Directory UMM :Data Elmu:jurnal:E:Economics of Education Review:Vol20.Issue1.2001:
Economics of Education Review 20 (2001) 15–26
www.elsevier.com/locate/econedurev
Rational choice under unequal constraints: the example of
Belgian higher education
Denis Rochat
a,b,*, Jean-Luc Demeulemeester
caUniversity of Cergy-Pontoise, 33 Boulevard du Port, F-95011, Cergy-Pontoise Cedex, France bCREBM Brussels, 27 rue Medaets, B-1150 Brussels, Belgium
cDepartment of Public Management, CP 145-Universite´ Libre de Bruxelles, 19 avenue F. Roosevelt, B1050, Brussels, Belgium
Received 21 May 1997; accepted 22 February 1999
Abstract
The virtues of laisser faire in the sphere of educational choices appear these days more and more doubtful when one looks at the apparently irrational students preferences for fields in low demand on the job market. In this paper, we try to give empirical content to the thesis advanced by Mingat and Eicher (Mingat, A., Eicher, J.C., 1982. Higher education and employment markets in France, Higher Education 11, 211–220), who suggest that students do not only take expected economic returns into account when choosing a discipline, but also their mere chances of academic success. If one assumes that more remunerative orientations are also riskier, and that poorer students give a heavier weight to the risk-component than richer ones, then one can reconcily economic rationality with labour market mis-matches. Using a three-step methodology based on Lee’s work (Lee, L.F., 1983. Generalized econometric models with selectivity. Econometrica 51, 507–512), this is precisely what we find. We show that this result has important policy implications, as tending at equalizing opportunities will make poorer students less sensible to the risk component and more concerned with market needs.2001 Elsevier Science Ltd. All rights reserved.
JEL classification: I20; J24
Keywords: Chance of success; Equity; Efficiency; Labour market; Higher educational choices
1. Introduction
There is currently a very heated debate in Western Europe concerning both the efficiency (internal as well as external) and the equity of higher education systems. They are under heavy pressure to reform (in various Eur-opean countries such as the United Kingdom, Germany or France)1 due to their alleged inefficiency, and their
* Corresponding author. CREBM Brussels, 27 rue Medaets, B-1150 Brussels, Belgium.
E-mail address: [email protected] (D. Rochat).
1 See for example Economist (1997) for a general
dis-cussion, as well as Die Zeit, no 29, 9 July 1998.
0272-7757/01/$ - see front matter2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 7 2 - 7 7 5 7 ( 9 9 ) 0 0 0 4 6 - 1
inability to cope with the large-scale economic trans-formations of the day. Moreover, they are accused of being extremely costly to the general taxpayer (OECD, 1993a) while primarily benefiting the children of well-off families. This heavy burden on the Treasury is parti-cularly badly resented in a period of hard budgetary con-straints linked with the desire to achieve EMU within the prescribed agenda set up by the Treaty of Maastricht. Another criticism frequently addressed to higher edu-cation systems is that the huge associated financial cost is partly due to a vast amount of internal waste, linked with huge participation and concomitant failure and drop-out rates (OECD, 1993b). Too many youngsters are participating in university education (some authors even point out the dangers of over-education, Hartog and Oos-terbeek, 1988; Alba-Ramirez, 1993; Beneito et al., 1997)
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and at the same time participating in higher technical and vocational orientations (Oosterbeek & Webbink, 1997). The orientations most demanded by the economy (including also the engineering and computing sciences orientations at the university) are less frequently chosen than human and social sciences, although the latter do not offer many occupational opportunities (see the recent concerns expressed by the Report of the “Groupe de re´flexion sur l’e´ducation et la formation” to the European Commission in December 1996, p. 26). Therefore higher education systems are criticized for performing badly in providing the economy with the skills it needs (Glytsos, 1989), both quantitatively and qualitatively.
The latter element leads us to question the degree of economic rationality embodied in student choices, and therefore the suitability of a laisser faire system. If some authors are doubtful vis-a`-vis the rationality of students expectation formation mechanisms (see Manski, 1995), others point out to the necessity of integrating equity and efficiency considerations in order to properly evaluate the students behaviors. The inefficiencies observed on the educational and subsequently labour markets (mismatches between the skill supply and the market needs) should not be so hastily attributed to the irration-ality of the students. Indeed, the students might at the same time be perfectly rational and nevertheless decide to choose apparently low-return orientations (as Humani-ties, Arts or Education in continental Europe).2 The
weight of the social background of the students, in other words equity considerations, can partly explain appar-ently such “bad” orientation choices. In a pioneering paper, Mingat and Eicher (1982), drawing from the insights of the CAPM financial theory, assumed that stu-dents operate a trade-off between the risk and return components of the orientation choice. If one assumes that orientations with a higher rate of return (i.e. which are in demand on the labour market) are also more difficult, and that students coming from poorer socio-economic background (Mingat & Eicher, 1982) are also more risk-averse (i.e. they give a heavier weight to the risk compo-nent in their computations than wealthier students), than one should observe that less privilegiated students will choose less risky (i.e. less difficult or shorter) and there-fore also less remunerative orientations.3 The
inef-2 One should keep in mind that employers in some countries
(UK, Japan) rely much more on the relative reputation of insti-tutions rather than on the precise subject chosen by the student when evaluating prospective applicants for a job. In such a con-text, it might be better to get a degree in arts from a well-known institution than an engineering degree from a second-class uni-versity (see on this topic, Knapp, 1995, p. 130).
3 Besides Mingat and Eicher (1982), recent important
contri-butions were made by Mortenson (1990) and Altonji (1993). Mortenson (1990) notes, that low-income families may be more risk-averse and that the latter could explain their reluctance to
ficiencies observed on the labour markets could then be compatible with a rational individual behaviour (Oosterbeek & Webbink, 1997).4
Mutatis mutandis, one could advance a very similar explanation in terms of ability, another important resource constraining the students free choice of disci-plines. Some subjects might be simply less academically demanding, i.e. less difficult (or less abstract) than tech-nical ones. Students of lower ability might prefer such orientations rather than more demanding ones because they expect higher chances of success in such subjects. Here also this choice results from a risk-averse strategy, and an avoidance of more difficult subjects, i.e. riskier ones for less able students. In this line of thought, stu-dents avoid more rewarding orientations because they feel they are not sufficiently able to succeed.
