬘
jt
X
ijt
⫹e
ijt
(1)
where X
ijt
denotes the observed component which is a
known function of the characteristics and socioeconomic
background of the individual as well as some environ-
mental variables, and e
ijt
is an unobserved, random
component.
Of course, total utility is unobservable; however, the
choice to persist is observable. Define the binary out-
come of persistence or dropout as:
y
i1
⫽
冓
1, if U
i1
⬎0
0, otherwise (2)
In period 2, conditional on having persisted in the first
period, individual iagain makes a decision to persist or
dropout. Formally:
y
i2
⫽
冓
1, if U
i2
⬎0
0, otherwise (3)
It is likely that the unobserved components e
i1
and e
i2
are correlated across individuals. However, we observe
data for the second period decision only when the student
has persevered after the first semester. In other words,
the observed persistence data are nonrandomly selected
from the set of persistent students after the first semester.
Formally, (y
i2
,x
i2
) is observed only when y
i1
=1. And
while e
i1
is defined over the population of all first-year
university students, e
i2
is defined only on the subpopul-
ation for which y
i1
=1. To deal with this problem, we
assume that the error components are drawn from a
bivariate normal distribution, corrected for a sample
selection, with a correlation coefficient r:
e
i1
,e
i2
苲N(0, 0, 1, 1, r).
The tree structure of Fig. 1 illustrates the simple
sequential decision model (the number of observations
at each decision node is different for the two sample
specifications considered).
It is easy to see that three categories of observation
are made with unconditional probabilities
8
: where
⌽
2
is
a bivariate normal cumulative distribution function and
⌽
is univariate normal cdf.
y
i1
⫽1, y
i2
⫽1: Prob(y
i1
⫽1, y
i2
⫽1)
⫽
⌽
2
[b⬘
1
X
i1
,b⬘
2
X
i2
,r]
y
i1
⫽1, y
i2
⫽0: Prob(y
i1
⫽1, y
i2
⫽0)⫽
⌽
2
[b⬘
1
X
i1
, (4)
⫺b⬘
2
X
i2
,⫺r]
y
i1
⫽0: Prob(y
i1
⫽0)⫽
⌽
[⫺b⬘
1
X
i1
]
The corresponding log-likelihood function is:
8
For earlier applications and discussions of the bivariate
probit model with sample selection, see van de Ven and van
Praag (1981) and Venti and Wise (1982). Technical details are
also presented in Greene (1991, 1993). In our presentation, we
have reversed the subscripts in accord with the tree structure
of Fig. 1.

479C. Montmarquette et al. / Economics of Education Review 20 (2001) 475–484
Fig. 1. A bivariate probit model with sample selection of university dropouts. 1 =persistent, 0 =dropout.
冘
y
i1
⫽1, y
i2
⫽1
ln
⌽
2
[b⬘
1
X
i1
,b⬘
2
X
i2
,r]
⫹冘
y
i1
⫽1, y
i2
⫽0
ln
⌽
2
[b⬘
1
X
i1
,⫺b⬘
2
X
i2
,r] (5)
⫹冘
y
i1
⫽0
ln
⌽
[⫺b⬘
1
X
i1
]
Eq. (5) is to be maximized with respect to the parameters
b
1
,b
2
and r.
4. The empirical results
Table 2 presents the bivariate probit with sample
selection estimations of the “determinants of university
dropouts”model for the two sample specifications.
9
In
the restricted sample specification the students who have
transferred or for whom a ZSCORE is not directly
observed are excluded, and the sample is restricted to
students enrolled in a program with an entrance quota.
The ZSCORE is a key element to gain access to a pro-
gram with an entrance quota, and we expect this variable
to be particularly important for this group of students.
For both samples, ZSCORE measures the quality of
the student making the first-semester decision. In the
second semester, the university grade point average after
the first semester (UGPA1) is used for the student quality
variable. Thus, the reference to past performance-grading
variables to measure student quality is exogenous to the
decision to persist or to drop out.
9
The estimations were done with LIMDEP.
