Demand for Higher Education Programs: The Impact of the Bologna Process
* IZA Bonn, e-mail: cardoso{at}iza.org
University of Minho, NIPE and IZA Bonn, e-mail: mangelo{at}eeg.uminho.pt
University of Minho, NIPE and CIPES
University of Minho and NIPE, e-mail: falex{at}eeg.uminho.pt
Corresponding author: Carla Sá, Escola de Economia e Gestão, Universidade do Minho, Campus de Gualtar, 4710 057 Braga, Portugal, e-mail: cangelica{at}eeg.uminho.pt.
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Abstract |
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 Top Abstract 1 Introduction2 The Bologna process3 Evaluating the impact...4 ConclusionReferences |
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While several aspects of the Bologna process deserve wide public support, the reduction of the length of the first cycle of studies to three years in several continental European countries, where it used to last for four or five years, is less consensual. This paper checks the extent of public confidence in the restructuring of higher education currently underway by looking at its impact on the demand for academic programs in Portugal. We concentrate on students revealed first preference when applying to higher education. Results indicate that the programs that restructured to follow the Bologna principles were subject to higher demand than comparable programs that did not restructure; that effect, however, varies across fields of study and with program size. (JEL codes: I28, I21, F15)
Key Words: European Higher Education Area • education policy • count data • first preference.
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1 Introduction |
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TopAbstract1 Introduction2 The Bologna process3 Evaluating the impact...4 ConclusionReferences |
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Major steps are currently being taken to create a European Higher Education Area by 2010. They include the creation of a comparable structure of academic degrees, mutual recognition of diplomas and course units, the assessment of academic institutions and programs based on common quality standards and direct incentives for geographical mobility of students and staff. The implementation of a common structure of academic degrees means that some continental European countries are moving away from a four- or five-year first cycle of studies to a shorter three-year one, which has led to some controversy. On the one hand, the advantages of having a degree recognized in a wider geographical space are praised, together with the re-development of curricula to make learning more student-centered and focused on the development of competencies, while enabling earlier entrance into the labor market. On the other hand, distrust has been expressed over the academic contents of the curricula and the adequacy to labor market needs of the competencies gained in a shorter three-year period, with fears that the employability of graduates will be reduced, when compared to graduates of the longer cycle.
This study concentrates on the reaction of students, as indicated by their revealed first preference, to analyze the impact of the Bologna restructuring on demand for academic programs by candidates to higher education. We focus on the Portuguese system.
We take advantage, first of all, of the legal setting in Portugal, where institutions were given the option to adjust their academic programs to the Bologna curricula starting in the academic year 2006/2007, or to defer adjustment to one of the two following years. Therefore, in 2006/2007 a group of early implementers co-exists with a group of academic programs that still have not undergone change, and students were free to choose where they would like to be admitted.
Second, the analysis is facilitated by the system of access to higher education in Portugal. Candidates must clearly rank up to six choices of institution and academic program, and a national competition follows, run by the Ministry of Science, Technology and Higher Education (MSTHE), which allocates candidates based on their relative performance and the number of available vacancies posted by each institution for each program. Third, we have a comprehensive data set on the application process, which renders this analysis feasible.
The article proceeds in Section 2 by describing the main characteristics of the Bologna process, emphasizing the potential advantages and disadvantages of the Anglo-Saxon two-tier system and its implementation in the Portuguese higher education system. Section 3 presents the data set, describes the method and discusses the results. Section 4 concludes.
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2 The Bologna process |
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TopAbstract1 Introduction2 The Bologna process3 Evaluating the impact...4 ConclusionReferences |
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2.1 Objectives and debates
Initial steps towards some convergence of European higher education systems were taken with the signature of the Sorbonne declaration by the Ministers in charge of higher education in France, Italy, the United Kingdom and Germany, in 1998, and later, in 1999, with the signature of the Bologna declaration. The Bologna process aims at creating a European Higher Education Area by implementing a comparable degree structure, common quality assurance standards and by promoting mobility of students and faculty.1
Globalization, technological change and increased international competition for scarce high-skilled labor highlighted the importance of making European higher education institutions attractive and competitive worldwide. A more integrated European Higher Education Market enhances competition between European universities—a necessary condition for producing leading-edge innovations and for catching up with the US economy (see, for example, Aghion 2006; van der Ploeg and Veugelers 2007), which has great influence in modernizing the European higher education (Van der Ploeg and Veugelers 2008).2
Even though the process is far-reaching and multifaceted, much of the attention has been devoted to the changes in the degree structure. Indeed, according to the model that predominated in most continental European countries, the first higher education degree was obtained after four to five years of successful study. Therefore, the curricula changes necessary to reduce the first degree to three years were implemented amidst some controversy.