The results of such kind of researches could be extremely important in terms of policy-making. If the thesis of Mingat and Eicher (1982) is right, it would be wiser for the State to try to limit as much as possible the weight of the social background of the students through some “corrective” measures (as positive discrimination). An educational policy aimed at increas-ing equity would also be the best means to increase efficiency in terms of the skills provision to the econ-omy. However, if the ability explanation is true, then the State could only improve upon the current state of affairs only as much as acquired ability is responsible for it (innate ability cannot be changed by assumption). The former is indeed partly conditioned by the social and cul-tural background of the students, and an increased invest-ment in primary and secondary education might be fruit-ful in alleviating the impact of a poorer family background.
This paper tries to provide some pieces of answer in this debate by evaluating the impact of expected chances of success in the students discipline choice process. Moreover, we will also try to take into account the role of socio-economic background versus ability in the choice behaviour of the students.
2. Empirical methodology
As already mentioned, we use in this article a three-step methodology based upon Heckman (1979), Lee
use loans to finance college. Altonji (1993) explores theoreti-cally the extent to which students make sequential decisions about whether to attend college, and once there, what field in which to major, and whether to drop out, based on uncertainties related to labor market returns, personal tastes, and abilities.
4 Mingat and Eicher (1982) give some descriptive statistics
on France confirming partly their assumptions. However, they provide no thorough econometric analysis.
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(1983) and Trost and Lee (1984), Lee (1983) and Trost & Lee (1984). The idea is to estimate the risk component of discipline choice process as the (a priori) probability of success for each student in every subject, and to test whether this variable influences or not the choice of orientation (by means of a conditional logit methodology), while also controlling for the future expected economic benefits (i.e. the return component in the discipline choice process). By an analysis of the behaviour of various groups of students, i.e. the poorest and the richest, we try to test for the validity of Mingat and Eicher’s main contentions, namely that the poorest students would pay more attention to the chances of suc-cess than the richest ones. We also try to take ability into account as a potential source of risk-averse behaviour by analysing the behaviour of both the brightest and the “dullest” students, in order to check whether the former (the latter) are indeed less (more) responsive to their expected chances of success when choosing a discipline. In order to account for a potential self-selection prob-lem associated with the fact that the probability of suc-cess can depend on the discipline chosen, we first esti-mate a multinomial logit model of orientation choice based on socio-demographic characteristics of the stu-dents in order to compute a self-selection variable (Heckman, 1979; Lee, 1983; Trost & Lee, 1984). The latter is introduced as an explanatory variable in a binary probit model explaining observed success and failure rates. The results of the latter estimations are used to forecast the probabilities of success of students in each of the alternative disciplines. Finally, a conditional logit model is tested to determine to which extent these a priori probabilities of success affect the choice of orien-tations, besides expected future economic benefits and length of studies (this variable might be interpreted both as another proxy for the risk component and as an indi-cator of the global financial cost necessary to obtain the final degree).
Formally, the first step consists in estimating the choice probability of an orientation (in a set of seven orientations, see later) by means of a multinomial logit procedure. In this step, we only consider socio-demo-graphic variables. The probability that an individual i, with the set of characteristics Yichooses the orientation j is given by the following expression:
Pij5 exp(aj9yi)
O
m
k51
exp(ak9yi)
j51,...m (1)
The aforementioned sample selection issue is treated following Lee’s (1983) work. In a polytomous choice model, the self-selection variables lijobtained for each
individual after a first step of multinomial logit might be written as follows:
lij5f(F−1(Pˆij))/(Pˆij) (2)
where Pˆij is the estimated probability that an individual i with the set of characteristics Yichooses the orientation j5,fis the standard normal density function and Fthe
standard normal cumulative function. This new variable is introduced as an explanatory variable in the second step which consists in estimating the probabilities of suc-cess in each of the six disciplines by means of a binary probit model. From the estimated coefficients, we can compute the probabilities of success in each of the six disciplines for all of the students in our sample.
These estimations of expected probabilities of success are based on actual success/failure rates for freshmen in the first year. In other words, we estimate students prob-abilities of success based on average socio-economic and demographic profile of successful students within each orientation. A shortcoming of such an approach is that we cannot disentangle within the determinants of chances of success between the part due to the peculiar socio-economic variables and the one linked with the general ability within a particular orientation. Following Willis and Rosen (1979), students might indeed select orientations on the basis of their absolute skill advan-tages. However, even if our procedure is indeed based upon the actual success rate, it nevertheless takes into account both the selection bias problem (i.e. the possible correlation between the choice for a specific discipline and the chances of success in it), as well as the impact of the socio-economic characteristics of the students on the probabilities of success. By this procedure, we obtain estimated coefficients on the various explanatory vari-ables which are partly sample-neutral and allow us to predict probabilities of success in each orientation, even those not actually chosen by the student.
Finally, the last step of the procedure consists in the estimation of a conditional logit model with the expected probability of success as well as characteristics related to each major. In such a model, the probability of student
i choosing major j is obtained from the following
equ-ation:
Pij5 exp(b9xij+d9Zj)
O
m
k51
exp(b9xik+d9Zj)
j51,...m (3)
where xij is the predicted probability of success in the jth orientation (j=1,...6) for student i and Zj is a vector
of characteristics6of discipline j. The impact of the
vari-able xij is assumed to be constant across alternatives.
This coefficientbhas an expected positive sign, i.e. that an individual should choose the discipline where he has
5 Estimated by means of Eq. (1).
6 Wage at entry-level for young graduates, a measure of
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Table 1
Definition of orientations
Orientation 1 Short cycle (2 to 3 years) in Economic and Social Sciences Orientation 2 Short cycle (2 to 3 years) in Paramedical studies
Orientation 3 Short cycle (2 to 3 years) in Artistic and Pedagogical studies
Orientation 4 Long cycle curricula (4 years) or university degree (4 to 7 years) in Natural and Medical Sciences Orientation 5 Long cycle curricula (4 years) or university degree (5 years) in Engineering
Orientation 6 Long cycle curricula (4 years) or university degree (5 years) in Business, Economics and Social Sciences Orientation 7 Long cycle curricula (4 years) or university degree (4 to 5 years) in Humanities and Psychology
the highest probability of success, given his socio-econ-omic background. This methodology has so far only been applied by Cannings et al. (1993) to a quite close topic
(namely the major choices in undergraduate
concentrations).
