The purpose of this paper was to apply the econometric models with qualitative variables in order to analyze two non academic behaviors at the level of the Romanian higher education system: cheating on the exams by copying or by direct or intermediary intervention at the professor

Andrei, Tudorel

Iacob, Andreea Iluzia E. S.

Stancu, Stelian

Teodorescu, Daniel

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
The Application of the Econometric
Models with Qualitative Variables in the
Analysis of the Non Academic Behaviors
at the Level of the Romanian Higher
Education System
Tudorel Andrei and Daniel Teodorescu and Andreea Iluzia E.
S. Iacob and Stelian Stancu
Academy of Economic Studies Bucharest, Institutional Planning &
Research, Emory University, Atlanta, USA
December 2007
Online at http://mpra.ub.uni-muenchen.de/6889/
MPRA Paper No. 6889, posted 26. January 2008 05:45 UTC
Prof. Tudorel ANDREI, PhD 
Academy of Economic Studies, Bucharest 
Daniel TEODORESCU, PhD 
Institutional Planning & Research, Emory University, Atlanta, SUA 
Associate Prof. Andreea Iluzia IACOB, PhD 
Academy of Economic Studies, Bucharest 
Prof. Stelian STANCU, PhD 
Academy of Economic Studies, Bucharest 
 
 
 
THE APPLICATION OF THE ECONOMETRIC MODELS WITH 
QUALITATIVE VARIABLES IN THE ANALYSIS OF THE NON 
ACADEMIC BEHAVIORS AT THE LEVEL OF THE ROMANIAN 
HIGHER EDUCATION SYSTEM1
 
The purpose of this paper was to apply the 
econometric models with qualitative variables in 
order to analyze two non academic behaviors at the level 
of the Romanian higher education system: cheating on 
the exams by copying or by direct or intermediary 
intervention at the professor. 
Key-words: econometrics, Logit Model, survey, 
sample, fraud. 
 
 
1. INTRODUCTION 
 
Romania, country of Eastern Europe, after the decision adopted at Helsinki 
in December 1999, began the negotiations to adhere at the European Union. In 
December 2004 it finished the negotiations to adhere at the European Union. Since 
January first, 2007 it became member of the European Union. 
The transition period generated a lot of important changes at the tertiary 
education system level. The process of reforms in the Romanian higher education 
system was accelerated after the signature of the treaty of Bologna. During the last 
16 years the number of the enrolled students registered a spectacular growth. If 
during 1990/1991 academic year were enrolled 192810 students, all in the tertiary 
education public institutions, during 2005/2006 academic year were enrolled 
                                                 
1 Research for this paper was supported by the excellence research project no. CEEX  
05-D8-65/10.11.2005 
Tudorel Andrei, Daniel Teodorescu, Andreea Iluzia Iacob, Stelian Stancu 
716464 students from which 513678 students followed the courses of the higher 
education public institutions. 
During this period, the ratio between the number of the pupils and the 
enrolled students decreased. Thus, if for 1990/1991 academic year the ratio was 
equal with 5,16, for 2005/2006 academic year the ratio was equal with 4,18. 
During this period the number of the students per 10000 inhabitants increased 
almost four times. 
In order to determine some characteristics of the higher education, in the 
University Center of Bucharest, during November 2005, was organized a research 
based on a statistical survey  
The objective of the research was the analysis of the academic behavior of 
the students and the professors, reported at the characteristics of the performances 
of the education process. 
The sample was stratified by field and year of study and included 1025 
students enrolled in day study programs at major state universities from Bucharest. 
The first-year students were not included in the study because of their limited 
experience in the field. The results were guaranteed with a 2% error.  
The structure of the students by year of study was as follows: second year - 
38.6%; third year -33.0%; fourth and fifth years - 28.4%. The distribution of the 
students by field of study was as follows: arts and sciences - 32.3%, technology - 
27.6%, economy - 22.2%, medicine - 6.7%, law - 5.5%, agriculture - 4.0% and 
physical training and sports - 1.8%.  
The obtained data at the sample level were used to analyze two non 
academic behaviors at higher education level: the fraud at the exam by copying or 
by the direct intervention or by intermediary at the professor.  
 