Jacobs and van der Ploeg (2006) discuss the potential benefits of a two-tier system of three- or four-year bachelor's degrees and one- or two-year master degrees, as in the UK, US, Canada, Australia and India. According to those authors, a comparable degree structure would make the system more transparent and obstacles to the mobility of students and workers are expected to be reduced. Additionally, the two-tier Anglo-Saxon system presents a better performance relative to Continental Europe—for example, in 2004, 39 percent of the US population aged 25–64 had attained tertiary education, against only 23 percent in Europe (Aghion 2006). Jacobs and van der Ploeg (2006) present several possible explanations for the better performance of the two-tier Anglo-Saxon system relative to Continental Europe. On the one hand, students can complete their studies more quickly. On the other hand, a two-tier system reduces the cost of wrong choices made by students. The two-tier system also promotes a more flexible progression into postgraduate studies by allowing students to enter the labor market sooner and to find out what competences they should develop when they go back to university to take a Master's degree. All those factors, it has been argued, may render the European higher education more responsive to the needs of an increasingly flexible labor market and, therefore, enhance graduate employability and returns to education.
However, critics of the Bologna process stress that new curricula are a compressed version of the longer programs, and that there will not be enough time for assimilation, reflection and a critical approach to learning, which will undermine the quality of the degree. Under these circumstances, the employability of the new graduates might be reduced, when competing with graduates from the previous system of a longer first cycle. However, Harmon, Oosterbeek and Walker (2003) found that in countries where the graduates enter the labor market earlier, as in the UK two-tier system, returns from education tend to be the highest, which may suggest diminishing returns of further years of study (Jacobs and van der Ploeg 2006). It is still too soon to evaluate here the impact of the implementation of the Bologna two-tier system on labor markets, namely, on graduates’ employability and wages.
Another argument against the two-tier system is that public funding may be restricted to the first (three-year) cycle, thus imposing a higher burden on students if they want to progress beyond the first degree, when compared to the system that used to guarantee public funding for four or five years. The relevance of this issue varies across scientific fields, with the problem usually not arising in the Humanities, while it is highlighted in several countries for occupations regulated by professional bodies (Reichert and Tauch 2005) and subject to specific European Union coordination mechanisms (Architecture and Health Sciences are two examples).
Between optimism and skepticism, it is not certain whether, during the period of adjustment, labor market agents and students will sort academic programs by looking at whether the curriculum has been adapted to Bologna. Although it would be very interesting to evaluate the reaction of labor markets to the Bologna process, we do not have the data to evaluate directly the impact of the Bologna process on the labor market, namely, on graduates’ employability and wages. In fact, Crosier, Purser and Smidt (2007), using survey evidence, concluded that, so far, there is insufficient information about the nature and potential benefits of this reform in society and labor markets. In this article, we circumvent those problems by assessing the confidence of society in this reform by measuring the impact of the adoption of the Bologna principles on students’ demand.
2.2 The Portuguese setting
The Portuguese setting is of particular interest to the study of the impact of the implementation of the Bologna process. Higher education institutions were given the option of implementing the required changes immediately in 2006/2007 or postponing to one of the two following academic years. Given that, in 2006/2007 a group of early implementers coexists with a group of old style study programs.
These changes took place in a framework of increasing competition between institutions. In 1990/1991, there were almost 200 thousand students enrolled in higher education; between 1990/1991 and 2002/2003 that number more than doubled; however, since then it has decreased. Therefore, Portugal has moved from a period of sharp rise in demand to excess supply. A number of factors have combined to generate excess of capacity and increasing competition for students between institutions. Among these factors, the MSTHE (2006) stresses: the decline in the number of candidates due to demographic changes; the increasingly strict admission conditions, following the reintroduction of national admission exams and minimum grades and the increased number of vacancies, due to large investments made in the public sector.3
This increased competition motivated strategies of differentiation by institutions, namely by defining different entry conditions, with the most recognized institutions setting higher entrance standards and, therefore, targeting different segments of the student population (MSTHE 2006). The speed of adjustment to the Bologna process has often been pointed out as an instrument in this strategy of differentiation. As in other continental European countries, the reduction of the length of the first cycle of studies was one of the more debated changes. The common duration of a higher education degree in Portugal used to be five years, until the mid-90s, it is reduced to four years; the Bologna process further imposes a reduction to three years. There is, nevertheless, the possibility to keep the duration of a program longer. Whereas the first cycle (licenciatura) has a normal duration of three years and the second cycle (mestrado) has a normal duration of one and a half or two years, in special cases it is feasible to offer a combined degree, the so-called integrated Master's, lasting for five to six years.
