Introduction

Academic freedom and global student mobility are topics high on the scientific and political agenda. Until now, however, there is no systematic cross-national investigation of the relationship between transnationalFootnote 1 student mobility and academic freedom in national higher education systems. High degrees of academic freedom—(roughly) defined as the freedom to teach to research and the right of institutions’ self-governance—might be an attractive feature for international students when choosing a study destination. It is not easy, however, to determine the net impact of academic freedom on the choice of a study destination since academic freedom might be highly correlated with the reputation of a countries’ higher education system, as well as with its economic performance. In liberal democracies, high degrees of academic freedom are not circumstantial, but often legally protected. High-quality scientific research and education require free thinking, free speech, and critique. Yet, there are countries with reputable higher education institutions (according to the Shanghai index) despite of severely restricted academic freedom.

In our study, we intend to answer the question of how a countries’ academic freedom shapes its attractiveness as a study place. We test the hypothesis that countries with higher levels of academic freedom attract international students from other countries, and at the same time are better able to retain students in their domestic higher education systems.

Aiming to identify an independent effect of academic freedom on global student mobility, we must control for important confounders. These confounders are indicators of the quality of the education system, but also cultural and geographical proximity (Racine et al., 2016; Perkins & Neumayer, 2014; Vögtle & Windzio, 2020, 2021, 2022), and GDP per capita (e.g., Lee & Tan, 1984; Vögtle & Windzio, 2022; Wei, 2013). We control for key demographic and geographic factors of migration and student mobility and show that academic freedom does indeed increase in-degree, thus is a source of attraction for international students, and decreases out-degree, thus lowers the probabilities of studying abroad for domestic students, in the student mobility network. However, there is considerable multicollinearity between a countries’ academic freedom, the rank of its higher education institutions in the Shanghai index and its economic performance. As we will show, academic freedom nevertheless has a robust effect on retaining students in the country. While our data covers 167 countries as receivers and senders, our network analysis takes the attributes of countries and their relationship to each other into account to estimate the net effect of academic freedom on ties in the network of global student mobility.

Individualization, academic freedom, and transnational student mobility

In the wake of emerging modern societies, people became individualized and more committed to formal institutions. Modern individuals tend to rely more on analytic thinking, to higher trust towards outgroup strangers (Henrich, 2020, p. 228–230) and to trust more on impartial third-party enforcement (Seabright, 2010, p. 70). This individualized culture and psychology paved the way for the legitimacy of formal institutions and bureaucracies (Weber, 1972) that today govern daily behaviour in Western democracies, but also influenced institutions in non-Western countries (Meyer et al., 1997).

Modern states govern by law, which requires a literate and educated population (Weymann, 2014). Education enables citizens to follow formal rules, but also to participate in mass communication and opinion formation. If organized by centralized state institutions, most public education is somehow standardized, corresponding with high degrees of homogenization and universalism within the respective educational level, and therefore also with individualization (Weymann et al., 1996, p. 32). Higher education corresponds with the ability of citizens to formulate individual opinions, based on an ethic of autonomy (Haidt, 2012, p. 116). It introduces (mostly) young adults into scientific ways of thinking in their fields of study. They learn scientific theories and research methods and become able to generate new knowledge, e.g., for improving technologies and methods of economic production (Hidalgo, 2015). At the societal level, social evolution of science and technology results from variation and selection of ideas (Luhmann, 1992) which requires an institutional environment that encourages discourse, pondering on different theories and explanations, experimentation, free thinking, trial-and-error practices, and open, subject-related critique. Thus, institutional environments allowing higher degrees of academic freedom are a necessary, although not sufficient, condition of dynamic and adaptive social evolution. But how can academic freedom be defined and assessed? How is it connected to the quality in higher education and overall democratic rule in a country?

What is academic freedom?

Humboldt’s principles of freedom of teaching and learning (Lehrfreiheit und Lernfreiheit), the unity of teaching and research (Einheit von Lehre und Forschung), and the unity of different scientific perspectives on natural history (Einheit der Wissenschaft) together constitute the theoretical and organizational paradigm which became the hallmark of the modern university (Karran, 2009, p. 193). Freedom of teaching means that professors are free to choose topics and their own ways to present them; the denomination of a chair does not pre-define the content of the lectures (Stichweh, 2016). The duality of research and teaching is at the core of the concept of academic freedom. Students shall not only receive training, but education through science (Hüther, 2010, p. 49); science became a goal in itself. However, the actual revolutionary idea was the concept of unity of teaching and research (Einheit von Lehre und Forschung), since until the eighteenth century, European universities existed to mainly preserve and transmit an established body of knowledge, but not to periodically review and eventually revise or substitute established knowledge. Likewise, universities like the Al-Azhar UniversityFootnote 2 have focused its teaching on Islamic justice, theology, and the Arabic language for centuries, instead of the expanded canon of subjects like technical, educational, and medical faculties that universities operate today.