 
2. THE APPLICATION OF THE LOGIT MODEL IN ORDER TO 
ANALYZE THE FRAUD AT THE EXAMS BY COPYING THE 
EXAM 
 
 
In order to define the Logit Model it is considered that the exam fraud by 
copying the exam (y) is dependant on the following characteristics: the sex of the 
person (x1), the level of the corruption in the university determined by the behavior 
of the professors (x2), the level of professional preparation of a student which is 
defined by the time spent for study, on average, during the week (x3) and the 
appreciation of the students concerning the level of preparation of the colleagues 
(x4), the quality of the education activity at the university level, appreciated by the 
relevance of the courses (x5) and by the presence of the students at the courses (x6), 
the manner of spending the spare time outside the university campus taking 
account of the time spent working off-campus during a week (x7), and the 
 2 
The Application of the Econometric Models with Qualitative Variables in 
the Analysis of the Non Academic Behaviors at the Level of the Romanian 
Higher Education System 
extraprofessional activities (x8), the tendency to cheat on exams taking account of 
the practice to cheat on exams during college (x9). 
 
1. The dependent variable of the logit model expresses the student exam fraud by 
copying the exam from a colleague or by using other sources, excluding the 
situation in which one intervenes directly or by intermediary at the professor. 
Information was recorded with the answers given at the question: “Suppose that, 
for the moment, there is no chance to pass on a certain exam. In this situation 
would you try to copy the exam from a colleague or by using other hidden sources 
(cribs, manual etc.)? ”. The answer is defined as a binary variable. Thus, one allots 
value 1 if the answer of the student was “Yes” and 0 for the answer “No” or “I 
don’t know”. 
 
2. The independent variables of the logit model are: 
 A. The sex of the person 
 B. The level of the corruption in the university is determined by the 
behavior of the professors. The collection of information was carried out analyzing 
the answers at the following questions: “Did a professor asked for or accepted 
money from the students in exchange of a passing grade on exams?”, “Did a 
professor asked for or accepted money from the students to guarantee the 
promotion at the University admission exam?” and “Do you know a professor who 
asked the students to buy a book or a handbook published by him?”. Using these 
three sets of data was defined a new variable, calculated as an average of the values 
of these three characteristics granted by each student. Using this new variable can 
be measured this element of the corruption in the university educational system 
perceived by the students as being determined by the professors. 
 C. The level of professional preparation of the students, which is measured 
using the following variables: the time spent for individual study during the week 
and the appreciation of the students concerning the level of preparation of the 
colleagues.  
 D. The quality of the teaching activities in the universities is measured 
using the following variables: the relevance of the courses for the future profession; 
the presence at the courses and at the seminars, which is defined as an average of 
the answers of the students at the following questions: “During 2004/2005 
academic year, how often did you participate at the courses?” and “During 
2004/2005 academic year, how often did you participate at the 
seminars/laboratories?”. 
 E. The manner of spending time off-campus was measured using the 
following characteristics: the time spent working off-campus and the manner of 
spending the spare time which is defined as an average of three variables which 
characterize the time spent with the friends or the colleagues, the time spent for 
Internet surfing and the time spent to play video games or in another manner. 
F. The tendency to fraud the exam, consequence of the behavior of the 
current students during college. This variable is defined by the answers at the 
 3 
Tudorel Andrei, Daniel Teodorescu, Andreea Iluzia Iacob, Stelian Stancu 
question: “On your opinion, which is the proportion of the colleagues who used 
illegal methods during college to obtain higher grades?”. 
Using these variables will be defined the following linear probability 
model: 
 
      ii xaxaxaxaxaxaxaxaxaaY ε++++++++++= 9988776655443322110   (1) 
 
Where iε  represents the residual variable which quantifies the influence of 
other factors which can determine the intention of a student to cheat on exams. This 
variable is normally distributed with zero mean  2( (0, )).N σ
Using the registered values for the past variables will be estimated the 
parameters of the linear probability model and will result the following model: 
 
            (2) 9988776655443322110ˆ xaxaxaxaxaxaxaxaxaaYi +++++++++=
 
Where iY
)
 is estimating the probability that 1.iY =  By estimating this model 
we’ll determine: 
1. The sign and the estimated value of each parameter, specifying thus if one 
factor has a positive or negative contribution on exam fraud. Each coefficient 
shows with how much is modified the probability that  if an 
independent variable is modified by a unit, while the others are maintained 
constant. 
0,iY =
 
2. The probability that a particular student’ profile can or can’t determine the 
exam fraud. For example, if for a particular combination of factors we’ll 
obtain that 0.4,iY =
)
 then this one is estimating the probability that . 
While the observed values of the variable  are 0 or 1, the estimated values 
1iY =
iY
iY
)
are included between the two extreme values. 
 