Some institutions saw the prompt implementation of the Bologna process as an opportunity to establish or reinforce their reputation as an up-to-date institution, whose graduates would benefit from the opportunities of a wider labor market. Institutions taking the lead might gain a comparative advantage over the late-comers, not also attracting more applicants in the first year after restructuring, but also gaining a reputation beneficial for future years. Other institutions, instead, opted to delay the process, arguing that changes should be thought over. The result of these two strategies is visible in Table 1, which shows that the adjustment of curricula to Bologna varied across higher education institutions. The decision taken by the University of Coimbra to defer the adoption of the new model to 2007/2008 (with exceptions authorized for programs on which a national consensus for change had been reached among institutions) is evident in the table, as is the fact that the University of Madeira did not adapt any of its programs. This decision contrasts with that of Universidade Nova de Lisboa and Instituto Superior de Ciências do Trabalho e da Empresa (ISCTE), which both moved ahead in restructuring most of their programs.
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In this context, the decisions by academic institutions and students can be interpreted within the conventional signaling framework (Gibbons 1992; Salanié 2000).4 Academic institutions decide whether to adopt the Bologna principles immediately and students decide whether to apply to a Bologna program. Institutions are in this case the informed players, who have insider information on program quality, which they can choose to reveal (or not) by means of signals. Interestingly, in the public debate surrounding the Bologna changes, the idea that institutions which adapted first were signaling their readiness for change and their higher quality was often stressed. Prospective students, on the other hand, are interested in attending institutions that guarantee a certain education quality (Long 2004). Whereas the program quality is the institution's private information, the decision to conform to the Bologna principles is publicly observed.
Referring to Portugal, the OECD stresses that on the students’ side "public information on course content, program goals, quality and opportunities and graduate employment is inadequate or unavailable" (OECD 2006, p. 27), which makes the impact of the implementation of the Bologna principles on demand for academic programs even more uncertain.
Therefore, in this article we test whether students sort academic programs by whether the curriculum has been adapted to Bologna. Some students may associate Bologna with a quality stamp and a guarantee of recognition of the degree in a wider geographical space, yielding better employment opportunities, whereas others may attach a higher importance to a more established older program. In this article, the agent we will consider are the candidates to a higher education degree and their demand for higher education programs.
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3 Evaluating the impact of the Bologna process on program demand |
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TopAbstract1 Introduction2 The Bologna process3 Evaluating the impact...4 ConclusionReferences |
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3.1 Data and sample
This study concentrates on the publicly funded Portuguese higher education system, which comprises 14 universities and 26 polytechnics. The analysis of the impact of Bologna on program demand is rendered feasible by the fact that admission into public higher education in Portugal is strictly regulated and implemented through a nation-wide competition. Enrolment in higher education is limited by a system of numerus clausus, with the number of vacancies defined yearly by the MSTHE. The application process takes place at the centralized national level and each candidate ranks up to six institution/program pairs. Demand for a given program can thus be quantified in an unequivocal way.5
The allocation of the candidates follows their stated preferences and is based on their grade point average, which is a weighted average of their marks in secondary school and in national examinations. The performance in national exams affects the pool of candidates that can apply to higher education first cycle programs. Traditionally hard subjects are: Mathematics, where only 26 percent of the students obtained a pass grade in 2006; Physics, where the share of students passing the exam in that year was 30 percent and Chemistry, where that share was 35 percent.
