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NATIONAL RESEARCH UNIVERSITY HIGHER SCHOOL OF ECONOMICS

Faculty of Business and Management

School of Business Administration

GRADUATE QUAILIFICATION WORK - MASTER THESIS

Investigating the dependence of university efficiency on its scale in Russia

Bulavskaia Veronika

Supervisor Filinov Nikolay

Moscow 2019



Table of contents

Introduction

1. Theoretical aspects of the dependence of the efficiency of the university on its scale

1.1 Determination of an approach to the efficiency of educational institutions

1.2 The impact of university scale on various aspects of its efficiency

2. Development of an approach to assess the efficiency of universities

2.1 Retrospective review of approaches to assessing the efficiency of educational institutions

2.2 Using the DEA method to evaluate the efficiency of educational institutions

3. Examination of the dependence of the efficiency of the university on its scale

3.1 Research method and data collection

3.2 Results and discussion

Conclusion

Bibliography

Appendix

Appendix 1 University codes

Appendix 2 Factors of the model after the initial selection

Appendix 3 Correlation test results

Appendix 4 The DEA model obtained results



Introduction

university dependence educational institution

The educational system is one of the most important social institutions in modern society, which is hard to overestimate, because it not only allows to transfer the knowledge accumulated by mankind, but also creates new and in general impacts on the face of a whole new generations. The existence of such a term as an academic rent shows that the level, and at the same time, undoubtedly, the quality of education has a direct impact on the standard of living of the person receiving an education.

On the one hand, educational institutions should provide a wide and highly professional base of knowledge and soft skills for their students. On the other hand, the government, as one of the important stakeholders of the educational system and its elements, is interested not only in the quality of universities, but also in their accessibility and financial efficiency. Both groups of external counterparties that influence educational institutions guide the approach to work for the universities themselves. Effectiveness, quality and availability form the concept of efficiency.

Therefore, the question of evaluating the efficiency became a multidimensional issue for study. At the same time, some educational institutions succeed in one area, others - in completely different. Thus, due to the specificity of elements of educational system, it is hardly possible to directly judge whether any of them cope with their tasks better or worse. Universities have a lot of parameters to evaluate their performance.

Hereat, among a lot of existing methods and tools for assessing these educational institutions, only small amount of them can provide relatively high level of objectivity. The evaluation of efficiency of the most of elements in multicriteria systems, such as educational institutions, becomes the result of subjective assessment of one person or a group of experts, which cannot be considered as a representative outcome of the comparison. Application of the Data Envelopment Analysis (DEA) method would allow to objectively assess a large number of multi-criteria objects of the tertiary education system using mathematical approach.

The crucial advantage of the applied model, in addition to its objectivity, is the possibility to project inefficient elements of the system onto the efficiency frontier in order to identify a hypothetical benchmark object - that is, to determine the potential that a specific element can realize by condition of eliminating the causes of inefficiency. The empirical outcome of applying this approach generally is the specification of the quality of the system as a whole, as well as the possibility of clustering the system objects to develop approaches for further work on their improvement.

The very concept of efficiency is complex in nature. Its measurement can be carried out most objectively with the help of the DEA method, since this method helps to avoid expert influence on the weight of criteria and uses objective values rather than experts' opinion.

Not only scientists are engaged in studying efficiency by themselves, but also ratings can be a vivid example of an attempt to assess the efficiency of world universities, as well as their comparison. At the same time, from the university management perspective, the crucial issue is not so much the position of the university in the ranking or its performance indicator according to one or another scale but understanding the sources of its efficiency. As part of this work, the question of whether and, if so, how and to what extend the scale of a university affects its efficiency, is being investigated. Is it possible to be small and efficient, or does achieving high efficiency necessarily require quantitative growth? That is to say, should the university invest in growth (attract students, professors), will this lead to an increase in quality?

The impact of the university scale on its efficiency has an ambiguous nature. University growth can serve as a source of resources for quality improvement. The scale of a university leads to a quantitative increase in scientific work produced, which, in turn, enhances the reputation of the university and attracts more talented professors and students. From this point of view, a university's desire for growth is a reflection of its desire to increase the quality of the services provided. However, according to the theory of microeconomics and economy of scale, from a certain point the effect of scale may be negative, and, consequently, financing - ineffective. All this leads to a strong dependence of the efficiency of the university in all aspects of its scale in theory.

Currently, there are several articles [5, 7, 10, 11, 13, 14, 15, 24, 28, 33, 35, 40, 41] on what aspects of the activities of universities are affected by their scale. Nevertheless, these works do not give an unambiguous answer on whether the efficiency of universities depends on its size. The relevance of the research project is due to the fact that at the moment the dependence between the scale of the university and its efficiency has not yet been properly studied, especially in Russia.

Thus, the purpose of the research is to study the dependence (presence and effect, if any) between the university's efficiency and its scale.

In order to fulfill this purpose, the following objectives of the study were developed as follow:

1. Determination the approach to the efficiency in relation to the university

2. Retrospective review of research on the impact of university scale on various aspects of its efficiency

3. Analysis of existing approaches to assessing the efficiency of educational institutions

4. Assessment of the efficiency of universities in Russia using DEA method

5. Study the dependence between efficiency and scale of universities in Russia

The object of the research is the efficiency of universities in Russia.