3. Data and model specification
Our microdata sample consists in 641 freshmen7
enrolled at Belgian (French-speaking) higher education institutions either in 1992 or 1993 (including univer-sities, long and short cycle non-university higher edu-cation institutions). This data set comes from the PSBH– CREPP (1993–95) survey of the French Community of Belgium. Of those 641 students, 220 are enrolled in short cycle curricula and 421 enrolled in long cycle and uni-versity curricula. We consider the students enrolling in 1992 and 1993 as belonging to a common sample.8We
classified the students in seven orientations (three for the short-cycle curricula and four for the long-cycle curric-ula and university orientations) on the basis of the insti-tutional peculiarities of the Belgian system and of the characteristics of the orientations (as well as the logical concomitant academic requirements). The list and defi-nition of these orientations are presented in Table 1.
Our students sample has the following characteristics: it is made up of 48.36% of men, 45.55% of students aged more than 18 when entering higher education,988.3% of
Belgian students. 26.70% of the students benefit either from a tuition fees reduction or of a scholarship, 43.7% come from households with net monthly revenues of 100,000 Belgian francs or more, 55.9% have father
hold-7 i.e. students who began their higher education studies. 8 Their number in some specific orientations are indeed too
small to allow for specific estimation on each year separately. Given the fact that exogenous factors do not change a lot from one year to another, we think that this choice does not incur a great cost.
9 31.4% of all students have repeated at least one year while
in high school and 34.8% of all students followed other higher education curricula prior their entry in their studies (only one quarter of them completed them).
ing higher education degree (and among them, 52.5% university degree), 51.1% have mother holding higher education degree (and among them only 25.9% univer-sity degree), 19.3% of the students have fathers holding “e´lite” occupation (see below), 47.4% of students come from households where both parents work, and 23.6% come from separate couples (divorce) or other atypical situations (dead parent, for example). Finally, 18.9% of the students work while studying and 34.5% live on their own. The average success rate is 65.91% in short-cycle curricula and 48% in long cycle curricula and univer-sity orientations.
As far as model specification is concerned, we present the set of socio-demographic and ascriptive explanatory variables used in the first two stages of the analysis in Table 2. The assignment procedure of the variables between the multinomial equation explaining choice of orientation and binary probit equation explaining aca-demic success relies upon careful examination of exist-ing literature on the topic (see Duru-Bellat and Mexist-ingat, 1993, for a survey on the individual and contextual deter-minants of orientation choices and Haveman and Wolfe, 1995 for a survey on students’ attainments) as well as compliance to identification requirements. This led us to retain some common factors in the two estimation steps on a priori grounds (age, gender, nationality, and vari-ables related to parental education and occupation) as well as some specific explanatory variables to each topic investigated (see list of variables in Table 2 below). The results of the third step are however quite invariant to minor specification changes made at these two pre-vious steps.
In the last step of the estimations (conditional logit), we included three more variables besides the estimated probability of success. The first one characterizes the entrance salary by discipline.10These data are available
for civil servants with short cycle higher education degree and with four years of university education in
10 Berger (1988) asserts that the variable to consider is the
expected life-cycle earnings stream rather than the entry-level salary. However, we believe that the latter correctly reflects the future hierarchy of wages.
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Table 2
List of explanatory variables and assignment of dummy variables
MNL Binary
estimations probit
Variable Dummy assignment for estimation
orientation for academic choice success
Gender 1 if male, 0 otherwise X X
Age 1 if 19 or more when entering X X
Nationality 1 if Belgian, 0 otherwise X X
Latin 1 if Latin while in high school X
Mathematics 1 if 6 h/week math or more X
Single parent family 1 if so, 0 otherwise X X
Father’s education 1 if university (probit) or higher education (MNL), 0 otherwise X X Mother’s education 1 if university (probit) or higher education (MNL), 0 otherwise X X
1 if father holds an “e´lite” occupation, i.e. top manager or civil
Father with “Elite” occupation X X
servant, or professional
Both parents work 1 if both parents work, 0 otherwise X X
1 if net monthly household’s income$100,000 Belgian francs, 0
Household’s income X
otherwise
Repetition during high school 1 if at least one year repeated while in high school, 0 otherwise X Prior studies 1 if prior studies (not necessarily completed), 0 otherwise X
Number of siblings number of siblings X
Change in living arrangements 1 if leaving parental home, 0 otherwise X Scholarship 1 if tuition fees reductions or holding a scholarship, 0 otherwise X
Job while studying 1 if working while studying, 0 otherwise X
More aged due to prior studies 1 if yes, 0 otherwise X
More aged due to repetitions 1 if yes, 0 otherwise X
humanities and natural sciences (Source: Moniteur Belge). They are also available for employees of the private sectors graduated from university: Business Schools (Source: Union des Inge´nieurs Commerciaux Solvay), Engineering (Source: FABI, Fe´de´ration Royale d’Associations Belges d’inge´nieurs Civils) and various Professions (Physicians and Lawyers; Source: MAKLU, Maastricht).11We expect that students will be drawn to
more remunerative orientations, everything else held
11 The relevance of such data deserves some comments. On
the one hand, the knowledge of students about their future earn-ings might be quite partial when entering the university. Betts (1995) showed indeed that students learn about the labor market over time and that their knowledge is basically limited to their field of study. On the other hand, even if students may hold a considerable degree of information about the labour market, the extent of its influence in structuring students preferences is at least open to question. For example, in a survey among US students, only a small proportion (16% in his survey) of them consider money as a very important factor in their choice of discipline (Freeman, 1989). Following this idea, one could argue that expected economic benefits mostly explain marginal changes among discipline choices from one year to another. Finally, even if students are influenced by labour market infor-mations, they may misuse this flow of informations (see Man-ski, 1995).
constant. It is true that some authors have pointed out that initial working conditions (as initial earnings) were less important than the lifetime expected conditions in explaining discipline choices (see Berger, 1988, for the importance of the relative present value of the predicted future earnings by subject). However, precise measure of long-term perspectives or career opportunities (as earnings stream) depend critically on very specific assumptions (earnings growth equation as in Willis and Rosen, 1979,12 assumptions concerning the nature of
expectations, etc...). As Oosterbeek and Webbink (1997), we do not include such forward-looking measures. This is mainly because we only have data on wages for groups of disciplines and not for each individuals having fol-lowed an orientation. And it would be quite risky to con-sider estimated lifetime earnings per discipline as good proxies given the very long run nature of educational
12 In their paper, Willis and Rosen (1979) model the choice
of whether or not to attend college with a probit model. For those who went to college and for those who did not, separate earnings equations and earnings growth equations are estimated to impute the expected earnings gain from college as an explanatory variable in the college choice equation. They find that a larger expected earnings gain leads to a higher probability to attend college.