The empirical analysis of the paper uses a comprehensive data set on the application process to public higher education, collected from the website where the Department of Higher Education (DGES) of the MSTHE announces the results of the process of allocation of candidates to higher education programs.6 Data for the academic years 2003/2004 to 2006/2007 and for the first and second phase of the application process in each year have been collected.7
The following variables are available: demand for each program (number of students who have selected each program as their first choice); number of vacancies available for each program in each of the two stages of the application process; national admission exams required by the program, with the major ones being Mathematics, Physics, Chemistry, Biology and Portuguese and the field of study of the program.8
Table 2 provides descriptive statistics on the dataset. A declining trend in the average number of applicants per study program can be detected between 2003/2004 and 2005/2006, with an increase in the number of applicants in the following year. The second phase of application involves, as expected, remarkably less applicants, since it is a residual phase. The table also shows a declining proportion of programs requiring an entrance exam in Mathematics, Physics, Chemistry, Biology or Portuguese. The share of applicants to each field of study has remained comparatively stable over time. Law and Social Sciences, Education and Humanities are the exception, as they show some variation in demand. In the academic year 2006/2007, 43 percent of the study programs have restructured according to the Bologna rules.
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3.2 Empirical model and variables
The present analysis aims at determining to what extent the introduction of the Bologna process has had an impact on the demand for academic programs. The dependent variable is operationalized as the number of applicants who placed a given program/higher education institution pair as their first option. The number of first options is a positive integer and its distribution is skewed to the right, which implies that count data models are the adequate tool (Cameron and Trivedi 1998). Since the over-dispersion test rejects the null hypothesis of absence of over-dispersion, the negative binomial model is more appropriate when compared to the Poisson alternative. Because the data have a panel structure at the level of program/institution, we estimated a conditional fixed-effects negative binomial model.
The analysis considers a set of program attributes as explanatory variables. The main program attributes are the so-called Bologna variables. These are three dummy variables that describe the way the Bologna process has been implemented in Portugal. The first dummy variable is simply Bologna implementer and takes the value one for programs that have been restructured according to the Bologna process. Bologna leader is another dummy variable, which takes the value one for implementers which were the only institution in the country that restructured that program. This group of early-implementers has set itself apart from the other institutions in the country, making an early move and most likely expecting to gain from its timing. Finally, the dummy for integrated masters achieves the value one for implementers that opted for combining the first and the second cycle into a single program, which leads to the Master's degree.
Apart from the Bologna variables, departing from a simpler specification, we successively control for additional program characteristics. Given sharp differences in the dimension of the different programs and across institutions, we control for the size of the program (number of vacancies posted in each phase). The dependent variable is a proxy for absolute demand, which depends on the number of places offered for each study program, with larger programs expected to get higher demand. We also control for the phase of the application process, with a dummy variable equal to one in the second phase, since this is a residual phase. Program attributes include whether it requires a national admission exam in a particular subject (dummy variables for Mathematics, Physics, Chemistry, Biology and Portuguese). Controlling for the subjects required as admission exams is particularly relevant. Indeed, a generally poor performance in the admission exam in a certain subject reduces the pool of candidates that can apply to programs requiring that exam. Finally, we control for the scientific field of the program (captured by nine dummy variables). Different scientific fields reacted differently to the implementation of the Bologna process (consider for example the contrast between Humanities and other fields).9 Estimation of the model including field-specific dummy variables can control for these differences. Interactions between Bologna and control variables enter the model specification as well, in the final richer specification, which is aimed at uncovering contrasts in the impact of Bologna within the higher educational system.
3.3 Impact of the Bologna process
This section presents results of the estimation of the negative binomial model described above. Alternative specifications of the model are reported in Table 3, where, as previously described, the dependent variable is the total number of candidates that chose the program as their first option.
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The first two specifications are simpler models presented for comparison purposes. In Specification 1 we only include the Bologna implementer dummy variable, and dummies for the phase, year and admission exam required. These control variables are required in order to control for aggregate changes in demand across time, considerable differences in demand between the first and the second phase, and the fact that programs requiring different admission exams face different segments of applicants to the higher education system. The results indicate that the adoption of the Bologna model led to a significant increase in demand. In Specification 2 we added the program size, attaining results qualitatively similar to Specification 1, a positive impact resulting from the Bologna stamp. The third specification accounts for the variation in the impact of Bologna across fields of study and program sizes. Specification 4 further allows the impact of Bologna to diverge between leader and non-leader programs. Specification 5 checks whether the impact of the Bologna process has been different for integrated Master's degrees. Finally, Specification 6 is a combination of the previous two specifications. Results are fairly robust across specifications. As such, we interpret the coefficients of Specification 6, which uses the most complete set of regressors.
