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What does the Shanghai Ranking really measure ?

Working paper

Comments and suggestions welcome

Olivier Berné 1 1 CNRS and Université de Toulouse, olivier.berne@irap.omp.eu

The notion of higher education as a global market is pervasive among policymakers. Attached to it is the generalization of national and international rankings, supposed to give an "objective" measure of the performances of Higher Education Institutions (HEI), including universities, and justified as necessary to provide guidelines to families and students when making their choices. The deep influence of rankings on the organization of higher education worldwide, and more generally on how knowledge is created and distributed, has been established (1; 2; 3; 4; 5; 6). Rankings have however been criticized in academic studies which have pointed out their methodological limitations (e.g. (7; 8; 9)). In addition, social science analyses suggest that rankings favor the reproduction of elites at a global scale (10; 11; 12). This paper aims at demonstrating that these later conclusions can be supported empirically.

Gathering financial data available publicly for universities, this paper shows that performance as measured by the Academic Ranking of World Universities (ARWU, a.k.a. the Shanghai Ranking, the oldest international ranking of HEIs ( 13)) correlates with wealth of the institutions (expressed in terms of annual budget per student) and with the amount of tuition paid by students. For US institutions, better ranking also correlates with higher income of students parents. Hence, the ARWU ranks economic capital of HEIs and of the families attending these HEIs, in summary, the ARWU ranks "the economic eliteness" HEIs. This supports theoretical analyses which suggest that international rankings of universities consolidate the domination of economic elites at a global scale, and favor social exclusion. In addition, by promoting a model of higher education with high tuition fees, the ARWU likely contributes to the expansion of the student debt.

Introduction

The field of higher education has changed progressively to become a worldwide "market", where universities are seen as corporations, competing at global scale (14; 8; 10; 15). In this competition, and in the eyes of neoliberal policymakers, international rankings play a crucial role as they standardize the criteria for evaluation of "excellence", at a global scale. Rankings have become an obsession, in the media, and amongst policy-makers (2; 16), and administrators now spend a significant amount of energy to bring (or maintain) their institutions amongst the first 100 in international rankings, with the hope of becoming a "World Class University" [START_REF] Deem | Transforming higher education in whose image? exploring the concept of the world-class university in europe and asia[END_REF]. Rankings have a profound influence on institutions of higher education : they modify how funding is distributed (in favor of departments likely to produce better rankings), modify hiring strategies (targeting prize winners), stimulate fusions of universities etc (see the recent review provided by Espeland & Sauder (18), references there-in, and (2; 5; 6)). These strategies are also supported (or enforced) at national levels, by governments who consider that their country's reputation is built -at least partially -on the quality of higher education (5; 19). In practice, this is often measured by how many universities on the national territory make it to the top 100 in international rankings (2; 20). Overall, it is clear that international rankings have deeply transformed the organization of higher education and it thus important to ask 1) whether the criteria in these rankings are pertinent, and 2) what this "ranking mania" (the term is taken from ( 16)) may produce in societies.

The oldest international ranking, which is the focus of this paper, is the Academic Ranking of World Universities (ARWU a.k.a. the Shanghai Ranking [START_REF] Cai | The story of academic ranking of world universities[END_REF]). The criteria used in the ARWU rely on the awards received by professors and alumni, the citation indexes and number of publications in Nature and Science. Influential scholars use its results in analyses aiming to demonstrate a causality between "performance" of universities (as in the ARWU) and, for instance, the level of either public investment by states in higher education, "autonomy" or "governance" ((20; 21)). However, several studies have shown the shortcomings of its methodology, and in particular it is highly criticized for not taking into account the quality of education ((7; 10; 9)). In addition to critics regarding their methodology, rankings of academic institutions have been critically analyzed with the support of classical sociological concepts. In a study on rankings of US law schools, Espeland & Sauder (1) found that these institutions modify their behaviors, so as to adapt to the criteria used in league tables. Hence, according to these authors, rankings do not act as a true measure, but simply confirm expectations, and this can be rationalized as an occurrence of a "self-fulfilling prophecy" as formulated by Merton (22). This e↵ect also extends to a global scale with international rankings : by declaring who detains prestige and power, they confer more prestige and power to already established "world class" institutions (see (12; 11)). As such, "world class-ness" can be seen as reflection of dominance, in the economic, intellectual, and political fields [START_REF] Amsler | University ranking as social exclusion[END_REF]. Rankings has also been critically analyzed (see e.g. (11; 23; 24; 25)) with the lens of Gramsci [START_REF] Gramsci | Selections from the prison notebooks[END_REF] and Foucault [START_REF] Foucault | Surveiller et punir. Naissance de la prison[END_REF]. In these theoretical frames they can be understood as tools which reinforce the hegemony of the dominant model (here the Anglo-American model of higher education) by issuing rewards (a good rank) and punishments (a bad rank, or no rank at all). Amsler & Bolsman consider that rankings are in fact political tools created by elites to preserve their status. This follows Bourdieu's (28) idea of the "club e↵ect" which consists in an e↵ort by club members to maintain their position of dominance, by consolidating "status prestige", here, thanks to rankings. The ARWU and other international rankings bring this strategy to a wider level : that of a "globalized field of elite power" [START_REF]Global field and global imagining: Bourdieu and worldwide higher education[END_REF].