First consider the results of the first-period decision
for the full sample model specification. The statistically
significant coefficient of AGE supports both the human
capital and the experimentation models of: for an older
student the opportunity cost and the cost of experi-
menting is higher so he or she will be more likely to
drop out after the first semester than a younger student.
A part-time university student experimenting
(voluntarily or otherwise) with both the labor market and
schooling is more likely to drop out than a full-time stud-
ent (see the coefficient of FLTIME). The PROGQ vari-
able shows that if a student is enrolled in a program with
an entrance quota, the probability of perseverance is sig-
nificantly higher. This is in accordance with the exper-
imentation model, as the academic requirements are
greater for programs with quotas than for other pro-
grams.
10
Also, programs with quotas are mainly pro-
fessional programs (in law, business or medical schools,
for example) generally better known by CEGEP students
than the sociology, anthropology or economics pro-
grams. As mentioned earlier, our reference to the model
of experimentation stems from the fact that the situation
in Que
´bec offers an interesting testing ground to examine
this model. However, we still have to consider the stud-
ent’s time opportunity cost of forgone earnings or the
opportunity cost of renouncing to complete a university
education. And again we emphasize that since there are
no specific variables unambiguously associated with the
model of experimentation, other interpretations of the
results are possible. Part-time students might be con-
strained by income problems. Students in more
10
Hartog et al. (1989) recognized that dropouts and graduates
have different access to information.

480 C. Montmarquette et al. / Economics of Education Review 20 (2001) 475–484
Table 2
A statistical analysis of “The determinants of university dropouts”with GMEAN and GMEAN2
a
Full sample Restricted sample
Variable First period Second period First period Second period
Personal characteristics
GENDER ⫺0.04275 (0.0707) ⫺0.07516 (0.0610) 0.1962* (0.0957) ⫺0.05996 (0.101)
AGE ⫺0.03541* (0.0142) ⫺0.03166** (0.0170) ⫺0.03034** (0.0183) ⫺0.02553 (0.0221)
ZSCORE 0.06300 (0.0564) –0.1222** (0.0726) –
UGPA1 –0.6148* (0.0262) –0.9560* (0.0425)
PUBLIC ⫺0.04437 (0.109) ⫺0.07278 (0.0878) ⫺0.3192* (0.161) ⫺0.1112 (0.126)
FLTIME 1.1313* (0.124) 0.5668 (0.456) 1.1669* (0.188) 0.7502 (0.491)
PROGQ 0.3869* (0.0768) 0.3078* (0.109) ––
Socioeconomic factors
MTONG ⫺0.08926 (0.140) 0.01790 (0.112) ⫺0.3280 (0.237) 0.1926 (0.167)
REGION 0.008362 (0.0818) 0.1342** (0.0693) 0.02774 (0.108) 0.2371* (0.0937)
Environmental variables
GMEAN 0.01262* (0.00435) –0.01232* (0.00587) –
GMEAN2 ⫺0.00007239* –⫺0.00007728** –
(0.0000303) (0.0000420)
Other statistics
Constant ⫺2.6208 (2.910) ⫺0.8353 (0.538) ⫺4.9701 (3.729) ⫺2.0718* (0.610)
r(1, 2) ⫺0.08895 (0.935) ⫺0.04037 (1.067)
Log of the ⫺1950.6 ⫺1093.6
likelihood function
a
Standard errors in parentheses. *Significantly different from zero at the 5 percent level; **significantly different from zero at
the 10 percent level.
demanding PROGQ programs might have a stronger
determination to complete college.
The individual’s relative academic performance in
CEGEP, the ZSCORE variable, offers an interesting
result about educational market signalling. With an insig-
nificantly positive coefficient in the econometric specifi-
cation, this variable suggests that a better relative aca-
demic performance in CEGEP does not reduce the
probability to drop out after the first semester.
11
In order
to explain this unexpected result, we posit that to
improve his or her ZSCORE, a student might have vol-
untarily chosen a lower-quality CEGEP and the easiest
possible curriculum to increase his chances of being
accepted in a selective program at the Universite
´de
Montre
´al.