Academic freedom also includes the right to self-governance (UNESCO, 1997, p. 26–35), thus the right of academic staff to take part in the governing bodies and the right to elect most representatives to academic bodies. For the overall level of academic freedom, academic self-governance and self-administration play a key role. Without protection from external influences, higher education institutions are vulnerable to political or religious censorship (Karran, 2009, p. 7) or to other entities controlling it politically and economically. According to Karran, the level of protection for academic freedom will be high if the rector is chosen from the faculty, by the faculty, and for a limited period in office (ibid., 2007, p. 303–304). In higher education systems where the rector is chosen from outside the university, appointed by an external agency or by state officials, she/he will be in a position to suppress academic freedom.

One problem of academic freedom as a concept has been the lack of a clear definition. There is no comprehensive definition of who is an academic, which freedoms are protected, and where—at which institutions—academics ought to be situated to have their academic freedoms protected. For the overall level of academic freedom, academic self-governance and self-administration play a key role. A certain degree of institutional autonomy, self-administration, and level of protection from direct external influence is deemed necessary to protect the freedoms of teaching and research. Expectations addressed towards the university from outside are channelled through the universities self-governance mechanisms and can thus never directly be cracked down. Autonomy can be perceived as a defence against external influences (Stichweh, 2016) and can broadly be described as ‘… a state of regulated autonomy in which the freedom of academics in teaching and research is necessary to the discharge of their normal functions, but these functions are exercised within boundaries controlled by government and management’ (Marginson, 1997, p. 359).

Academic freedom mirrors countries’ general freedoms such as free speech (Connolly, 2000, p. 71). To a certain extent, academic freedom reflects the general level of democratic rule within the wider community and is indicative of the preservation of other basic human rights. Attacks on academic freedom hint to a societies’ development towards becoming more authoritarian (Preece, 1991) and a decline in academic freedom hints at an overall decline of civil liberties. As ‘… knowledge is created by challenging orthodox ideas and beliefs …’ (Karran, 2009, p. 191), scholars constantly questioning traditional knowledge claims are more likely to get into conflict with governments and other seats of authority. Even though authoritarian countries do maintain and finance higher education systems, higher education institutions might not provide a liberal environment for the unrestricted search for knowledge. Academic activity in the pursuit of knowledge involves dissemination and public debate. Thus, full academic freedom cannot exist in a society with limited freedom of speech and citizens’ rights, but still, ‘academic freedom and freedom of expression are distinct concepts. Important dimensions of academic freedom—such as the freedom to research and teach, institutional autonomy, and the freedom to exchange research findings with other scholars—cannot be subsumed under freedom of expression’ (Spannagel & Kinzelbach, 2022:5).

Most young adults who are eligible to enrol in higher education have passed higher secondary exams and thus have already invested much time and effort into their personal development. Since higher education based on standardized curriculums fosters individualization (Weymann, 2014; Weymann et al., 1996), these adults might be more interested in learning and in their own personal development than the average population (Carney et al., 2008). Personal development, in turn, requires cognitive input from a variety of sources. Otherwise, there is no sophistication, reorganization, or ‘accommodation’ of cognitive structures (Piaget, 1962). In a similar way that social progress and adaptation results from evolution by variation and selection (Luhmann, 1992), also learning and personal development can be thought of as an (ontogenetic) evolutionary process (Piaget, 1962). This argument is in line with research on the association between liberal attitudes and strong preferences for autonomy (Haidt, 2012, p. 128) on the one hand, and personality traits of educated persons that embrace new experience (neophilia) on the other hand (Carney et al., 2008; Iyer et al., 2012). As a result, more educated and individualized persons tend more to appreciate liberal environments conductive to new experience, new information, and self-development—which is a reason why high levels of academic freedom might be attractive for educated adolescents.