The question addressed in this paper is whether there is a way to illustrate empirically the connections between economic dominance and performance in the Shanghai Ranking. These connections are suggested by earlier studies which have shown that countries investing more funds in tertiary education generally perform better in the ARWU (e.g. in terms of the number of institutions they place in the top 100 (11; 21; 29)). Some rankings actually use financial indicators (annual budgets) as criteria, and hence it is obvious that they at least partially measure wealth of institutions [START_REF] Pusser | University rankings in critical perspective[END_REF]. Kaba & [START_REF] Kaba | Analyzing the anglo-american hegemony in the" times higher education" rankings[END_REF] shows that performance in the Times Higher Education (THE) international ranking is related to the endowment of HEIs. Some hints are also found in the literature connecting economic capital and rank in league tables : Hazelkorn [START_REF] Hazelkorn | Learning to live with league tables and ranking: The experience of institutional leaders[END_REF] notes that most highly ranked institutions have annual budget above $ 1 billion, and Salmi [START_REF] Salmi | The challenge of establishing world class universities[END_REF] shows that the budgets per students in several top institutions is well over $100,000 per year. The fact that elite institutions have more students from the richest families is also well established (see e.g. [START_REF] Duncan | Whither opportunity?: Rising inequality, schools, and children's life chances[END_REF] for the US, [START_REF] Jerrim | Family background and access to high status universities[END_REF] for the UK and (34) for France), however how this relates to rankings is not documented. This paper investigates connections between economic capital and rank in the ARWU empirically in several ways :

• Is there a direct relationship between annual budget / student of HEIs and their performance in rankings ?

• Are HEIs with highest tuitions fees those performing best ?

• Are institutions with children from richest families those which perform the best in ARWU?

In the first section, the data collected for this study is presented. This is followed by a description of the general results derived from the data analysis. The connection between economic capital and rank is discussed in Sect. ??. The following section discusses the role of the Shanghai ranking in the Anglo-American hegemony of HEIs and on the global student debt.

Data

Collected variables

The first objective of this paper is to compare economic capital and performance indicators given in the ARWU. The performance indicators in the ARWU are the score and the rank obtained by a university. These two figures are linked as universities are ranked by score. The score results from the concatenation of various "objective" parameters such as the number of publications in Science of Nature, the number of Nobel Prizes etc.

In order to capture economic capital, we have collected four variables. The first variable is the annual budget (or annual operating expenses) of HEIs reflecting the absolutes financial means of the institution. Of course, when comparing an university against another, one must bear in mind that the number of students may vary significantly, and hence it may be more accurate to consider the normalized budget per student as indicator. This implies to obtain for each institution the number of students, which is the second variable we have collected. The third variable we have considered is the annual amount of tuition fee paid annually by students. Finally, we have included in this study the average annual income of parents of students within each institution, when available.

In summary, the variables we have collected are, for each HEI is:

• The rank in ARWU

• The score in ARWU

• The number of students

• The total budget

• The tuition fees

• The income of the parents.

Data collection

We have limited the collection of data to the first 100 HEIs of the ARWU. This choice is motivated by several reasons : i) the top 100 is considered as a reference in terms of objective and assessment of quality by policymakers (2), ii) the score is given only for the top 100 universities in the ARWU, and the ranks are grouped in clusters of 50 beyond rank 100, iii) for less renowned universities it is often more di cult to obtain detailed financial information.

For the top 100 universities, the rank and scores in ARWU are directly available from the 2007 Shanghai Ranking website. The other three variables (number of students, total budget, tuition fees) were collected from o cial documents of the universities, mostly annual reports and financial statements.

The number of student is relatively easy to find for any university. This is generally found on the institution's website, or annual report.