Class size in the first-year mandatory courses, usually
taught by an experienced teacher, affects the probability
of persistence in a nonlinear way (GMEAN and
GMEAN2). A group of less than 87 students will
increase the probability of persistence over an early dro-
pout. Above this level, the size effect is negative. Run-
ning simulations for the full sample with respect to class
size, we have found that the probability of persistence
after the first semester of a class size of up to 60 students
11
This was also observed by Dagenais and Dagenais (1988).
increases steadily. Over the range of 60–110 students,
the curve is rather flat, with the probability of persistence
increasing very slowly up to 87 students and then
decreasing also very slowly over the 87–110 range. The
decrease in the probability of persistence after the first
semester becomes rather important when it surpasses a
class size of 110 students. These results are similar to
the restricted sample, and they appear to contradict the
vast literature on the effect of class size, where only for
a very small class has a consistent effect on learning
been found. On outcomes such as retention and motiv-
ation, a majority of studies favor small classes.
12
An
explanation to the initial positive effect on persistence of
adding more students to very small class sizes is that it
may encourage the professor to do a better preparation
for his lecture, and it is also quite likely to financially
justify using better equipment, since fixed costs can be
12
Hoxby (1996) has questioned the exogeneity of the class-
size variable to explain students’achievements at the elemen-
tary level of education. She suggested new evidence on this
issue from natural population variation. At the university level
and across fields of study, class size is more affected by natural
variations in the student population and by financial consider-
ations rather than by specific academic policies to reduce the
dropout rates.

481C. Montmarquette et al. / Economics of Education Review 20 (2001) 475–484
spread out over more people. Then, when the group is
sufficiently large in a mandatory course —say, more
than 30–45 students —funding is usually available for
graduate teaching assistants. After each lecture, the
teaching assistants meet with students in separate sub-
groups for discussions, thus favoring a better interaction
and a sense of connection between the institution and
the students. This explanation clearly relates to a Tinto
interaction effect and is supported by the recent finding
of Williford and Lee (1997). These authors, using a
multivariate analysis of variance, show that the effects
of a class-size environment vanish when controlling for
the presence of a teaching assistant who permits feed-
back, knowing other students, personal recognition and
other forms of interaction. When a class size reaches
more than 110 students, the effect of an additional teach-
ing assistant (TA), if financially affordable, is less
important based on a mere material fact that, in our uni-
versity, an auditorium is required to handle any groups
of more than 110 students. These auditoriums are gener-
ally built to hold 150–500 students, thus creating a real
space “disconnection”between teachers and students that
is difficult to overcome by teaching assistants.
Although the TA argument provides a reasonable
explanation for the results, some limits to this interpret-
ation need to be expressed. By construction, we have one
class size per department or program. The problem is
therefore to control for the difficulty of material taught
or grading practice to distinguish the class-size effect
from a program effect. And, obviously, we cannot enter
the class-size variable and program dummies simul-
taneously in the regression because we have a perfect
collinearity problem: the class-size variable is a weighted
sum of the program dummies. Estimating the model with
the program dummies, the coefficients on these dummies
turn insignificant, while the coefficients (and their level
of statistical significance) on the other variables remain
the same as those estimated with the class-size variable
specification (see Table 3 in Appendix A). This is
expected because of the collinearity issue, but with the
more parsimonious and nonlinear class-size variable
specification, we are able to gain a little more insight
into this particular determinant of persistence.
13
With the data nonrandomly selected according to first-
semester university persistence, maximum likelihood
estimation of the bivariate probit model with sample
selection yields simultaneous estimates of the second-
13
In Table 4, the class size effect is apprehended with dumm-
ies for groups of less than 41 students, GR1 (the omitted
variable), GR2 are groups or departments with 41–100 students
and GR3 are groups with more than 100 students. Note that the
difficulty with this specification of the group effects is where
to cut the groups. We have, however, explored different possi-
bilities with basically the same results.
period decision including a correlation estimate between
the error terms of the two periods. The AGE variable
remains relatively significant and the coefficient of the
regional home base variable, REGION, is significantly
different from zero at the 10 percent level. A student
from the Montre
´al region, already adjusted to living in
a large metropolitan area and possibly still living with
his family, stands a greater chance of staying at the uni-
versity. This situation lowers the costs of experimenting
and favors a better economic and emotional environ-
ment. The PROGQ variable continues to be a strong
determinant of persistence, but the most statistically
influential variable is the university grade point average
obtained by the student after the first semester (UGPA1).