In the case of the Logit Model, the distribution function which defines the 
probability ( 1i ip P y )= = is the logistic distribution function and is defined: 
 
0 1 1
*
0 1 1
0 1 1 0 1 1
[ ]
( 1) ( ) ( ( ))
( ) ( )
1
1 i p pi i
i i i i i i i p pi
i i p pi i i i p pi
a a x a x v
p P y P v v P v a a x a x
P a a x a x v F a a x a x v
e
ε
ε ε
− + + −
= = = > = > − + +
= < + + − = < + + −
=
+ L
L
L L i    (3) 
 
 
 
 4 
The Application of the Econometric Models with Qualitative Variables in 
the Analysis of the Non Academic Behaviors at the Level of the Romanian 
Higher Education System 
The distribution function can be also written in the equivalent form: 
 
0 1 1
0 1 1
[ ]
[ ]( 1) 1
i p pi i
i p pi i
a a x a x v
i i a a x a x v
ep P y
e
+ + −
+ + −= = = +
L
L             (4) 
 
The proprieties of this function are: 
1. In the conditions in which 0 1 1 0i p pi ia a x a x v+ + −L >
∞
∞
)
, the 
probability  The maximum value of  is 1 and it’s 
obtained for the situation in which is verified the condition 
 The  value of is equal with zero if 
the following condition is verified: 
Using this function are eliminated the 
situations in which the estimated values 
[0,1].ip ∈ ip
0 1 1 .i p pi ia a x a x v+ + − →L ip
0 1 1 .i p pi ia a x a x v+ + − → −L
( 0i iY P Y= =
)
 are not 
included in the interval [0, 1]. The logistic function is estimating the 
linear probability model. 
 
2. The distribution function is a symmetric one. From the relation (3) it 
results that:  ( ) 1 ( ) ( ).F x F x F x− = − =
 
3. A transformation of the model defined by the relation (3) allows us 
to write it in the same manner as the linear probability model defined 
in the relation (1): 
 
0 1 1ln .1
i
i p pi
i
p a a x a x
p i
ε⎛ ⎞ = + + +⎜ ⎟−⎝ ⎠ L              (5) 
 
In these conditions is obtained the following equality: 
 
( 1) ln
1
i
i
i
pP Y
p
⎛ ⎞= = ⎜ ⎟−⎝ ⎠
              (6) 
 
 
 
 
 
 
 
 
 
 5 
Tudorel Andrei, Daniel Teodorescu, Andreea Iluzia Iacob, Stelian Stancu 
The estimated results of the Logit Model and its characteristics are 
presented in the following table: 
 
The estimated results of the Logit Model and its characteristics in order to 
analyze the fraud at the exams by copying the exam 
Table 1 
Variable B S.E. Wald Sig. Exp (B) 
A. The sex of the person (x1) - 0,0261 0,191 1,867 0,172 0,770 
B. The level of the corruption 
in the university educational 
system (x2) 
0,203 0,089 5,237 0,022 1,225 
C. The level of preparation of 
the students      
C1. The individual study (x3) - 0,238 0,067 12,630 0,000 0,788 
C2. The evaluation of the 
students concerning the level of 
preparation of the colleagues 
(x4) 
0,183 0,110 2,759 0,097 1,201 
D. The quality of the education 
activities in the universities      
D1. The relevance of the 
courses (x5) 
- 0,224 0,087 6,605 0,010 0,799 
D2. The presence at the courses 
(x6) 
- 0,543 0,164 10,934 0,001 0,581 
E. The manner of spending the 
spare time      
E1. Time spent working-off 
campus (x7) 
- 0,133 0,044 9,067 0,003 0,876 
E2. Extraprofessional activities 
(x8) 
0,268 0,070 14,631 0,000 1,307 
F. The tendency to copy the 
exam during college (x9) 
0,268 0,094 3,434 0,064 1,190 
Constant 0,488 0,749 0,424 0,515 1,628 
 
