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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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