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investments. Proxying lifetime earnings prospects into the educational choice equation does not mean that our model is at odds with the human capital framework. Indeed age-earning profiles show that starting salaries at least partially reflect future earning differentials (see Woodhall, 1987; Demeulemeester, 1995 for evidence on the Belgian labour market).
We also introduced a measure of the easiness of inser-tion into the labour market for young graduates by orien-tation.13These statistics were taken from
Demeulemees-ter and Rochat (1995). This measure might be seen as a complement to our measure of expected future benefits (besides wage). Ceteris paribus, we expect that students will prefer orientations whose graduates are perceived to insert more easily on the labour market. Finally, we also introduced the legal minimum length of studies to get the final degree. This will allow us to take into account the risk linked with the increased length of studies, as well as the direct and indirect costs of studies. We expect the latter to be deterrent.
4. Empirical results
The first part of the analysis is a multinomial logit estimation of discipline choice, where explanatory vari-ables are only of socio-demographic and ascriptive nat-ure. The results are presented in Table 3 below. They have to be interpreted with reference to the first orien-tation, i.e. “short cycle economic and social vocational
non universitary higher education”. The latter
encompasses various types of studies, as accountancy, computer sciences, social assistant and is quite represen-tative of the basic, average clerk worker in Belgium (the lower stratum of the middle class). Our findings clearly highlight the role of variables such as age (negative and significative impact in all orientations but the second, suggesting that the older the student, the less likely he will choose lengthier orientations as university education) and gender (men typically choose less fre-quently short cycle orientations of a non-economic nat-ure, and prefer engineering and technical subjects). These results are perfectly in line with the theoretical results obtained by the investment in human capital literature in a life-cycle perspective (Ben-Porath, 1967). One can also note the influence of father holding an “e´lite” occupation14(as the professions, high ranked civil
13 These statistics are based on the number of graduates
rela-tive the number of unemployed in the same field. Both the entry salary and easiness of insertion are calculated per discipline from the aforementioned sources whereas probabilities of suc-cess by discipline are measured at individual levels.
14 This variable can also proxy the social capital available to
the student.
servants or top manager in the private sector) on students choosing engineering or business-related fields (law, economics, business...) rather than short cycle economic curricula. Similarly, higher parental incomes (possibly linked with positions in the business or legal spheres) favour the choice of Economics and Business as well as Legal orientations. The two latter results might suggest a possible link between specific parental occupation and students orientation choices. Finally, parental education (proxied by mother or father holding higher education degrees) seems also to favour the choice of long-cycle social, economic, legal and literary orientations over short cycle economic ones. All these effects suggest the pertinence of the role/models approach developed by sociologists and development psychologists, as well as of human capital investment arguments (parental edu-cation or profession proxying for a higher income and less severe budget constraints enabling the students to choose longer or riskier studies, see Becker, 1967).
The type of curriculum followed while in high school also influences the choice orientation, in the sense that graduates from “math-intensive” sections typically prefer scientific, medical, engineering or economic subjects at university over short-run economic cycles, while the same is true for “classics-intensive” graduates in literary orientations of the university.15 Shortly stated, these
results, besides the role of gender (linked with the role models approach and the assignment of tasks between men and women) and age, highlight the influence of prior experiences and models (type of curriculum fol-lowed while in high school, influence of parental sphere of activity) on the choice of disciplines made when entering university.
The second part of the analysis aims at ascertaining the main contributive factors of success in first year of post-compulsory education in each of the seven retained orientations, after a correction for the potential selection bias. The results are presented in Table 4 below. Some variables are significant in the long-cycle and university education orientations only. This is the case for the vari-able accounting for age. Being more aged reduces the probability of success in Natural and Medical Sciences, Engineering and Economics and Business orientations. This suggests the role of the depreciation of human capi-tal in disciplines which heavily rely on the mathematical
15 There are no entry requirements for the technical studies
in Belgium, except for the narrow segment of engineering at universities. The students have to pass an entrance examination based upon prior knowledge of mathematics. Students coming from “math-intensive” sections in high school have higher chances of success, but nothing impedes the students from other sections to take the examination. Very often, however, these students take a complementary year devoted especially to math-ematics.