Finding the total budget requires more e↵ort. For universities in the UK, US, Canada, Australia, the data can generally be found either from the institutions financial statements or annual reports. Some of these universities have rather complex budget which includes assets etc. The figure we have taken is the "operating budget", or the "net expenses". When not available we have used the net revenue (which most often is very close to the net expenses in the universities we have studied). For most European and Asian institutions the data can be found on their websites ("facts and figures") or in their annual reports (sometimes not in English). Chinese universities do not provide the numbers directly, hence the data mainly comes from the press or indirect sources. French institutions do not publish their financial statements, however the data can be found in other o cial documents. Overall, for the vast majority of the top 100 institutions it has been possible to find reliable sources of information to obtain their annual budget. Four "universities" are however problematic, because of their peculiarity. These are medical schools in the US, which have a small number of students, and whose budget dedicated higher education activities cannot be separated from their activity as an hospital. These are: The University of California San Francisco (⇠ 3000 students), The Rockfeller University (⇠ 200 students), The Medical Center at Dallas (⇠ 5000 students), and the Mayo Medical School (⇠ 200 students). Therefore, they have not been considered in the analysis presented in the section below, although they are reported in Table 1 for completeness.

Tuition fees are relatively easy to find for most institutions as this information is made available for prospective students on the institution websites. We have always taken the values applied to resident (i.e. non-foreign) students. For US universities this means that we have collected the tuition fee applied to in-state students. The fees are those applied to undergraduate students for full-time enrollment. In some cases, the tuition fees depend on the chosen program. In these (rare) cases we use the average value.

The conversion of currency to US dollars was done with the rate of the day when collecting the data i.e. in winter-spring 2018. The variations of exchange rate over this period are minor, and therefore this does not a↵ect our results. We note that the data we have used is not corrected for purchasing power parity. This is done intentionally : in the context of globalization of higher education we have considered that it is more relevant to use the raw values.

The resulting data is presented in Table 1 and the data itself with the direct links to the sources for each university is provided as supplementary information.

Regarding the income of the parents, the data is available only for the US institutions. It was collected as part of The Equality of Opportunity Project 1 from a large sample of anonymous tax fillings and tuition records. Unfortunately such data is not available for the other countries represented in the top 100 of the Shanghai ranking. For the 42 US universities in the top 100, we have gathered the data and it is presented in Table 2.

3 Results

General results

A general investigation of the economic and ARWU performance variables is instructive. For instance, the total budget for the first 100 universities in ARWU is $213 billion, comparable to the GDP of New Zealand. The average number of students in universities is around 31,000, with a standard deviation of ⇠ 17 500 (see Figure 1 for details). It must be noted that there is no correlation between the number of students and score in Shanghai (correlation coe cient of -0.22) : bigger is not better. The average annual budget per student in the top 100 is ⇠ $84,000. The distribution of tuition fees (see Fig. 2) is bimodal, with peaks on the minimal and maximal fee bins (respectively $0 -10k and $50-60k per year), with minimal fees found in continental Europe and maximal fees in the United States.

ARWU and economic capital

This section focuses on the links between economic capital and performance of HEI in the ARWU. We use three indicators of economic capital :

• The annual budget per student of each HEI as an indicator of the economic capital of individual HEI. We ignore the endowment, assets, immovable capital and other part of the total capital of HEIs;

• The tuitions fees of each HEI, as an indicator of the capital of the families of students attending individual HEIs;

• The average income of parents of students of US HEIs as a indirect measure of the capital of the families of students, in the United States.

We first present these raw indicators and compare them to the ARWU variables in Sect. 3.2.1, and we then study the trends of these indicators when compared to groups of rank in ARWU in Sect. 3.2.2.

Far clarity in the following sections, let us write the score for a university of rank j g(j), the annual budget for a university as b(j), the number of students as s(j), and the tuition fees as t(j). The annual budget per student is k(j) = b(j)/s(j). We label the average income of parents of students attending a university of rank j I(j).

Inspection of raw data

Fig. 3 compares the tuition and annual budget per student in a scatter plot. Information regarding the geographical location of HEIs is also labeled, as well as the rank of the top 10 universities, and the Ivy League institutions are identified. First, it should be noted that there is a moderate yet significant correlation between fees and budget per student (correlation coe cient of 0.68). This indicates that tuitions fees play a significant role in the funding of higher education in the top 100 universities of the ARWU. In this graph, the lower left corner, corresponding to low or zero tuition fees and low to moderate annual budgets per students is filled exclusively by European universities. Instead, the upper right corner (high tuitions and high budgets) is filled with US institutions only. Countries other than the US and EU are all located in the space between these two poles. This segmentation will be discussed in more details in Sect. 4.1 when addressing the hegemony of Anglo-American HEIs. Fig. 4 compares the score obtained by HEIs, in the ARWU and their annual budget per student. There is a correlation between score and average annual budget per students (correlation coe cient of 0.65). This indicates that the score obtained in the ARWU is somehow indirectly connected to the budget of HEIs, since budget is not a criteria for calculating the score in this Ranking.