In this case, the Logit Model is defined by:  
 ( )
( )
( )987654321
987654321
268,0268,0133,0543,0224,0183,0238,0203,00261,0488,0exp1
268,0268,0133,0543,0224,0183,0238,0203,00261,0488,0exp
xxxxxxxxx
xxxxxxxxx
copyingbyexamtheatfraudtheP
++−−−+−+−+
++−−−+−+−=
=
 
The characteristics which measure the time spent for individual study 
during the week, the relevance of the courses and the presence of the students at the 
courses determine a decrease of the probability of cheating on exams. The students 
 6 
The Application of the Econometric Models with Qualitative Variables in 
the Analysis of the Non Academic Behaviors at the Level of the Romanian 
Higher Education System 
which develop regularly an activity off-campus are less tempted to cheat on exams. 
On the contrary, extraprofessional activities like: the time spend with the friends, 
the time spent on Internet surfing or playing video games conduce the fraud at the 
exam. More the time spent by a student for these activities, larger will be its 
intention to cheat on exams. The absence of objectivity in the evaluation of the 
level of preparation of the colleagues determines a growth of the intention towards 
the fraud at the exams. The sex of the person has a reduced relevance in the 
decision to cheat on exams. 
 
 
3. THE APPLICATION OF THE LOGIT MODEL IN THE 
ANALYSIS OF THE FRAUD AT EXAMS BY INTERVENTION AT 
THE PROFESSOR 
 
The dependent variable is represented in this model by the intention of a 
student to cheat at the exam by direct intervention or by intermediary at the 
professor. For this variable one allots value 1 for the students who intervene at the 
professor in order to fraud the exam and 0 for the ones which do not intervene or 
do not know how to proceed.  
The independent variables of this model are: the sex of the person, the 
level of the corruption in the higher education system, the number of reported 
frauds at the direction of the university and the number of punished frauds. 
The estimated results of this Logit Model and its characteristics are 
presented in the following table: 
 
The estimation results of the Logit Model and its characteristics in order to 
analyze the fraud at the exam by intervention at the professor 
Table 2 
Variable B S.E. Wald Sig. Exp (B) 
The sex of the person (x1) - 0,672 0,359 3,498 0,061 0,511 
The level of the corruption in the 
higher education system (x2)
 0,298 0,162 3,384 0,066 1,348 
Number of reported frauds at the 
direction of the university (x10) 
0,494 0,217 5,184 0,023 1,639 
Number of punished frauds (x11) 0,582 0,280 4,312 0,038 1,789 
Constant - 2,799 0,807 12,034 0,001 0,061 
 
( )
( )111021
111021
582,0494,0298,0672,0799,2exp1
582,0494,0298,0672,0799,2exp
)int(
xxxx
xxxx
professortheaterventionbyexamtheatfraudtheP
+++−−+
+++−−=
=
 
 
 7 
Tudorel Andrei, Daniel Teodorescu, Andreea Iluzia Iacob, Stelian Stancu 
In this case, this model marks out a different behavior between the boys 
and girls in the attempt to cheat on exams by direct intervention or by intermediary. 
The other three variables included in the model have a negative influence on the 
level of the moral integrity in the university. The rarely report of the cases of 
corruption at the direction of the university and also the absence of severe 
measurements to punish the professors who encourage the fraud at the exams 
represent factors which lead to the reduction of moral integrity.  
 