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Table 3
The determinants of educational choices: MNL estimations
n=641 Orientationa
Variable 2/1 3/1 4/1 5/1 6/1 7/1
Coeff t-stat Coeff t-stat Coeff t-stat Coeff t-stat Coeff t-stat Coeff t-stat
Constant 20.353 20.62 0.260 0.45 20.227 20.39 21.880 22.57** 0.276 0.57 0.740 1.48
Gender 21.440 23.94* 20.703 21.96** 20.042 20.13 2.390 4.49* 0.007 0.03 20.344 21.07
Age 0.637 1.65*** 20.976 22.64* 21.530 24.59* 21.730 24.45* 21.240 24.03* 21.080 23.19*
Nationality 20.515 21.16 20.206 20.42 0.441 0.89 20.197 20.38 20.170 20.42 21.046 22.60*
Latin 0.591 1.33 0.035 0.07 0.006 0.02 20.892 21.57 0.550 1.43 0.828 2.06**
Mathematics 0.559 1.27 0.534 1.19 1.022 2.67* 1.627 3.93* 0.980 2.68* 0.345 0.83
Single parent family 0.351 0.95 20.291 20.70 0.059 0.17 20.390 20.89 0.028 0.08 20.129 20.35 Father’s education 0.394 1.04 20.027 20.07 0.457 1.28 0.551 1.30 0.436 1.31 0.710 1.95***
Mother’s education 0.347 0.88 0.239 0.59 0.467 1.29 0.277 0.64 0.558 1.66*** 0.651 1.77***
Father with “Elite” occupation 20.279 20.45 1.027 1.95*** 0.572 1.17 1.107 2.13** 0.930 2.08** 0.736 1.54
Both parents work 0.138 0.38 0.601 1.59 20.159 20.47 20.193 20.49 20.340 21.09 20.244 20.72 Household’s income 20.177 20.44 20.528 21.24 0.311 0.85 0.146 0.34 0.695 2.05** 0.131 0.35
Log likelihood at convergence 21068.6
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Table 4
Determinants of success by orientation: empirical resultsa
Orientation 1 Orientation 2 Orientation 3 Orientation 4 Orientation 5 Orientation 6 Orientation 7 Variable
(n=90) (n=70) (n=60) (n=102) (n=65) (n=157) (n=97) Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat
Constant 22.02 22.48** 1.701 2.03** 22.206 21.30 21.37 20.92 5.537 1.64*** 0.25 0.27 22.796 23.19*
Age 0.72 1.31 - – – – 22.51 22.17** 22.174 22.61** 21.55 23.99* – –
Gender 20.007 20.02 0.875 1.51 21.539 21.95***20.141 20.41 23.962 21.45 20.337 21.19 20.393 20.91
Repetition during high school 20.324 20.81 20.202 20.53 – – – – 0.937 0.76 – – 1.751 1.45 Prior studies 20.694 20.70 0.618 0.59 1.796 1.45 – – – – 0.61 1.11 20.206 20.27 Nationality 1.557 3.23* 20.428 20.74 2.741 1.86*** 20.31 20.39 22.33 21.81***20.43 21.10 2.056 3.72*
Number of Siblings 20.066 20.45 20.31 22.60* 20.615 22.16** 0.048 0.39 20.095 20.32 20.055 20.56 0.027 0.16
Change in living arrangements 20.5 21.36 20.43 21.01 2.748 1.61 0.098 0.29 20.539 20.66 0.247 0.86 0.534 1.42 Scholarship 1.061 2.53** 0.539 1.10 2 2 0.059 0.14 2.47 2.33** 0.367 1.18 1.389 2.79*
Job while studying 20.23 20.56 21.163 22.37** 1.021 1.25 20.59 21.22 20.53 20.64 20.276 20.74 20.745 21.51
Single parent family 20.6 21.43 20.213 20.53 2 2 20.089 20.22 20.3 20.32 20.59 21.87***20.712 21.43
Father’s education (university) 0.56 0.87 0.890 1.51 2 2 1.33 3.68* 2.67 3.18* 0.105 0.35 20.085 20.20
Mother’s education (university) – – 20.729 20.71 1.481 1.23 – – – – 1.172 4.07* 2.367 4.47*
Father with “Elite” occupation 20.53 20.66 0.304 0.31 20.444 20.32 20.53 21.07 0.754 0.83 0.396 1.23 0.211 0.49 Both parents work 0.637 1.80*** 20.278 20.68 0.362 0.53 20.194 20.54 1.145 1.31 0.193 0.75 20.5 20.97
More aged due to prior studies 0.954 0.91 20.263 20.24 20.962 20.71 1.139 1.22 – – 0.064 0.09 0.021 0.03 More aged due to repetitions – – – – – – 0.561 0.63 21.49 20.90 – – 22.743 22.04**
Selection variable 20.786 20.95 20.042 20.06 20.889 20.56 22.23 21.08 0.924 0.92 20.445 20.24 21.732 21.55 Log likelihood at convergence 245.81 235.30 213.13 241.41 213.59 274.10 235.54 Percentage correct predictions 74.44% 74.28% 88.33% 82.35% 90.76% 74.52% 81.44%
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and scientific prior knowledge acquired while in high school (Ben-Porath, 1967).
Parental education seems also to foster academic suc-cess in long-cycle and university orientations. Typically, having father holding university degree promotes success in scientific orientations as Medical and Natural Sciences or Engineering while having mother with university degree seems to foster the chances of success in more literary subjects (Law, Social sciences and Humanities) where a good command of the language is essential. Lei-bowitz (1974) showed indeed the essential role of the mother in transmitting verbal skills and literacy. The lat-ter effect relating to the importance of maslat-tering the mother tongue, may also partially explain why being Belgian increases the probability of success in Econ-omic, Social, Pedagogical and Artistic short cycles as well as in the Humanities orientation of the university. The negative impact of being more aged due to rep-etitions while in high school on success in Humanities might also be partially explained by a common factor, namely a lack of a good command of his own language (see for instance, Ribar, 1993).
Our results also highlight the effect of some variables in some peculiar orientations. For instance, the family size as well as the fact of working while studying are both found to exert a negative effect on the probability of success (in two orientations for family size16 and
one — at least at the 5% level — for a job market partici-pation during studies). The sign of the coefficient found (in some orientations) for the variable accounting for the matrimonial status of the student’s parents seems to be in line with the idea that having two parents in a family foster normal personality development (Seltzer, 1994).17
The sign of the coefficient found (in some orientations) for the variable accounting for the fact that both parent work can be interpreted in a “working mother perspec-tive” where increased parental income might outweigh the reduction in students care time (Hetherington et al., 1983). Finally, coming from a poorer background — and for this reason obtaining a scholarship — seems to play a rather positive role on success in at least three orien-tations. This result might be explained through the motivational lines of reasoning of Tinto (1975, 1987) if one considers the concession of a scholarship as a form of contract.18
16 This result illustrates the idea of a reduced transfer of
human capital on each children (Hanushek, 1992) due to time constraints (see, Becker, 1965).
17 The presence of two parents might strengthen parental
con-trol and monitoring, and weaken thereby the potential adverse influence of other role models.
18 The variables accounting for the professional position of
student’s father, change in student’s living arrangements or pre-vious higher education studies made before starting current cur-riculum were found to play a significant role in explaining aca-demic success.
We now turn to the last step of the analysis which should enable us to ascertain the validity of Mingat and Eicher (1982) thesis concerning the relative weights given by students to risk and return components in the orientation choice process. The results of the estimated conditional logit model are presented in Table 5 below. We test for the significativity of (a priori) probability of success on the orientation, i.e. whether prospective stu-dents tend to choose disciplines where they have the highest probabilities of success given their socio-demo-graphic and ascriptive characteristics — while con-trolling for length of studies and expected economic returns (wage and insertion). For the complete sample of 641 students, it seems indeed that youngsters pay atten-tion not only to expected economic benefits, but also to the length of studies and the mere probability of suc-ceeding in the chosen orientation. In this sense, the mod-elling approach of Mingat and Eicher (1982) seems
parti-cularly suited to the actual behaviour of the
prospective students.