Average trends in ranks vs economic capital

In order to asses the potential links between economic capital and performance in the ARWU, the three variables of economic capital will be compared to 5 groups within the ARWU. These groups are defines as follows : the groups containing the best 20, 40, 60, 80 and 100 universities. For each group, we derive average value for the three indicators of economic capital. The first indicator is the average budget per student x(i), calculated for each group i, with i = 1 5. The second indicator is the average tuition fee x 2 (i), calculated for each group i. Finally, we also compute the average income of parents of students in universities of each group i, x 3 (i). It must be noted that, for each derivation, the averages are computed ignoring the 4 medical schools mentioned above, and for the income of parents, ignoring the universities for which there is no data (non-US). The calculated x 1 , x 2 and x 3 are displayed for each group i in Figs. 5, 6 and 7, respectively. Inspection of Fig. 5 shows that universities with largest budget per student belong to the groups with the best ranks, hence that "performance" in the Shanghai Ranking is related to budget per student. The best universities, in the top 20, spend over twice as much per student as compared to the universities in the top 100. Fig. 6 shows that the average value of tuition fees increases for groups obtaining the best ranks. The average tuition in universities of the Top 20 is twice that of tuitions in the Top 100. Finally, Fig. 7 shows that best ranked universities are also those, in average, where students parents have the highest incomes. These results therefore suggest that performance in the ARWU is related to the economic capital of HEIs, and of the families of the students attending these institutions.

Discussion

ARWU and the hegemony of the Anglo-America model

As discussed in the introduction, several authors refer to the position of US, and more generally Anglo-American universities, as "hegemonic", and it can be argued that rankings reinforce this hegemony (11; 30; 24; 25). The "Anglo-American" model of HEI is relatively merely defined and sometimes referred to as the "Anglo-Saxon" model (e.g.( 25)). In fact, Marginson [START_REF] Marginson | Global university rankings[END_REF] argues that this model does not exist in reality, and is an idealized view of HEIs in the minds of policymakers. Nevertheless, he provides some hints of what these Anglo-American HEI are : "centrally focused on knowledge production; emphasizing research and graduate studies; excellence and prestige; tied to business and knowledge economy; competitive for students and fund; internationally oriented" to which he adds and is particularly interesting when studying the economic capital of HEIs as here : "achieving greater autonomy via financial diversity, including tuitions [...]". Marginson notes that "the US Ivy League private universities are closest to this model in the real world", and obviously Harvard is the canonical example. Obviously, Anglo-American HEIs are also tied to English speaking countries. Hegemony is in this paper understood as in the classical definition of Gramsci [START_REF] Gramsci | Selections from the prison notebooks[END_REF] : " 'spontaneous' consent given by the great masses of the population to the general direction imposed on social life by the dominant fundamental group". Hegemony of the Anglo-American model of higher education, and the action of the ARWU to support this hegemony, can here be investigated in the frame of this definition and with the data presented in the previous sections.

The ARWU top 10 universities are indicated in Fig 3 which displays the tuitions of HEIs vs their budget per student. 7 of them are in the upper right hand corner (high tuitions and high budget per student) and 3 are in the middle range (medium tuitions and medium budget per student). None are in the lower left hand corner (low tuitions and low budget per student) where all continental Europe HEIs lay. The Ivy League universities are also indicated in this Figure . They are all in the upper right hand corner. Here the "dominant fundamental group" is thus well identified : it is the one occupying the upper right part of the figure, and the institutions found there correspond well to the definition of Anglo-American HEI discussed above : English speaking, Ivy-League and "achieving greater autonomy via financial diversity, including tuitions". The direction given by this group, is the one of expensive and rich institutions, and the 'spontaneous' consent is obtained thanks to the publicity of the ARWU in the media. In conclusion, the hegemony of the Anglo-American model is well illustrated here by merging ARWU and economical data of individual institutions.

ARWU and social exclusion

Amsler & Bolsmann [START_REF] Amsler | University ranking as social exclusion[END_REF] suggest that rankings are tools of economical policy, which are used by the economical elite to exclude non-members of this elite from top HEIs, so as to preserve social reproduction. We can investigate this proposal with the data presented in the above sections.