Higher education institutions educate (predominantly) young adults in sciences and scientific ways of thinking. The essence of scientific thinking and communication is to ask, to criticise, and to disprove, which enhances the existing stock of knowledge, but also challenges existing or taken for granted knowledge. Academic freedom is fundamental for scientific progress, the pursuit of truth, research collaboration, and quality higher education (Spannagel & Kinzelbach, 2022, p.18). Freedom of thinking and expression should therefore be central for students pursuing higher education. Authoritarian regimes, where academic freedom is restricted or even absent, pose a threat to students who are willing to get politically involved and appreciate access to uncensored information (Kaczmarska, 2020; Saliba, 2020). Moreover, in authoritarian regimes, there even is a risk of being attacked or prosecuted (Kaczmarska, 2020, p. 130; Saliba, 2020, p.165) for partaking in political activities. Thus, students from authoritarian countries, where critical thinking and freedom of expression are restricted, might be prone to seek a more liberal environment where to pursue their higher education and students should be more inclined to choose study destinations with high levels of academic freedom. That levels of academic freedom are especially high in the so-called Global North is not coincidental, but connected to the predominant WEIRD culture (western, educated, industrialized, resourceful, democratic; see Henrich, 2020) in these countries. We thus expect global student mobility to be directed from countries with low levels of academic freedom to countries with high levels of academic freedom. At the same time, academic freedom might be an attractive characteristic of a country to retain students in its domestic higher education system.

Measurements, data, and methods

Dependent variable

The dependent variable in our analysis is the network of global student mobility (see below). The UNESCO Institute for statistics (UIS) provides data on degree mobility for a comprehensive set of countries in the world. Although this data has some limitations due to missing data for some countries in the Global South (and unfortunately also for China), the UIS provides the best data available (Vögtle & Windzio, 2022). For our network analysis, we generate binary outcomes (tie = 1; no tie = 0). Unfortunately, there is a considerable amount of missing data; in most cases, the data is missing because a negligible number of outgoing students have not been reported. For instance, in 2014, 21.09% of cells in the adjacency matrix are labelled with ‘n: Magnitude nil or negligible’, whereas 1.83% are labelled ‘x: Data included elsewhere under another category’ (see Table B1 in online Appendix B for an overview). Although such administrative data is not without measurement error, setting the ‘nil or negligible’ category to zero should be unproblematic. However, the 1.83% are real missing values. Listwise deletion of missing data is not an option in social network analysis since the deletion of one node affects the whole network. Yet, we only consider relevant mobility: in our definition, a network tie exists only if an origin i countries’ relative share of outgoing students (a transpose of the matrix of incomings) going into a particular destination j at i’s outgoing population is > 1.30 times the average. Our binary indicator of a network tie is thus rather conservative. Even though this procedure does not entirely solve the missing data problem, the conservative threshold in our binary indicator ensures that missing data due to low levels of student mobility or generally imprecise data have only a minor effect on the statistical models (Vögtle & Windzio, 2022). As a robustness check, we also estimated the same model specification based on data with a 1.10 threshold that is 10% above the average (Table B 2, Online-Appendix B).

The data is available on a yearly basis and covers in absolute numbers how many students from one country went to study in another country. Thus, the raw data already displays the dyadic structure we also rely on in our empirical analysis (see Table 1 and Online-Appendix A for a list of included countries).

Expert ratings: the academic freedom index (AFi)

Academic freedom is not only a political concern; it is also a legal concept, which is why many studies on the topic focus on the analysis of legal texts (Spannagel, 2020). However, the ‘main problem with a purely legal analysis at a global level is that it risks capturing a misleading picture when not compared to a country’s de facto situation of academic freedom, as discrepancies between law and practice are likely to be high in many countries around the world’ (Spannagel & Kinzelbach, 2022, p.3).

A purely legal analysis would not yield valid assessments of the actual state of academic freedom in a country since constitutional or legislative protection of academic freedom does not safeguard from its infringement. For instance, as one of the countries where academic freedom is protected by the constitution continuously since 1924,Footnote 3 Turkey is the country where overall academic freedom has declined sharply over the last decade (see Fig. 1, see Kinzelbach et al., 2022, p. 4). The same, but to a lesser extent, holds for Hungary (constitutional protection of academic freedom since 1949), Russia (since 1993 academic freedom is protected by the constitution), Ukraine (same here since 1996), Bulgaria (constitutional provision since 1991), and Poland (newly introduced in the constitution in 1997). In Russia, academic freedom is protected by the constitution since 1993; Article 29 of the Russian constitution guarantees the freedom of ideas and speech and bans censorship, and Article 44 guarantees the freedom of research and teaching. Despite this, several regulations directed against non-state actors restrict the freedom of speech and information and have created a climate that is not conducive to the unrestrained pursuit of research and teaching. Scholars report that the phenomenon of self-censorship is widespread and that legislative measures were taken to narrow the corridor of what is debatable at higher education institutions. The narrowing contours of public debate contribute to the emergence of ‘red lines’—that is, topics and issues that should not be discussed or challenged (Kaczmarska, 2020, p. 103). Since in Russia rectors are chosen from outside the university and appointed by state officials, they are in a position to suppress academic freedom. This was also the case at the University of Theatre and Film Arts, Budapest, Hungary, in autumn 2020 or at Bogazici University in Istanbul, Turkey, in January 2021—countries where academic freedom is protected by the constitution as well. These examples demonstrate the need for empirically based indicators for academic freedom that rely on assessments of the de facto situation within a country.