When one concentrates on the poorest students (i.e. the 171 students holding a scholarship), one is indeed confronted with a decisional structure where they are more risk-averse as they have less financial wealth and are therefore less inclined to take risk. Indeed expected chances of success receives a significant weight, while this is not the case for wage (or length of study). The only economic reward which seems to interest those stu-dents is the (expected) greater ease of entry on the labour market (insertion). These results perfectly match our theoretical a priori expectations and are even reinforced by the results found for the wealthiest students of the sample. Indeed, the richest students (defined as those coming from household with high level of income and with father holding university degree) have a very orig-inal choice behaviour, in the sense that they seem to fol-low just their own preferences. They do not appear to be sensitive to either the expected chances of success or the economic benefits linked with their orientation choice.19
We also try to test whether ability could be the source of the risk-averse behaviour of the students. We therefore turn to the case of the brightest students (i.e. those with the ex ante highest chances of success in all the disciplines). One is struck by their keen interest in the financial benefits of their educational investment: they give heavy weight to wage. However, as expected, they do not seem to pay much attention to their expected chances of success. This is quite intuitively appealing as such event — failure — is quite improbable for them, whathever their choice. And, ceteris paribus, they are also attracted in shorter studies. Finally, when one con-centrates on the “dullest” students, i.e. those with the
19 This sub-sample of students is only made of university
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Table 5
Effect of expected success ratea
Full sample Top 10% of Top 15% of Bottom 10% of Bottom 15% of Scholarship Wealthier students (n=614) studentsb studentsb studentsc studentsc students (n=171)d (n=113)e
Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat
Expected success rate 0.494 3.86* 20.146 20.257 0.025 0.06 20.050 20.08 0.191 0.412 0.626 2.52** 20.073 20.191
Wage (in BFR) 0.36E25 3.69* 0.812E-5 2.81* 0.748E253.13* 0.206E244.75* 0.228E24 5.33* 0.214E-5 1.11 20.75E-7 20.039
Graduates insertion on the labour
0.0084 1.636*** 0.0172 0.96 0.00432 0.30 0.056 2.20** 0.041 1.99** 0.0162 1.74*** 0.00203 0.159
market
Length of studies (in Years) 20.751 23.687* 21.723 22.13** 21.388 22.69* 25.647 26.03* 25.826 26.88* 20.563 21.38 20.308 21.04
Log likelihood at convergence 21227.49 2120.29 2175.70 285.86 2128.57 2326.37 2155.76
a *significant at 1% level,**at 5% level and***at 10% level.
b The 10% or 15% of students who have an expected probability of success above a common threshold across all disciplines. c The 10 and 15% of students who have the lowest expected probabilities of success in each orientation.
d Students whose household’s revenue is such (low) that they benefit from a governmental financial aid.
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lowest probabilities of success in every discipline, one is also struck by their interest in the expected economic benefits as wage and ease of insertion. However, they do not seem to pay much attention to their expected chances of success which are low in any cases. Those results seem to indicate that ability may be less important than the socio-economic background in explaining a risk-averse behaviour, with the related avoidance of more dif-ficult but more remunerative (and demanded) orien-tations.
Our results tend to confirm those of Cannings et al. (1993) although ours are obtained within a generalized structure allowing us to jointly test for the importance of ex ante probability of success and expected economic benefits. Cannings et al. (1993) found that the choice of college concentration depends on the perceived prob-ability of success in a particular concentration for all of the students. Similarly to our own findings they put for-wards that brightest students do not pay attention to their perceived probability of success. However, contrarily to our results and quite astonishingly, they find that stu-dents coming from high-income families appear to be more risk-averse in their choice of major than students from low-income family.
Globally, the overall picture seems to support quite well Mingat and Eicher (1982) theoretical contentions, namely the fact that students do take into account two dimensions of their prospective educational choice (economic returns and a priori chances of success), and that poorest students give a heavier weight to the risk component. However, it might also be true that less priv-ilegiated students tend to avoid disciplines where the post-studies performance requires more social capital (Coleman, 1988). But we concentrate on the perform-ance during higher education studies, and in such a con-text we have already tried to assess the impact of those variables on the probabilities of success across orien-tations.
5. Concluding remarks
In this paper, we addressed the impact of (expected) success rates on the higher education orientation choice process, besides mere expected economic returns. We applied a classical three-step methodology on a sample of freshmen enrolled at Belgian (french-speaking) higher education institutions in 1992 and 1993. Globally, our results seems to support quite well Mingat and Eicher (1982) theoretical contentions, namely the fact that stu-dents do take into account two dimensions of their pro-spective educational choice (economic returns and a priori chances of success), and that poorest students (more than the less able ones) give a heavier weight to the risk component. Such results should lead us to ques-tion the relevance of the laisser faire soluques-tion prevailing today as far as higher educational choices are concerned.
If one accepts the idea that the apparently unwise choices made by students from poorer background for less demanded educational orientations are in fact the results of a rational decison process under severe socio-economic constraints, one could more easily accept the idea that interventionism would promote both efficiency and equity. By some kind of affirmative action or posi-tive discrimination (Evetts, 1976), one can restore equal-ity of educational opportunequal-ity. The objective would be that students from poorer background would not be impeded to choose lengthier or riskier orientations because of environmental constraints. One can hope that students will therefore pay more attention to expected economic returns and that labour market imbalances would be reduced. In this sense, one would achieve more efficiency as well as more equity. The concrete measures have to be discussed, but it does not seem that the current debates focusing on the relevance of some quantitative barriers to entry would promote economic efficiency.
Acknowledgements
We would like to thank K. Mayhew, J. Krishnakumar and A. de Palma for helpful comments, as well as the Wiener—Anspach Foundation Brussels for its financial support.