An academically successful first semester plays a major
role for a student in his or her decision to continue at the
university. Finally, we note the negative but insignificant
correlation coefficient estimate between the error terms.
For the first-period decision, the results for the restric-
ted sample confirm the importance of being a full-time
student, FLTIME, and the positive influence of smaller
class size (less than 80 students) in mandatory courses
(GMEAN, GMEAN2). AGE remains a statistically sig-
nificant variable at the 10 percent significance level. In
those more competitive academic sectors with entrance
quotas, being female (GENDER) increases the prob-
ability of persisting at the university. Students who have
attended a public CEGEP, PUBLIC, drop out more than
those graduating from a private CEGEP. The coefficient
estimate of ZSCORE is positive and statistically signifi-
cant at the 10 percent level. This result is coherent with
a positive effect on persistence for those having attended
a private CEGEP and the educational market signalling
effect of the Z-score system discussed above: if private
CEGEPs attract better-quality students, an average-qual-
ity high school student attending a public CEGEP will
obtain a better ZSCORE than if he or she had to compete
with more talented students of a private CEGEP. The
student’s“good”ZSCORE helps him to get into the pro-
gram where he remains an average-quality student with
lower academic preparation.
In the second-period choice, a high grade point aver-
age after the first semester is the most important and
almost the sole determinant of persistence at the univer-
sity. The student is able to confirm his level of ability
with respect to the chosen program within a single sem-
ester of study. All models of attrition recognize the
importance of academic performance. For Tinto’s stud-
ent integration model it is an indicator of academic inte-
gration; whereas for Bean’s student attrition model,
grades are an outcome resulting from academic experi-
ences and social psychological processes.
14
Being orig-
14
Cabrera, Nora, and Casta
˜neda (1993) have offered some
empirical support for those models.

482 C. Montmarquette et al. / Economics of Education Review 20 (2001) 475–484
inally from the Montreal region, closer to his or her fam-
ily, also improves the probability for a student continuing
in the same program after the first full academic year.
5. Conclusion
With a longitudinal data set, the statistical analysis
presented in this paper offers interesting results on the
determinants of university dropouts. The variables that
explain persistence (or early dropouts) are related to a
nontraditional class-size effect in the first-year manda-
tory courses taken by the student and to details particular
to the type of university program. After the first sem-
ester, a strong academic performance is the key element
in the decision to persist at the university. Although these
results are consistent with other modelling approaches to
dropout behavior, the experimental model offers a differ-
ent policy approach to the problem of student attrition.
For example, the ZSCORE variable was found to send
mixed signals to future university students. These mixed
signals enhance the need for more experimentation. In
attending university, the individual makes substantial
investment in time, but low tuition fees and various
Table 3
A statistical analysis of the determinants of university dropouts with program dummies
a
Full sample Restricted sample
Variable First period Second period First period Second period
Personal characteristics