Fig. 1
figure 1

Map of academic freedom indicator (AFi) values between 1997 and 2017 (cross-sectional)

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Until recently, public debates and scholarly discussions about the state of academic freedom have been marked by a lack of empirical data (Karran, 2007, p. 291). With the academic freedom index (AFi),Footnote 4 there exists an elaborated and highly reliable index available with both a wider geographical and temporal breadth. It is the first dataset providing near-global and longitudinal coverage (Spannagel & Kinzelbach, 2022, p. 18), designed to provide an aggregated measure that captures the de facto realization of academic freedom (Coppedge et al., 2021).Footnote 5 Especially when looking at the history of academic freedom (see above), the AFi is the most accurate measurement relating to the origins of the current definition of academic freedom while the design of the academic freedom index (AFi) is based on international law and ‘seeks to do justice to the multi-faceted nature of the concept’ (Spannagel & Kinzelbach, 2022, p. 5). The operationalization allows for the disaggregation of indicators, which also provides the opportunity to analyse different dimensions separately (ibid., p. 5). Since the AFi includes a comprehensive set of indicators of actual academic freedom, we regard the academic freedom index as a more valid measurement than limiting the perspective to a country’s constitution on thus only focusing on the de jure assessment.

The academic freedom index (AFi) is part of the Varieties of Democracy (V-Dem) project and dataset (Coppedge et al., 2021), which relies on country experts who code a variety of ordinal variables and provide subjective assessments of latent—i.e., not directly observable—regime characteristics over time. The concepts that the V-Dem project asks raters to measure—such as degree of academic freedom—are ‘inherently unobservable, or latent’, and an obvious way to objectively ‘quantify the extent to which a given case “embodies” each of these concepts’ (Pemstein et al., 2022, p. 2) does not exist; raters instead observe manifestations of these latent traits. Experts—regarding the AFi, at least three country experts per indicator and country-year—are asked to place values on a country-year basis and for different cases on a rough scale from low to high, with thresholds defined in plain language. Each of these experts works independently and because raters may disagree with each other due to disagreement or errors in coding, systematic tools that allow modelling these patterns of disagreement are applied. With these tools, the V-Dem researchers combine the ratings into point estimates of latent concepts and quantify the uncertainty around these point estimates (for a detailed description of this model, please refer to Pemstein et al., 2022). They assume that these judgements are realizations of latent concepts that exist on a continuous scale (Pemstein et al., 2022, pp. 3–15).

This underlying model is also applied to the academic freedom index (AFi) and is composed of five indicators: the indicator ‘freedom to research and teach’, the indicator ‘freedom of academic exchange and dissemination’, the indicator ‘institutional autonomy of universities’, the indicator ‘campus integrity’, and the indicator ‘freedom of academic and cultural expression’. These indicators are rated by experts on an ordinal scale (Spannagel & Kinzelbach, 2022; Spannagel et al., 2020).