Bologna restructuring is associated with higher demand for a study program, when compared to programs that did not restructure. However, that effect decreases with the size of the study program. For example, in the Humanities, the overall impact is equal to 100 x [exp(0.2250 – 0.0024 x size) – 1]. In this case, a restructured study program offering 40 vacancies would be subject to 13.8 percent higher demand, whereas for a study program posting 80 places the impact would be about 3.4 percent. However, as will be discussed below, these marginal effects are not statistically significant.
In fact, the statistical significance of those marginal effects needs to be checked. In the presence of interaction terms, Table 3 only reports limited information for the test of the marginal effect of being a Bologna implementer. Figure 1 is particularly relevant for the analysis, as it reports the marginal effects of being a Bologna implementer by field of study according to program size, as well as their 95 percent confidence intervals based on the correct standard errors accounting for interaction terms.10 Vertical lines in each graph indicate the 10th, 50th and 90th percentile of vacancies for each field of study. Additionally, the 99th percentile of vacancies is indicated. A horizontal line is placed at the null marginal effect.
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We conclude from Figure 1 that the impact of Bologna restructuring differs across educational programs and as a function of the program's size. The impact is positive for education programs and negative for health programs, regardless of the size of those two programs. Evidence of positive impact is found for very small programs in Law and Social Sciences and Economics and Business, while a negative impact is observed for large programs in Law and Social Sciences, Architecture, Natural Sciences and Technologies. Finally, demand for programs such as Humanities, Agriculture and Sports and Arts appears not to be affected by Bologna's restructuring.11 In one field of study (Education), implementation of Bologna had an unequivocal positive impact on demand and in another (Health), there has been lower demand for programs restructuring along Bologna's directives, which might indicate that students/public were skeptical about the restructuring.
We further checked whether the impact of the Bologna process could be different depending on the implementation strategy. Firstly, we considered whether being a national leader in a certain program implementing the Bologna curricula was associated with some benefit (or penalty) in terms of demand by prospective students. Results for Specification 6 in Table 3 reveal that being a leader in the implementation of the Bologna curricula had no impact on demand for a program as a first choice, above the increase experienced by Bologna implementers in general. This effect holds irrespective of the size of the program.
Second, we checked whether restructuring to offer a joint first and second cycle degree (i.e. integrated Master's) of a longer duration yielded some benefit in terms of demand. Results indicate that there was a positive impact on demand for programs that restructured and kept a long duration, above the impact for Bologna implementers in general; this increase in demand took place irrespective of the size of the program.
As expected, larger programs attract a larger number of candidates. In the second phase, the number of applicants is remarkably lower. Admission exams in Biology, Mathematics or Physics, known to be the toughest, reduce the pool of potential applicants and thus lower the demand for the program. The demand for university programs decreased between 2003 and 2005, recovering in 2006.
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4 Conclusion |
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TopAbstract1 Introduction2 The Bologna process3 Evaluating the impact...4 ConclusionReferences |
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The Bologna process aims at creating a European Higher Education Area where inter-country mobility of students and staff, as well as workers holding comparable degrees, is facilitated. Despite the advantages of the Bologna process, it has been implemented amidst some controversy. The emphasis of the public discussion has centered on the changes in the degree structure, namely the reduction of the first cycle of studies to three years and its implications for knowledge acquisition and the integration of the graduates into the labor market.
In this article, we have checked the degree of public confidence in the Bologna changes in curricula in Portugal. Namely, we have looked at students’ demand behavior during the period of adjustment, as expressed by their first choice when applying to higher education. Precise quantification of the demand for each academic program is facilitated by the rules of access to higher education, in a nation-wide competition, where candidates must list up to six preferences of institution and program pairs.
We use regression analysis applied to count data, estimating negative binomial models on the number of students who placed a program/institution pair as their first option. Results indicate, in general, a positive impact on demand for programs that have adapted to the Bologna rules. We observe an unambiguous higher demand for programs in the field of education adopting the Bologna principles. At the same time, the lower demand for health programs that followed Bologna's directives might reflect some skepticism. For some programs, namely in Economics and Business, Law and Social Sciences, Architecture, Natural Sciences and Technologies, the impact of Bologna turns out to be conditional on the size of the program; for some other Bologna does not have any impact (Humanities, Agriculture and Sports and Arts). Programs that restructured to offer an integrated Master degree were subject to rising demand.