 
REFERENCES 
 
[1] Andrei, T. (2004) – Statistică şi Econometrie, Ed. Economica, 
Bucureşti. 
[2] Bandura, A. (1986) - Social Foundations of Thought and Action: A 
Social Cognitive Theory, Prentice-Hall, Englewood Cliffs, NJ. 
[3] Gourieroux, C. (1984) - Econometrie des Variables Qualitatives, Ed. 
Economica, Paris. 
[4] Kramer, J. S. (1991) – The Logit Model for the Economists, Edward 
Arnold Publishers, London. 
[5] Maddala, S. (1983) – Limited Dependent and Qualitative Variables in 
Econometrics, Cambridge University Press, New York. 
[6] McCabe, D. L., Trevino, L. K. (1997) - Individual and Contextual 
Influences on Academic Dishonesty: A Multi-Campus Investigation, 
Research in Higher Education, 38(3), 379-396. 
[7] McCabe, D. L., Trevino, L. K. (1993) - Academic Dishonesty: 
Honour Codes and Other Contextual Influences, Journal of Higher 
Education, 64, 520-538, 1993. 
[8] Pulvers, K., Diekhoff, G. M. (1999) - The Relationship between 
Academic Dishonesty and College Classroom Environment, Research in 
Higher Education, 40, 487-498, 1999. 
[9] Whitley, B. E. Jr. (1998) - Factors Associated with Cheating among 
College Students: A Review, Research in Higher Education, 39(3), 235-274. 
 
 8 


The Application of the Econometric Models with Qualitative Variables in the Analysis of the Non Academic Behaviors at the Level of the Romanian Higher Education System