GENDER 0.39322E⫺01 ⫺0.70941E⫺01 0.19533 (0.1280) ⫺0.92498E⫺01
(0.8897E⫺01) (0.6112E⫺01) (0.8420E⫺01)
AGE ⫺0.40197E⫺01* ⫺0.32362E⫺01* ⫺0.41984E⫺01** ⫺0.21436E⫺01
(0.1719E⫺01) (0.1397E⫺01) (0.2158E⫺01) (0.1793E⫺01)
ZSCORE ⫺0.30896E⫺01 –⫺0.32760E⫺02 (0.1052) –
(0.7577E⫺01)
UGPA1 –0.61764* (0.2757E⫺01) –0.91397* (0.5472E⫺01)
PUBLIC ⫺0.62715E⫺01 (0.1218) ⫺0.50781E⫺01 ⫺0.35732* (0.1804) ⫺0.99641E⫺01 (0.1162)
(0.8870E⫺01)
FLTIME 1.2079* (0.1343) 0.50350** (0.2626) 1.2123* (0.2022) 0.47490** (0.2601)
PROGQ 0.31401 (0.4336) 0.31541* (0.7018E⫺01) ––
Socioeconomic factors
MTONG ⫺0.42060E⫺01 (0.1757) 0.38562E⫺01 (0.1106) ⫺0.16219 (0.2727) 0.20205 (0.1458)
REGION 0.46714E⫺01 0.15718* (0.7041E⫺01) 0.48037E⫺01 (0.1338) 0.22862* (0.9268E⫺01)
(0.9878E⫺01)
Other statistics
Constant 5.8210 (0.3754E+05) ⫺0.82078** (0.4381) 5.0109 (0.2149E+05) ⫺1.7191* (0.5875)
r(1, 2) ⫺0.20304 (0.4564) ⫺0.65365 (0.4004)
Log of the ⫺1847.0 ⫺1059.1
likelihood function
a
Standard errors in parentheses. *Significantly different from zero at the 5 percnet level; **significantly different from zero at
the 10 percent level. Coefficient estimates for 30 program dummies (full sample) and 26 program dummies (restricted sample) are
not presented but available on request. Because many departments are of small size (we have excluded the very small ones) a near
collinearity problem with the constant is to be feared.
governmental financial support programs make this
experience a less expensive private decision. Or if Tinto
is correct the university should provide experiences that
engaged the student more effectively. Thus, the social
and private prices of accessing the university are perhaps
in need of being re-evaluated.
Acknowledgements
The authors thank the Universite
´de Montre
´al for
access to their data bank and members of the Bureau de
recherche institutionnelle, notably Yvon Pinel, for their
advice. Jean-Michel Cousineau and other colleagues
have offered interesting comments on an earlier version
of this paper. Comments by Stephen A. Hoenack were
very useful in the revision of this paper. The first author
gratefully acknowledges financial support from the
Social Sciences and Humanities Research Council of
Canada and the Que
´bec FCAR fund.

483C. Montmarquette et al. / Economics of Education Review 20 (2001) 475–484
Table 4
A statistical analysis of “The determinants of university dropouts”with GR1, GR2 and GR3
a
Full sample Restricted sample
Variable First period Second period First period Second period
Personal characteristics
GENDER 0.04007 (0.0707) ⫺0.07501 (0.0613) 0.2008* (0.0955) ⫺0.05954 (0.107)
AGE ⫺0.03772* (0.0142) ⫺0.03174** (0.0175) ⫺0.03114** (0.0182) ⫺0.02559 (0.0228)
ZSCORE 0.07046 (0.05720 –0.1347** (0.0741) –
UGPA1 –0.6148* (0.0279) –0.9560* (0.0425)
PUBLIC ⫺0.04424 (0.109) ⫺0.07282 (0.0878) ⫺0.3195* (0.161) ⫺0.1116 (0.129)
FLTIME 1.1444* (0.123) 0.5569 (0.524) 1.1878* (0.188) 0.7547 (0.563)
PROGQ 0.3627* (0.0772) 0.3069* (0.119) ––
Socioeconomic factors
MTONG ⫺0.08578 (0.139) 0.01813 (0.112) ⫺0.3407 (0.237) 0.1921 (0.173)
REGION 0.008974 (0.0823) 0.1340** (0.0693) 0.02129 (0.110) 0.2372* (0.0938)
Environmental variables
GR2 0.2197* (0.0883) - 0.2082** (0.122) –
GR3 0.1777 (0.120) - 0.1758 (0.180) –
Other statistics
Constant ⫺2.6739 (2.950) ⫺0.8219 (0.601) ⫺5.3525 (3.791) ⫺2.0754* (0.637)
r(1, 2) ⫺0.09889 (1.051) ⫺0.03172 (1.239)
Log of the ⫺1953.0 ⫺1094.5
likelihood function
a
Standard errors in parentheses. *Significantly different from zero at the 5 percent level; **significantly different from zero at
the 10 percent level.
Appendix A
Tables 3 and 4
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