However, the degree of confidence of labor market agents in the changes in curricula should be the object of future research, since the evaluation of the integration of the new graduates into the labor market will be the real test to the current reform of the European Higher Education Area. Crosier, Purser and Smidt (2007), using survey evidence, concluded that there is much to be done to translate the priority of employability into institutional practice, suggesting that the objective of employability of the current European higher education reform was not yet fulfilled.
In this article we focused on the demand for first cycle programs. However, an assessment of the two-tier system also implies an evaluation of the demand for second cycle degrees. Although we will have to wait for the data to make an accurate analysis, Crosier, Purser and Smidt (2007) concluded from survey analysis that, in some countries, the duration of studies may have actually increased rather than decreased as the old long cycle degree programs were divided into two cycles. Additionally, there is evidence that higher education institutions have been encouraging students not to leave for the labor market before finishing the two cycles.
As remarked by Jacobs and van der Ploeg (2006), for the Bologna reform to materialise its potential benefits, two conditions must be observed. In the first place, the reform of the European Higher Education System should result in more competition. Second, students should make more informed choices and become more critical consumers. For these conditions to be verified, better communication between higher education institutions, employers and students of the results and implications of the reforms is called for (Crosier, Purser and Smidt 2007). More transparency, namely through common quality assurance systems, in the new degree structures and their learning outcomes is necessary to guarantee the more efficient and competitive European Higher Education System, which is at the core of the Bologna process. Additionally, for students to vote with "their feet", they should have the material means to choose the best program, which means that more grants and student loan schemes should be promoted.
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Footnotes |
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We profited from discussions with Nelson Areal and the participants in the NIPE Seminar (Universidade do Minho, Braga, Portugal, 2007) and the CESifo Summer Institute (Venice, Italy, 2007). We also benefited from extremely useful comments by Romina Boarini, Rick van der Ploeg and anonymous reviewers.
1 See European Ministers of Education (1999). 
2 See also Stephan (2008) on the issue of the increased reliance by governments on universities as a source of growth.
3 Portela et al. (2007) provide a detailed analysis of the recent imbalances in the Portuguese Higher Education System as a whole, and per institution and field of study.
4 For an example of a signaling game applied to the higher education system, see Mizrahi and Mehrez (2002).
5 Throughout the text, a program is meant to refer to a institution/academic program pair, unless otherwise explicitly explained.
6 Direcção Geral do Ensino Superior, at http://www.acessoensinosuperior.pt.
7 Students who are not successful in the first phase, or who are successful but wish to change the institution/program where they were placed, and those who did not apply in the first phase, are eligible to apply in the second phase.
8 We have consistently used the classification adopted by the Ministry in 2006, which includes ten areas: Agriculture, Architecture, Natural Sciences, Law and Social Sciences, Economics and Business, Sports and Arts, Education, Humanities, Health and Technologies.
9 In Humanities, 58 percent of the programs adopted the Bologna principles, while for example, in Health Sciences only 9 percent did so and in Natural Sciences 39 percent.
10 For a discussion on the analysis of interaction effects see, for example, Brambor, Clark and Golber (2006).
11 Looking at Figure 1, we conclude that for study programs in the field of humanities, the impact of the Bologna stamp is not statistically different from zero, irrespective of the program size. The same conclusion holds for studies in the fields of Agriculture, and Sports and Arts. In architecture studies, the effect of the Bologna stamp is almost always statistically not significant, and becomes negative in programs posting more than 88 vacancies, which is above the 90th percentile. On the other hand, in the field of education the marginal effect of being a Bologna implementer, though decreasing with program size, is always positive. For economics and business programs the marginal effect is statistically positive for programs with less than 45 vacancies, which coincides with the 50th percentile, and it becomes statistically negative after 207 vacancies, which only occurs for three programs in this field. Similarly, in the field of Law and Social Sciences, the marginal effect is statistically positive for programs with less than 40 vacancies (the median of the field). This corresponds to 167 programs, for which the marginal effect of the Bologna stamp is bounded between 14 percent and 25 percent. The marginal effect becomes negative only after the 90th percentile, namely for programs posting more than 173 vacancies (i.e. two programs). In the field of technologies, only those programs with a size above the 90th percentile (i.e. 27 programs) show a statistically negative marginal effect. This effect is bounded between –27 percent and –14 percent. When looking at programs in the field of natural sciences, the marginal effect is statistically negative for the eight study programs posting more than 71 vacancies. In health, for study programs offering more than 33 places (just below the median) the marginal effect is statistically negative. For the corresponding 81 programs the effect is between –51 percent and –12 percent.
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