The indicator ‘freedom to research and teach’ measures if scholars are free to develop and pursue their own research and teaching agendas without interference. Violations of this freedom are, for instance, if research agendas or teaching curricula are drafted, restricted, or fully censored by a non-academic actor; if scholars being externally induced to self-censor, including public pressure; or if the university administration abuses its position of power to impose research or teaching agendas on individual scholars (Spannagel et al., 2020). The indicator ‘freedom of academic exchange and dissemination’ measures if scholars are free to exchange and communicate research ideas and findings, including unrestricted access to research material, unhindered participation in national or international academic conferences, and the uncensored publication of academic material. Free dissemination also refers to the unrestricted possibility for scholars to share and explain research findings in their field of expertise to non-academic audiences through media engagement or public lectures (Spannagel et al., 2020). The indicator ‘institutional autonomy’ assesses to what extent universities exercise institutional autonomy, defined as the independence of institutions of higher education from the state and all other forces of society to independently take decisions regarding its internal government, finance, and administration (Spannagel et al., 2020).Footnote 6 The indicator ‘campus integrity’ assesses to what extent campuses are free from politically motivated surveillance or security infringements, whereas ‘campus’ refers to all university buildings as well as digital research and teaching platforms. Campus integrity means an open learning and research environment marked by an absence of a climate of insecurity or intimidation on campusFootnote 7 (Spannagel et al., 2020). With the indicator ‘freedom of academic and cultural expression’, it is assessed if academic and cultural expressions are respected by public authorities (Coppedge et al., 2021). The indicator focuses exclusively on ‘the ability to express political views while not addressing academics’ ability to work freely’ (Spannagel & Kinzelbach, 2022, p.4).

The academic freedom index (AFi), composed of the abovementioned five indicators, is obtained through aggregation by point estimates drawn from a Bayesian factor analysis model (cf. Coppedge et al., 2021; Spannagel & Kinzelbach, 2022). AFi values range between 0 and 1—with 1 indicating the highest degree of academic freedom and 0 indicating the complete absence of it (see Fig. 1)—in addition to codes for missing values (Kinzelbach, 2020). Due to its reliance on expert coding, the advanced and well-established data collection and transformation, and due to its geographical as well as its temporal breadth, the AFi is the best available data source for cross-national comparative assessment of academic freedom.

Quality of higher education systems: the Shanghai ranking

A crucial difference in the attractiveness of a country as a study place could lie in the reputation of the higher education systems. The Shanghai index, which indicates the number of universities in a country in various rankings (e.g., the five hundred or two hundred best), can serve as an indicator of this reputation. Historically, academic education has been globalized to a certain extent even in its early stages (Weymann, 2014), and we assume that a high reputation increases the attractiveness of a country as a study place and thus attracts students from other countries. A good reputation could—besides being attractive as a study place for foreign students—have a retention effect for domestic students, but also facilitate the mobility of domestic students due to well-established international networks between elite universities (Vögtle & Windzio, 2022).

Geographical proximity and demography

We control for factors identified in migration studies as influential on students’ degree seeking or long-term mobility. Geographic proximity affects cross-border student mobility and migration (see Delhey et al., 2020; Windzio et al., 2021), mainly due to lower costs (Knight, 2008; Macrander, 2017), but often these exchanges are unbalanced and consist of unidirectional exchanges (Vögtle & Fulge, 2013; Vögtle & Windzio, 2020 for OECD countries). It has been shown that population size is crucial for mobility between countries: the more densely a country is populated, the higher the absolute number of people who migrate (Windzio, 2018). In a similar vein, the larger the population in the destination country, the larger the labour market for immigrants (Lewer & van den Berg, 2008). It is assumed that high population density encourages out-migration (Durkheim, 1965), usually measured by the number of people divided by the area of the country (Windzio, 2018), which corresponds to the number of people per square kilometre. Like general out-migration (Windzio, 2018), student out-migration could be negatively related to absolute population size in countries with limited tertiary education capacity (Kritz, 2016). According to gravitation theory, a large population may ceteris paribus attract students to domestic education systems, as they offer a wide range of educational and employment opportunities. Since the above factors have been shown to be influential on migration patterns and we assume that they are also relevant for the mobility of degree-seeking students, we include them as control variables in our model on the impact of academic freedom on student mobility.

Economic factors

According to the arguments laid out in the first section, countries with high levels of academic freedom might be particularly attractive for transnationally mobile students. However, the singular impact of academic freedom on student mobility patterns is not easy to disentangle. The WEIRD culture (western, educated, industrialized, resourceful, democratic) is not limited to affect peculiar forms of cognition (Henrich, 2020). It also corresponds with a strong importance of anonymous markets, where actors carry out economic transactions with strangers (Seabright, 2010) sine ira et studio, that is, without considering ascriptive traits of the other person. This is one reason why medieval urban communities in Europe established universities and showed the highest rates of economic growth (Henrich, 2020, p. 319). As a result, academic freedom and the quality of the education system might also correlate with economic performance, which we thus control in our multivariate models.