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Variable 2/1 3/1 4/1 5/1 6/1 7/1
Coeff t-stat Coeff t-stat Coeff t-stat Coeff t-stat Coeff t-stat Coeff t-stat
Constant 20.353 20.62 0.260 0.45 20.227 20.39 21.880 22.57** 0.276 0.57 0.740 1.48
Gender 21.440 23.94* 20.703 21.96** 20.042 20.13 2.390 4.49* 0.007 0.03 20.344 21.07
Age 0.637 1.65*** 20.976 22.64* 21.530 24.59* 21.730 24.45* 21.240 24.03* 21.080 23.19*
Nationality 20.515 21.16 20.206 20.42 0.441 0.89 20.197 20.38 20.170 20.42 21.046 22.60*
Latin 0.591 1.33 0.035 0.07 0.006 0.02 20.892 21.57 0.550 1.43 0.828 2.06**
Mathematics 0.559 1.27 0.534 1.19 1.022 2.67* 1.627 3.93* 0.980 2.68* 0.345 0.83
Single parent family 0.351 0.95 20.291 20.70 0.059 0.17 20.390 20.89 0.028 0.08 20.129 20.35
Father’s education 0.394 1.04 20.027 20.07 0.457 1.28 0.551 1.30 0.436 1.31 0.710 1.95***
Mother’s education 0.347 0.88 0.239 0.59 0.467 1.29 0.277 0.64 0.558 1.66*** 0.651 1.77***
Father with “Elite” occupation 20.279 20.45 1.027 1.95*** 0.572 1.17 1.107 2.13** 0.930 2.08** 0.736 1.54
Both parents work 0.138 0.38 0.601 1.59 20.159 20.47 20.193 20.49 20.340 21.09 20.244 20.72
Household’s income 20.177 20.44 20.528 21.24 0.311 0.85 0.146 0.34 0.695 2.05** 0.131 0.35
Log likelihood at convergence 21068.6
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Table 4
Determinants of success by orientation: empirical resultsa
Orientation 1 Orientation 2 Orientation 3 Orientation 4 Orientation 5 Orientation 6 Orientation 7 Variable
(n=90) (n=70) (n=60) (n=102) (n=65) (n=157) (n=97)
Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Constant 22.02 22.48** 1.701 2.03** 22.206 21.30 21.37 20.92 5.537 1.64*** 0.25 0.27 22.796 23.19*
Age 0.72 1.31 - – – – 22.51 22.17** 22.174 22.61** 21.55 23.99* – –
Gender 20.007 20.02 0.875 1.51 21.539 21.95***20.141 20.41 23.962 21.45 20.337 21.19 20.393 20.91
Repetition during high school 20.324 20.81 20.202 20.53 – – – – 0.937 0.76 – – 1.751 1.45
Prior studies 20.694 20.70 0.618 0.59 1.796 1.45 – – – – 0.61 1.11 20.206 20.27
Nationality 1.557 3.23* 20.428 20.74 2.741 1.86*** 20.31 20.39 22.33 21.81***20.43 21.10 2.056 3.72* Number of Siblings 20.066 20.45 20.31 22.60* 20.615 22.16** 0.048 0.39 20.095 20.32 20.055 20.56 0.027 0.16 Change in living arrangements 20.5 21.36 20.43 21.01 2.748 1.61 0.098 0.29 20.539 20.66 0.247 0.86 0.534 1.42
Scholarship 1.061 2.53** 0.539 1.10 2 2 0.059 0.14 2.47 2.33** 0.367 1.18 1.389 2.79*
Job while studying 20.23 20.56 21.163 22.37** 1.021 1.25 20.59 21.22 20.53 20.64 20.276 20.74 20.745 21.51 Single parent family 20.6 21.43 20.213 20.53 2 2 20.089 20.22 20.3 20.32 20.59 21.87***20.712 21.43 Father’s education (university) 0.56 0.87 0.890 1.51 2 2 1.33 3.68* 2.67 3.18* 0.105 0.35 20.085 20.20
Mother’s education (university) – – 20.729 20.71 1.481 1.23 – – – – 1.172 4.07* 2.367 4.47*
Father with “Elite” occupation 20.53 20.66 0.304 0.31 20.444 20.32 20.53 21.07 0.754 0.83 0.396 1.23 0.211 0.49 Both parents work 0.637 1.80*** 20.278 20.68 0.362 0.53 20.194 20.54 1.145 1.31 0.193 0.75 20.5 20.97 More aged due to prior studies 0.954 0.91 20.263 20.24 20.962 20.71 1.139 1.22 – – 0.064 0.09 0.021 0.03
More aged due to repetitions – – – – – – 0.561 0.63 21.49 20.90 – – 22.743 22.04**
Selection variable 20.786 20.95 20.042 20.06 20.889 20.56 22.23 21.08 0.924 0.92 20.445 20.24 21.732 21.55
Log likelihood at convergence 245.81 235.30 213.13 241.41 213.59 274.10 235.54
Percentage correct predictions 74.44% 74.28% 88.33% 82.35% 90.76% 74.52% 81.44%
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in scientific orientations as Medical and Natural Sciences or Engineering while having mother with university degree seems to foster the chances of success in more literary subjects (Law, Social sciences and Humanities) where a good command of the language is essential. Lei-bowitz (1974) showed indeed the essential role of the mother in transmitting verbal skills and literacy. The lat-ter effect relating to the importance of maslat-tering the mother tongue, may also partially explain why being Belgian increases the probability of success in Econ-omic, Social, Pedagogical and Artistic short cycles as well as in the Humanities orientation of the university. The negative impact of being more aged due to rep-etitions while in high school on success in Humanities might also be partially explained by a common factor, namely a lack of a good command of his own language (see for instance, Ribar, 1993).
Our results also highlight the effect of some variables in some peculiar orientations. For instance, the family size as well as the fact of working while studying are both found to exert a negative effect on the probability of success (in two orientations for family size16 and one — at least at the 5% level — for a job market partici-pation during studies). The sign of the coefficient found (in some orientations) for the variable accounting for the matrimonial status of the student’s parents seems to be in line with the idea that having two parents in a family foster normal personality development (Seltzer, 1994).17 The sign of the coefficient found (in some orientations) for the variable accounting for the fact that both parent work can be interpreted in a “working mother perspec-tive” where increased parental income might outweigh the reduction in students care time (Hetherington et al., 1983). Finally, coming from a poorer background — and for this reason obtaining a scholarship — seems to play a rather positive role on success in at least three orien-tations. This result might be explained through the motivational lines of reasoning of Tinto (1975, 1987) if one considers the concession of a scholarship as a form of contract.18
16 This result illustrates the idea of a reduced transfer of human capital on each children (Hanushek, 1992) due to time constraints (see, Becker, 1965).
17 The presence of two parents might strengthen parental con-trol and monitoring, and weaken thereby the potential adverse influence of other role models.