Munich RePEc Personal Archive

MPRAMunich Personal RePEc ArchiveThe Application of the EconometricModels with Qualitative Variables in theAnalysis of the Non Academic Behaviorsat the Level of the Romanian HigherEducation SystemTudorel Andrei and Daniel Teodorescu and Andreea Iluzia E.S. Iacob and Stelian StancuAcademy of Economic Studies Bucharest, Institutional Planning &Research, Emory University, Atlanta, USADecember 2007Online at http://mpra.ub.uni-muenchen.de/6889/MPRA Paper No. 6889, posted 26. January 2008 05:45 UTCProf. Tudorel ANDREI, PhD Academy of Economic Studies, Bucharest Daniel TEODORESCU, PhD Institutional Planning & Research, Emory University, Atlanta, SUA Associate Prof. Andreea Iluzia IACOB, PhD Academy of Economic Studies, Bucharest Prof. Stelian STANCU, PhD Academy of Economic Studies, Bucharest    THE APPLICATION OF THE ECONOMETRIC MODELS WITH QUALITATIVE VARIABLES IN THE ANALYSIS OF THE NON ACADEMIC BEHAVIORS AT THE LEVEL OF THE ROMANIAN HIGHER EDUCATION SYSTEM1 The purpose of this paper was to apply the econometric models with qualitative variables in order to analyze two non academic behaviors at the level of the Romanian higher education system: cheating on the exams by copying or by direct or intermediary intervention at the professor. Key-words: econometrics, Logit Model, survey, sample, fraud.   1. INTRODUCTION  Romania, country of Eastern Europe, after the decision adopted at Helsinki in December 1999, began the negotiations to adhere at the European Union. In December 2004 it finished the negotiations to adhere at the European Union. Since January first, 2007 it became member of the European Union. The transition period generated a lot of important changes at the tertiary education system level. The process of reforms in the Romanian higher education system was accelerated after the signature of the treaty of Bologna. During the last 16 years the number of the enrolled students registered a spectacular growth. If during 1990/1991 academic year were enrolled 192810 students, all in the tertiary education public institutions, during 2005/2006 academic year were enrolled                                                  1 Research for this paper was supported by the excellence research project no. CEEX  05-D8-65/10.11.2005 Tudorel Andrei, Daniel Teodorescu, Andreea Iluzia Iacob, Stelian Stancu 716464 students from which 513678 students followed the courses of the higher education public institutions. During this period, the ratio between the number of the pupils and the enrolled students decreased. Thus, if for 1990/1991 academic year the ratio was equal with 5,16, for 2005/2006 academic year the ratio was equal with 4,18. During this period the number of the students per 10000 inhabitants increased almost four times. In order to determine some characteristics of the higher education, in the University Center of Bucharest, during November 2005, was organized a research based on a statistical survey  The objective of the research was the analysis of the academic behavior of the students and the professors, reported at the characteristics of the performances of the education process. The sample was stratified by field and year of study and included 1025 students enrolled in day study programs at major state universities from Bucharest. The first-year students were not included in the study because of their limited experience in the field. The results were guaranteed with a 2% error.  The structure of the students by year of study was as follows: second year - 38.6%; third year -33.0%; fourth and fifth years - 28.4%. The distribution of the students by field of study was as follows: arts and sciences - 32.3%, technology - 27.6%, economy - 22.2%, medicine - 6.7%, law - 5.5%, agriculture - 4.0% and physical training and sports - 1.8%.  The obtained data at the sample level were used to analyze two non academic behaviors at higher education level: the fraud at the exam by copying or by the direct intervention or by intermediary at the professor.    2. THE APPLICATION OF THE LOGIT MODEL IN ORDER TO ANALYZE THE FRAUD AT THE EXAMS BY COPYING THE EXAM   In order to define the Logit Model it is considered that the exam fraud by copying the exam (y) is dependant on the following characteristics: the sex of the person (x1), the level of the corruption in the university determined by the behavior of the professors (x2), the level of professional preparation of a student which is defined by the time spent for study, on average, during the week (x3) and the appreciation of the students concerning the level of preparation of the colleagues (x4), the quality of the education activity at the university level, appreciated by the relevance of the courses (x5) and by the presence of the students at the courses (x6), the manner of spending the spare time outside the university campus taking account of the time spent working off-campus during a week (x7), and the  2 The Application of the Econometric Models with Qualitative Variables in the Analysis of the Non Academic Behaviors at the Level of the Romanian Higher Education System extraprofessional activities (x8), the tendency to cheat on exams taking account of the practice to cheat on exams during college (x9).  1. The dependent variable of the logit model expresses the student exam fraud by copying the exam from a colleague or by using other sources, excluding the situation in which one intervenes directly or by intermediary at the professor. Information was recorded with the answers given at the question: “Suppose that, for the moment, there is no chance to pass on a certain exam. In this situation would you try to copy the exam from a colleague or by using other hidden sources (cribs, manual etc.)? ”. The answer is defined as a binary variable. Thus, one allots value 1 if the answer of the student was “Yes” and 0 for the answer “No” or “I don’t know”.  