Linguistic factors and similarity in religion

As one of the most important cultural predictors of the transnational flow of students, we estimate the effect of common (official) language between two countries (e.g., Racine et al., 2016). To classify a countries’ dominant language, we used the Ethnologue database (Eberhard et al., 2009). Languages are grouped at different hierarchical levels. For instance, there are six branches at level I, in which the branch of the Indo-European family comprises more than 400 languages spoken by nearly three billion people in more than 70 countries in Europe, Asia, and America. In the following analysis, we used the finer-grained level II classification, which comprises 33 categories of much higher internal linguistic similarity of languages. To give an example, the dominant language in Brazil is Portuguese, which is an Indo-European language (level I) and belongs together with 45 other languages to the ‘Italic’ sub-branch at level II. In addition, we mirror similarity in dominant religion(s); we account for sharing the same religion out of Christianity, Islam, or other (see Windzio, 2018).

Methods

We estimate the effect of academic freedom on global student mobility in a longitudinal social network model. In this model, explanatory variables predict the log odds of a tie between two nodes (Harris, 2014), which—in our case—are two countries. For the definition of network ties, we first computed the average share of outgoing students from country A to all other countries. If the share of outgoing students from country A to country B is greater than 30% of this average share of A’s outgoing students, we indicate a tie in this network. By applying this procedure, we generate N = 167 × 167 adjacency matrices for the years 2009–2017. We use temporal exponential random graph modelsFootnote 8 with bootstrapped standard errors (bTERGM) (Leifeld et al., 2017) to estimate the effects of our explanatory variables on the log odds of observing a tie in a dyad in the respective network. This model predicts the deviation of the empirically observed network (or temporal sequence of networks) from a large set of random networks the respective node set could form. As a result, the model searches for those effects of the specified covariates that make the empirically observed network most likely compared with the random networks.

The academic freedom index: descriptive results

To get an impression if and how degrees of academic freedom have changed over time, we mapped the AFi values. The colours used in Fig. 1 are equivalent to values in the AFi measure, with green indicating values close to one, which means full academic freedom. The redder the colour is, the lower the values on the AFi. We also calculated the mean, the standard deviation, and the minimum and maximum values for our sample (see Table B5 in Online-Appendix B). To be able to grasp the changes for individual countries over the last 20 years before the last year of our period of observation (2017), we opted for a graphical representation of the academic freedom index (see Fig. 1).

Even though Fig. 1 displays considerable changes in AFi values over the period observed, these changes are not adequately captured looking at changes in the mean, variance, and standard deviations over time (see Online Appendix B). This is vested in the fact that we use unweighted AFi values for our analyses; thus, every country enters the calculation on the averages etc. with the same weight regardless of population size or size of the higher education sector. A recent study by Kinzelbach et al. (2022) accounted for this problem and weighted the AFi data by population size (ibid., 3–4) and compared changes between the years 2011 and 2021. This analysis revealed substantial and statistically significant decline in academic freedom in 19 countries in 2021 compared with the situation in 2011. Thirty-seven percent of the world’s population live in these 19 countries and territories with major recent drops in academic freedom (ibid., 3). Thus, taking affected population in account, the decline in academic freedom is much more pronounced, and all world regions except sub-Saharan Africa show substantial declines in academic freedom (ibid., 3). In line with our graphical representations of the AFi values in Fig. 1, Kinzelbach et al. (2022) also find that populous countries such as China, India, Russia, and Turkey exhibit substantially less academic freedom in 2021 than in 2011 (ibid., p. 3). We opted not to weight the AFi data by other country-specific characteristics such as population size since in our descriptive analyses, since we include population size as a control factor in our multivariate analyses (see Table 1). Regarding academic freedom, we are interested in the net effect of the country-specific situation while controlling other factors separately.

Figure 2 shows the network of global student mobility in 2010. In this figure, colours indicate world regions (not levels of academic freedom as in Fig. 1), whereas node size indicates levels of academic freedom: the larger the node, the higher is the level of academic freedom. We see that most European countries (yellow) had the highest levels of academic freedom in 2010. Academic freedom is also high in some countries in North and Central Africa (red), but here, we also find several countries where academic freedom is comparatively low (e.g., Tunisia (TUN); Djibouti (DJI); Burundi (BDI)). The same is true for Middle and Southern Africa (magenta), but overall, the share of countries with low academic freedom is highest in Central West Asia (dark brown), including e.g., Kazakhstan (KAZ); Oman (OMN); Uzbekistan (UZB); Tajikistan (TJK); and Saudi Arabia (SAU). Although there is no perfect pattern, countries with high academic freedom tend to concentrate in the middle of the graph, which means that countries with high academic freedom are those with the most student mobility ties with other countries in the network. According to Kinzelbach et al. (2022), the ‘decline in academic freedom also appears to have accelerated in Western Europe and North America, including in the United Kingdom and the United States of America’ (ibid., p.3) which is not obvious in Fig. 1 since our analysis stops in the year 2017. From the point of view of the major focus of our study, these developments are especially worrisome, since the USA, the UK, and Western European countries are, from a network perspective, the most central countries in the transnational network of student mobility (see Fig. 2).