18 The variables accounting for the professional position of student’s father, change in student’s living arrangements or pre-vious higher education studies made before starting current cur-riculum were found to play a significant role in explaining aca-demic success.
conditional logit model are presented in Table 5 below. We test for the significativity of (a priori) probability of success on the orientation, i.e. whether prospective stu-dents tend to choose disciplines where they have the highest probabilities of success given their socio-demo-graphic and ascriptive characteristics — while con-trolling for length of studies and expected economic returns (wage and insertion). For the complete sample of 641 students, it seems indeed that youngsters pay atten-tion not only to expected economic benefits, but also to the length of studies and the mere probability of suc-ceeding in the chosen orientation. In this sense, the mod-elling approach of Mingat and Eicher (1982) seems
parti-cularly suited to the actual behaviour of the
prospective students.
When one concentrates on the poorest students (i.e. the 171 students holding a scholarship), one is indeed confronted with a decisional structure where they are more risk-averse as they have less financial wealth and are therefore less inclined to take risk. Indeed expected chances of success receives a significant weight, while this is not the case for wage (or length of study). The only economic reward which seems to interest those stu-dents is the (expected) greater ease of entry on the labour market (insertion). These results perfectly match our theoretical a priori expectations and are even reinforced by the results found for the wealthiest students of the sample. Indeed, the richest students (defined as those coming from household with high level of income and with father holding university degree) have a very orig-inal choice behaviour, in the sense that they seem to fol-low just their own preferences. They do not appear to be sensitive to either the expected chances of success or the economic benefits linked with their orientation choice.19
We also try to test whether ability could be the source of the risk-averse behaviour of the students. We therefore turn to the case of the brightest students (i.e. those with the ex ante highest chances of success in all the disciplines). One is struck by their keen interest in the financial benefits of their educational investment: they give heavy weight to wage. However, as expected, they do not seem to pay much attention to their expected chances of success. This is quite intuitively appealing as such event — failure — is quite improbable for them, whathever their choice. And, ceteris paribus, they are also attracted in shorter studies. Finally, when one con-centrates on the “dullest” students, i.e. those with the
19 This sub-sample of students is only made of university stu-dents.
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Rochat,
J.-L.
Demeulemeester
/
Economics
of
Education
Review
20
(2001)
15–26
Table 5
Effect of expected success ratea
Full sample Top 10% of Top 15% of Bottom 10% of Bottom 15% of Scholarship Wealthier students (n=614) studentsb studentsb studentsc studentsc students (n=171)d (n=113)e Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat Expected success rate 0.494 3.86* 20.146 20.257 0.025 0.06 20.050 20.08 0.191 0.412 0.626 2.52** 20.073 20.191 Wage (in BFR) 0.36E25 3.69* 0.812E-5 2.81* 0.748E253.13* 0.206E244.75* 0.228E24 5.33* 0.214E-5 1.11 20.75E-7 20.039 Graduates insertion on the labour
0.0084 1.636*** 0.0172 0.96 0.00432 0.30 0.056 2.20** 0.041 1.99** 0.0162 1.74*** 0.00203 0.159 market
Length of studies (in Years) 20.751 23.687* 21.723 22.13** 21.388 22.69* 25.647 26.03* 25.826 26.88* 20.563 21.38 20.308 21.04
Log likelihood at convergence 21227.49 2120.29 2175.70 285.86 2128.57 2326.37 2155.76
a *significant at 1% level,**at 5% level and***at 10% level.
b The 10% or 15% of students who have an expected probability of success above a common threshold across all disciplines. c The 10 and 15% of students who have the lowest expected probabilities of success in each orientation.
d Students whose household’s revenue is such (low) that they benefit from a governmental financial aid.
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seem to indicate that ability may be less important than the socio-economic background in explaining a risk-averse behaviour, with the related avoidance of more dif-ficult but more remunerative (and demanded) orien-tations.
Our results tend to confirm those of Cannings et al. (1993) although ours are obtained within a generalized structure allowing us to jointly test for the importance of ex ante probability of success and expected economic benefits. Cannings et al. (1993) found that the choice of college concentration depends on the perceived prob-ability of success in a particular concentration for all of the students. Similarly to our own findings they put for-wards that brightest students do not pay attention to their perceived probability of success. However, contrarily to our results and quite astonishingly, they find that stu-dents coming from high-income families appear to be more risk-averse in their choice of major than students from low-income family.
Globally, the overall picture seems to support quite well Mingat and Eicher (1982) theoretical contentions, namely the fact that students do take into account two dimensions of their prospective educational choice (economic returns and a priori chances of success), and that poorest students give a heavier weight to the risk component. However, it might also be true that less priv-ilegiated students tend to avoid disciplines where the post-studies performance requires more social capital (Coleman, 1988). But we concentrate on the perform-ance during higher education studies, and in such a con-text we have already tried to assess the impact of those variables on the probabilities of success across orien-tations.
5. Concluding remarks
In this paper, we addressed the impact of (expected) success rates on the higher education orientation choice process, besides mere expected economic returns. We applied a classical three-step methodology on a sample of freshmen enrolled at Belgian (french-speaking) higher education institutions in 1992 and 1993. Globally, our results seems to support quite well Mingat and Eicher (1982) theoretical contentions, namely the fact that stu-dents do take into account two dimensions of their pro-spective educational choice (economic returns and a priori chances of success), and that poorest students (more than the less able ones) give a heavier weight to the risk component. Such results should lead us to ques-tion the relevance of the laisser faire soluques-tion prevailing today as far as higher educational choices are concerned.
idea that interventionism would promote both efficiency and equity. By some kind of affirmative action or posi-tive discrimination (Evetts, 1976), one can restore equal-ity of educational opportunequal-ity. The objective would be that students from poorer background would not be impeded to choose lengthier or riskier orientations because of environmental constraints. One can hope that students will therefore pay more attention to expected economic returns and that labour market imbalances would be reduced. In this sense, one would achieve more efficiency as well as more equity. The concrete measures have to be discussed, but it does not seem that the current debates focusing on the relevance of some quantitative barriers to entry would promote economic efficiency.
Acknowledgements
We would like to thank K. Mayhew, J. Krishnakumar and A. de Palma for helpful comments, as well as the Wiener—Anspach Foundation Brussels for its financial support.
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