2. The independent variables of the logit model are:  A. The sex of the person  B. The level of the corruption in the university is determined by the behavior of the professors. The collection of information was carried out analyzing the answers at the following questions: “Did a professor asked for or accepted money from the students in exchange of a passing grade on exams?”, “Did a professor asked for or accepted money from the students to guarantee the promotion at the University admission exam?” and “Do you know a professor who asked the students to buy a book or a handbook published by him?”. Using these three sets of data was defined a new variable, calculated as an average of the values of these three characteristics granted by each student. Using this new variable can be measured this element of the corruption in the university educational system perceived by the students as being determined by the professors.  C. The level of professional preparation of the students, which is measured using the following variables: the time spent for individual study during the week and the appreciation of the students concerning the level of preparation of the colleagues.   D. The quality of the teaching activities in the universities is measured using the following variables: the relevance of the courses for the future profession; the presence at the courses and at the seminars, which is defined as an average of the answers of the students at the following questions: “During 2004/2005 academic year, how often did you participate at the courses?” and “During 2004/2005 academic year, how often did you participate at the seminars/laboratories?”.  E. The manner of spending time off-campus was measured using the following characteristics: the time spent working off-campus and the manner of spending the spare time which is defined as an average of three variables which characterize the time spent with the friends or the colleagues, the time spent for Internet surfing and the time spent to play video games or in another manner. F. The tendency to fraud the exam, consequence of the behavior of the current students during college. This variable is defined by the answers at the  3 Tudorel Andrei, Daniel Teodorescu, Andreea Iluzia Iacob, Stelian Stancu question: “On your opinion, which is the proportion of the colleagues who used illegal methods during college to obtain higher grades?”. Using these variables will be defined the following linear probability model:        ii xaxaxaxaxaxaxaxaxaaY ε++++++++++= 9988776655443322110   (1)  Where iε  represents the residual variable which quantifies the influence of other factors which can determine the intention of a student to cheat on exams. This variable is normally distributed with zero mean  2( (0, )).N σUsing the registered values for the past variables will be estimated the parameters of the linear probability model and will result the following model:              (2) 9988776655443322110ˆ xaxaxaxaxaxaxaxaxaaYi +++++++++= Where iY) is estimating the probability that 1.iY =  By estimating this model we’ll determine: 1. The sign and the estimated value of each parameter, specifying thus if one factor has a positive or negative contribution on exam fraud. Each coefficient shows with how much is modified the probability that  if an independent variable is modified by a unit, while the others are maintained constant. 0,iY = 2. The probability that a particular student’ profile can or can’t determine the exam fraud. For example, if for a particular combination of factors we’ll obtain that 0.4,iY =) then this one is estimating the probability that . While the observed values of the variable  are 0 or 1, the estimated values 1iY =iYiY)are included between the two extreme values.  In the case of the Logit Model, the distribution function which defines the probability ( 1i ip P y )= = is the logistic distribution function and is defined:  0 1 1*0 1 10 1 1 0 1 1[ ]( 1) ( ) ( ( ))( ) ( )11 i p pi ii i i i i i i p pii i p pi i i i p pia a x a x vp P y P v v P v a a x a xP a a x a x v F a a x a x veεε ε− + + −= = = > = > − + += < + + − = < + + −=+ LLL L i    (3)     4 The Application of the Econometric Models with Qualitative Variables in the Analysis of the Non Academic Behaviors at the Level of the Romanian Higher Education System The distribution function can be also written in the equivalent form:  0 1 10 1 1[ ][ ]( 1) 1i p pi ii p pi ia a x a x vi i a a x a x vep P ye+ + −+ + −= = = +LL             (4)  The proprieties of this function are: 1. In the conditions in which 0 1 1 0i p pi ia a x a x v+ + −L >∞∞), the probability  The maximum value of  is 1 and it’s obtained for the situation in which is verified the condition  The  value of is equal with zero if the following condition is verified: Using this function are eliminated the situations in which the estimated values [0,1].ip ∈ ip0 1 1 .i p pi ia a x a x v+ + − →L ip0 1 1 .i p pi ia a x a x v+ + − → −L( 0i iY P Y= =) are not included in the interval [0, 1]. The logistic function is estimating the linear probability model.  