Fig. 2
figure 2

Academic freedom and global student mobility network in 2010

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Multivariate results

Table 1 shows the results of temporal exponential random graph models (Leifeld et al., 2017). The outcome of these models is the log odds of a tie in the network of global student mobility 2009–2017. Model 1 (M 1) includes the network-structural effects of mutuality, transitive triads, and open-2-paths (see Appendix A for the interpretation of the effects), and geographic distance between countries capitals, as well as the effects of the number of universities in the top five hundred ranking (Shanghai index) and the memory term.

Table 1 Determinants of ties in the network of global student mobility 2009–2017, N = 167 countriesa, bTERGM, 30% threshold
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Except for mutuality, the network-structural effects and effects of geographic distance are robust across all model specifications in Table 1. The effect of transitive closure is positive and significant, whereas the effects of open-2-paths and geographic distance are significantly negative (see Appendix A). The combination of positive effects of transitive closure and negative effects of open-2-paths indicates a latent hierarchy of attractiveness among countries, that is, differences in attractiveness between countries according to unobserved characteristics (Leal, 2021; Windzio, 2018; Windzio et al., 2021). Transitive closure implies a hierarchy in terms of ‘friends of my friends are my friends’: if there is a connection between country A and B and from B to C, transitive closure (GWESP) estimates the tendency to form a connection from A to C, which would close the triad in a hierarchical way (A < B < C). It is hierarchical because the connection from C to A is conditional on the tie from B to C and the outgoing tie from A to B. To give an example, if Mexico is an attractive destination for migrants from Venezuela, and Mexicans have at the same time a high propensity to migrate to the USA, it is very likely that the USA is also attractive for migrants from Venezuela.

The effects of observed indicators of attractiveness are as expected in M 1: the higher the number of universities in the Shanghai Top 500 ranking, the higher is the in-degree. In other words, the higher the ranking in the Shanghai index, the more ingoing ties a country gets from other countries. In addition, the number of outgoing ties decreases with higher values of the Shanghai index. Taken together, these effects indicate significant ‘attraction’ as well as ‘bonding’ effects. The latter means that high reputation of countries’ universities binds students to the respective country.

While effects of the Shanghai index on in-degree and out-degree remain robust in M 2, the effect of academic freedom on in-degree reverses its sign. It was insignificantly positive in M 1, whereas it is now significantly negative in M 2. Thus, academic freedom has a significantly negative effect on out-degree in both models. Excluding the Shanghai index in M 3 and including indicators for cultural similarity (same language group in accordance with the Ethnologue dataset and same religion of a dyad) as well as geographic and demographic factors, the effect of academic freedom is in line with our expectation: it increases in-degree and decreases out-degree (see Fig. 3). Accordingly, there is considerable multicollinearity between academic freedom, the Shanghai index, and GDP per capita. By re-including the Shanghai index into Model 4 (M 4), the effect of academic freedom on in-degree turns insignificant again. It is not surprising that academic freedom binds young adults pursuing higher education to countries with high levels of academic freedom in the network of global student mobility, thus reducing the out-degree for these countries. Academic freedom correlates with higher levels of academic performance, indicated by the Shanghai ranking, and GDP per capita. However, this goes not without exceptions as countries such as Kuwait, Bahrain, and Qatar are economically wealthy, but display very low levels of academic freedom. Thus, although the multicollinearity between GDP per capita, the Shanghai index, and academic freedom is considerable in our models, multicollinearity does not lead to non-convergence of the statistical models. Overall, we find that a high level of academic freedom indeed constitutes an attractive characteristic for a country as a destination for transnationally mobile students.

Fig. 3
figure 3

Effects of same religion, same language, academic freedom, and population on ties in the network of global student mobility, Model 3 in Table 2

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Figure 3 highlights selected effects from M 3 in Table 2. We see in the upper panel effects of same religion and same language being considerable and significantly greater than zero. The same is true for the effect of academic freedom on in-degree, whereas it is comparatively strong and significantly negative on out-degree. This is what we expected according to our theoretical considerations: students tend to stay where academic freedom is high and not to choose study destinations where academic freedom is low. Moreover, results of population size are in line with expectations from gravity theory (Boyle et al., 1998): the higher the population, the lower is the in-degree and the higher the out-degree. Finally, according to the effects of GDP/capita, global student mobility tends to be an issue of comparatively affluent countries since GDP/capita increases both in- and out-degree (lower panel in Fig. 3).