Figs. 5,6, 7 indicate that there is a relationship between economic capital and performance in the Shanghai ranking. In practice, this could be seen as anecdotal, or even useful as anyone could then use the ARWU as a useful scale to measure "economic capita", or "power" [START_REF] Pusser | University rankings in critical perspective[END_REF]. However, this is not the advertised aim of the ARWU, and it is therefore never understood as such by the thousands of academics, parents, prospective students etc. who consult its results. Who are those who advertise rankings ? Mostly administrators and policymakers, in other terms elite members. And these administrators and policymakers, perhaps unconsciously, promote rankings not as measure of economic eliteness, but as a certification of the quality of education and research activities. It is thus fair to conclude, as proposed by Amsler & Bolsmann [START_REF] Amsler | University ranking as social exclusion[END_REF], that the ARWU (and likely other international rankings) are used as tools of social exclusion, at a global scale.

ARWU and the funding of higher education

Another aspect which is perhaps less discussed in the literature is the e↵ect of international rankings on funding of higher education and student debt. In the worldwide competition to obtain the "world class university" label which translates into a good rank in the ARWU [START_REF] Deem | Transforming higher education in whose image? exploring the concept of the world-class university in europe and asia[END_REF], the Ranking can be seen as an incentive pushing institutions and/or governments to increase the budget per student. There are several ways to increase the budget per student in universities, but for a large majority of the institutions this has been materialized by increasing the share of private funding [START_REF] Carpentier | Public-private substitution in higher education: Has cost-sharing gone too far?[END_REF] mostly through the increase of tuition fees. It is however noticeable that some countries, in particular in Latin America, have decided to express resistance against this dominant (hegemonic, Sect. 4.1) paradigm of expensive education [START_REF] Ordorika | International rankings and the contest for university hegemony[END_REF]. For many others, reforms have resulted in a rise of tuitions and of the national the student debts (36; 37; 38; 39). Because the rank in the ARWU has turned from a reference "measure" to an "objective" for many governments, and because those rich universities costing more to parents are those performing best in the ARWU as we have seen above, it is likely that the model favoring high tuition fees will continue to spread. Therefore, the student debt is likely to become global, as well as the issues related to its growth [START_REF] Stiglitz | Student debt and the crushing of the american dream[END_REF].

Conclusions

Using financial data available publicly, it is shown in this study that the Shanghai Ranking is mostly a ranking of economic capital of HEIs and of the families of students attending the HEIs. Overall, the ARWU can be seen as a ranking of economic eliteness. The ARWU can be considered as a tool acting at the global level which 1) helps reinforcing the hegemony of the Anglo-American model of expensive research universities which is likely to promote the rise of the global student debt, and 2) as a tool used by elites to exclude non-elite members from their club, i.e. as a tool of social exclusion.

Table 1: For the first 100 universities in the ARWU 2017, the 6 variables used in this study, i.e. rank j, score, number of students s(j), annual budget b(j), tuition fees t(j) and income of parents I(j).

Figure 1 :

 1 Figure 1: Histogram of the number of students, in universities of the top 100 in the ARWU.

1 6 Figure 2 :

 62 Figure 2: Histogram of the tuition fees, in universities of the top 100 in the ARWU

Figure 3 :

 3 Figure 3: Budget per student and tuition fees in the Top 100 universities of the ARWU. Digit labels are the ranks in ARWU, for the top 10 universities, namely and in order Harvard, Stanford, Cambridge, MIT, Bekeley, Princeton, Oxford, Columbia, Caltech and University of Chicago.

Figure 4 :

 4 Figure 4: Score of universities in the ARWU 2017 versus their annual budget per student.

Figure 5 :

 5 Figure 5: Averaged per-student annual budgets in top universities of the Shanghai ranking. The averages are derived for the top 100, 60, 40 etc. universities in the ranking. e.g. the average annual budget per students in universities of the Top 20 is 181.2 k$.

Figure 6 :

 6 Figure 6: Averaged tuitions fees in top universities of the Shanghai ranking. The averages are derived for the top 100, 60, 40 etc. universities in the ranking. e.g. the average tuition fees in universities of the Top 20 is 34.7 k$.

Figure 7 :

 7 Figure 7: Averaged income of parents in top US universities of the Shanghai ranking.The averages are derived for the top 100, 60, 40 etc. universities in the ranking. e.g. the average annual income of parents of students in universities of the Top 20 is 155.9 k$. The median US home income for 2017 is indicated.

Rank