2. The distribution function is a symmetric one. From the relation (3) it results that:  ( ) 1 ( ) ( ).F x F x F x− = − = 3. A transformation of the model defined by the relation (3) allows us to write it in the same manner as the linear probability model defined in the relation (1):  0 1 1ln .1ii p piip a a x a xp iε⎛ ⎞ = + + +⎜ ⎟−⎝ ⎠ L              (5)  In these conditions is obtained the following equality:  ( 1) ln1iiipP Yp⎛ ⎞= = ⎜ ⎟−⎝ ⎠              (6)           5 Tudorel Andrei, Daniel Teodorescu, Andreea Iluzia Iacob, Stelian Stancu The estimated results of the Logit Model and its characteristics are presented in the following table:  The estimated results of the Logit Model and its characteristics in order to analyze the fraud at the exams by copying the exam Table 1 Variable B S.E. Wald Sig. Exp (B) A. The sex of the person (x1) - 0,0261 0,191 1,867 0,172 0,770 B. The level of the corruption in the university educational system (x2) 0,203 0,089 5,237 0,022 1,225 C. The level of preparation of the students      C1. The individual study (x3) - 0,238 0,067 12,630 0,000 0,788 C2. The evaluation of the students concerning the level of preparation of the colleagues (x4) 0,183 0,110 2,759 0,097 1,201 D. The quality of the education activities in the universities      D1. The relevance of the courses (x5) - 0,224 0,087 6,605 0,010 0,799 D2. The presence at the courses (x6) - 0,543 0,164 10,934 0,001 0,581 E. The manner of spending the spare time      E1. Time spent working-off campus (x7) - 0,133 0,044 9,067 0,003 0,876 E2. Extraprofessional activities (x8) 0,268 0,070 14,631 0,000 1,307 F. The tendency to copy the exam during college (x9) 0,268 0,094 3,434 0,064 1,190 Constant 0,488 0,749 0,424 0,515 1,628  In this case, the Logit Model is defined by:   ( )( )( )987654321987654321268,0268,0133,0543,0224,0183,0238,0203,00261,0488,0exp1268,0268,0133,0543,0224,0183,0238,0203,00261,0488,0expxxxxxxxxxxxxxxxxxxcopyingbyexamtheatfraudtheP++−−−+−+−+++−−−+−+−== The characteristics which measure the time spent for individual study during the week, the relevance of the courses and the presence of the students at the courses determine a decrease of the probability of cheating on exams. The students  6 The Application of the Econometric Models with Qualitative Variables in the Analysis of the Non Academic Behaviors at the Level of the Romanian Higher Education System which develop regularly an activity off-campus are less tempted to cheat on exams. On the contrary, extraprofessional activities like: the time spend with the friends, the time spent on Internet surfing or playing video games conduce the fraud at the exam. More the time spent by a student for these activities, larger will be its intention to cheat on exams. The absence of objectivity in the evaluation of the level of preparation of the colleagues determines a growth of the intention towards the fraud at the exams. The sex of the person has a reduced relevance in the decision to cheat on exams.   3. THE APPLICATION OF THE LOGIT MODEL IN THE ANALYSIS OF THE FRAUD AT EXAMS BY INTERVENTION AT THE PROFESSOR  The dependent variable is represented in this model by the intention of a student to cheat at the exam by direct intervention or by intermediary at the professor. For this variable one allots value 1 for the students who intervene at the professor in order to fraud the exam and 0 for the ones which do not intervene or do not know how to proceed.  The independent variables of this model are: the sex of the person, the level of the corruption in the higher education system, the number of reported frauds at the direction of the university and the number of punished frauds. The estimated results of this Logit Model and its characteristics are presented in the following table:  The estimation results of the Logit Model and its characteristics in order to analyze the fraud at the exam by intervention at the professor Table 2 Variable B S.E. Wald Sig. Exp (B) The sex of the person (x1) - 0,672 0,359 3,498 0,061 0,511 The level of the corruption in the higher education system (x2) 0,298 0,162 3,384 0,066 1,348 Number of reported frauds at the direction of the university (x10) 0,494 0,217 5,184 0,023 1,639 Number of punished frauds (x11) 0,582 0,280 4,312 0,038 1,789 Constant - 2,799 0,807 12,034 0,001 0,061  ( )( )111021111021582,0494,0298,0672,0799,2exp1582,0494,0298,0672,0799,2exp)int(xxxxxxxxprofessortheaterventionbyexamtheatfraudtheP+++−−++++−−==   7 Tudorel Andrei, Daniel Teodorescu, Andreea Iluzia Iacob, Stelian Stancu In this case, this model marks out a different behavior between the boys and girls in the attempt to cheat on exams by direct intervention or by intermediary. The other three variables included in the model have a negative influence on the level of the moral integrity in the university. The rarely report of the cases of corruption at the direction of the university and also the absence of severe measurements to punish the professors who encourage the fraud at the exams represent factors which lead to the reduction of moral integrity.    REFERENCES  [1] Andrei, T. (2004) – Statistică şi Econometrie, Ed. Economica, Bucureşti. [2] Bandura, A. (1986) - Social Foundations of Thought and Action: A Social Cognitive Theory, Prentice-Hall, Englewood Cliffs, NJ. [3] Gourieroux, C. (1984) - Econometrie des Variables Qualitatives, Ed. Economica, Paris. [4] Kramer, J. S. (1991) – The Logit Model for the Economists, Edward Arnold Publishers, London. [5] Maddala, S. (1983) – Limited Dependent and Qualitative Variables in Econometrics, Cambridge University Press, New York. [6] McCabe, D. L., Trevino, L. K. (1997) - Individual and Contextual Influences on Academic Dishonesty: A Multi-Campus Investigation, Research in Higher Education, 38(3), 379-396. [7] McCabe, D. L., Trevino, L. K. (1993) - Academic Dishonesty: Honour Codes and Other Contextual Influences, Journal of Higher Education, 64, 520-538, 1993. [8] Pulvers, K., Diekhoff, G. M. (1999) - The Relationship between Academic Dishonesty and College Classroom Environment, Research in Higher Education, 40, 487-498, 1999. [9] Whitley, B. E. Jr. (1998) - Factors Associated with Cheating among College Students: A Review, Research in Higher Education, 39(3), 235-274.   8 

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The Application of the Econometric Models with Qualitative Variables in the Analysis of the Non Academic Behaviors at the Level of the Romanian Higher Education System

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