We also find the expected pattern for area size. The larger a country’s area size, the higher in-degree and the lower the out-degree (Table 1, M 1–M 4). Accordingly, area and population size attract mobile students and bind their domestic students to the respective country. However, please note again that the effect of academic freedom on in-degree becomes insignificant in M 4 in Table 2 after controlling also for the Shanghai Index, indicating the considerable degree of multicollinearity between these variables.

For simplicity of reading and interpretation, the confidence intervals based on bootstrapped standard errors are not shown in Table 1. Table B3 in Online-Appendix B (online supplement) includes the 0.05–99.95% bootstrapped confidence intervals. In addition, Online-Appendix B also includes a robustness check where we re-ran our models but changing the threshold of defining a relevant tie in the mobility network to 10%, instead of 30% as applied in Table 1. Here, also the mutuality effects in M2 and M3 turned insignificant, as did the effect of the Shanghai index on out-degree in M4. Aside from that, all effects are robust and changed only slightly.

Conclusion

Higher education institutions educate in sciences and scientific ways of thinking; the essence of scientific thinking and communication is to ask, to criticise, and to disprove, which requires a certain degree of academic freedom. We thus expected students to be more inclined to choose study destinations with high levels of academic freedom, which are especially high in the countries of the so-called Global North due to their predominant WEIRD culture (Henrich, 2020). The results of the multivariate model are in line with these assumptions; they indicate that a high level of de facto academic freedom binds, and potentially attracts, students to the respective countries. The same holds for a (perceived) high reputation of a country’s higher education system, as indicated in league tables such as the Shanghai ranking. Moreover, the results of the multivariate analyses indicate a latent hierarchy of attractiveness between countries, thus differences in (perceived) attractiveness between countries as study destinations for transnationally mobile students (Leal, 2021; Windzio, 2018; Windzio et al., 2021).

We regard the academic freedom index (AFi) as a rich source for the comparable, overall cross-country assessment of academic freedom. However, due to its broad temporal and cross-country focus, it thus naturally has some limitations regarding in-depth knowledge on aspects aligned with more country-specific characteristics of the higher education systems. For instance, the AFi does not entail data on academic employment and working conditions, on funding of higher education institutions, and on the students’ perspective. One might argue that universal rights to free speech and articulation cover students’ academic freedom. However, the exercise of their rights within the universities’ self-governance is still not covered. And in some countries, students’ academic freedom has been under attack, on and off campus, for instance by threatening or exercising forced de-registration of students in case of participation in demonstrations, as has been the case in Belarus in summer 2020 or in Iran in autumn 2022. Especially for the group of transnationally mobile students, students’ academic and overall freedoms should largely impact on considering a country as study destination. Even though the AFi is unable to cover students’ academic freedom from a first-hand perspective like it would be possible in a survey, it is the most valuable resource for the de facto assessment and cross-country comparison due to its reliance on expert ratings (see Spannagel & Kinzelbach, 2022).

In our analyses, we find the expected effects of academic freedom on in- and out-degree, thus on the probabilities to attract international students as well as to be able to retain domestic students in the national higher education system. However, we find this in a rather simple model specification. In models adjusted for including control variables, when accounting for the combined effect of GDP per capita and the Shanghai index, the effect of academic freedom on in-degree turns out to be unstable and insignificant in our final model specification (M 4 in Table 1). The multicollinearity of academic freedom with GDP per capita and the Shanghai index suggests that student mobility could be embedded in an overarching set of institutions, where institutional indicators are strongly correlated and relate to latent institutional variables. In our view, future research on transnational student mobility should thus account for the underlying institutional dimensions of the quality of higher education systems and countries’ economic wealth. Which mechanisms and which institutional settings impact on levels of academic freedom, economic performance, academic reputation, but also democratization and institutional fragility (Vögtle & Windzio, 2022)? To unravel mechanism and institutional settings favourable to academic freedom, high quality of education institutions and economic wealth of a country, institutional sub-dimensions could be combined into a two-mode network of institutional embeddedness, as has been done in previous studies with respect to global cultures (Windzio & Martens, 2022).