The subject of research is the impact of university scale on its efficiency.

For the research purpose following methods were used:

· Literature review

· Data Envelopment Analysis

· Regression modeling

Following data and information sources were used:

· Information and analytical materials on the results of monitoring the effectiveness of educational institutions of higher education in Russia in 2017

· Electronic Library Resources of NRU HSE

· Library Recourses of NRU HSE

· Science Citation Databases Web of Science and Scopus

· 

1. Theoretical aspects of the dependence of the efficiency of the university on its scale

1.1 Determination of an approach to the efficiency of educational institutions

Evaluation of the efficiency of educational institution has always been an important issue. At the same time, the term efficiency itself is contradictory in nature and depends heavily on the point of view of a decision-maker and its nature. Three main actors in these interrelations are: students, universities and society in general, represented by a government.

As for students, efficiency of their education mostly lies in an employment and future wages perspective field. According to a recent Deloitte survey [55], among the most important aspects of a work life for today's graduates financial reward is number one.

Exhibit 1 Reasons to leave the current job in the next two years (in percent)

Source: Deloitte Survey

More than a half of about 16,5 thousand respondents noted that high salary is crucial for them while choosing a job. High remuneration and employment rate also define the most attractive fields of education based on possible salary after graduation. For instance, in 2019, Glassdoor [51] points out in their research, among these professions there are mostly IT and strategic management related ones.

Table 1

The list of highest paying jobs for new graduates

Entry-level Job	Base Salary, $
Data Scientist	95 000
Software Engineer	90 000
Product Manager	89 000
Investment Banking Analysis	85 000
Product Designer	85 000
UX Designer	73 000
Implementation Consultant	72 000
Java Developer	72 000
Systems Engineer	70 000
Software Developer	68 000

Source: Glassdoor

This fact can also explain results of the Times Higher Education research [61] of most and least popular undergraduate courses, among which business administration and technology ones prevail. In addition, it is well known, that graduates' wages vary noticeably with a degree of education. This phenomenon is called “Education premium”, “Academic rent” or “Returns to education”.

Education premium is the difference in earnings between the more and less highly educated. This premium is created by a willingness of employers to pay more considering that employees with higher level of education have more skills and knowledge. Thus, they are ready to pay more to better educated employees.

For instance, OECD Education report 2018 [54] mentioned that the possibility to earn more than the median is in direct proportion to educational attainment. Two-thirds of adults with tertiary education earn more than the median while only one quarter of people without secondary education can overcome this threshold. In the same report it is disclosed that secondary education on average brings 20% to a salary and tertiary education increase earnings by 55%. As can be seen from the exhibit below, there is a tendency to a vast difference in salaries between those who doesn't have any secondary education and those who got a tertiary education all around the world.

Exhibit 2 An education impact on relative earnings of workers among OECD countries (2016)

Source: OECD Report

It means that education plays one of the crucial roles in a modern labor market to define a remuneration for each employee. Initially neoclassical economic theory associated the existence of academic rent with the assumption of better performance of students with higher education. However, it was found out by Serbian professors [30] K. Josifidis and N. Supic that this connection is not necessarily linear or even exist, which means that employers tend to unevenly remunerate employees not as much for their performance as for the fact that a graduate has higher education.

Thereby, as a consequence, students interpret efficiency of education as their capability to get relatively high level of their personal performance to be competitive in a labor market after obtaining an education in certain university and certain field of study.

Universities, in turn, is another substantial party of worlds' educational process. In the paradigm of pedagogy, the definition of efficiency, which is considered canonical, heavily corresponds to the content of effectiveness. This definition is one given by V. M. Blinov [8] in developing an approach to assessing the quality of education:

“Effectiveness of education is a socially significant quality of education, by means of which the results of students' performed activities are assessed according to how close are they to the general educational goal, corresponding to the generalized view of the individual's learning”.

According to a given definition, the role of universities as those who share knowledge with their students is emphasized as an essential one. Teaching next generations and cumulating collected human expertise are the vital reasons for educational institutions to be organized. But it is obviously not the only one value that universities bring to the society. They also produce new knowledge through their scientific activities in a vast variety of fields. In addition, educational institutions, like every institution, is an important social construct, which creates social dynamics within them and also influences personality formation of each attendee, including students and professors as much as administrative and support personnel. Thus, there are three main aspects to be assessed in order to distinguish more efficient universities from less efficient ones based on crucial activities of universities:

· Education, which could be measured by academic scores of students;

· Scientific activities, traditionally estimated with citation ranking of scientific publications made in the university;

· Social activities could be in some degree measured by international activities of a university.

Based on this, efficient university is the one which can provide a high-quality result in all these dimensions. Efficiency of each university is a very important indicator that has to be shown to attract new and the most talented students. So that is why universities are usually compared by local or worldwide rankings.

Members of the Netherlands Bureau of Economic Policy Analysis, P. Koning and K. van der Wiel [31], point out that traditionally the ranking of schools in the Netherlands is based on the academic achievements of students, that is, the average grade point (GPA) of students, the percentage of graduates and others. According to them, this indicator is not only relevant and reflects the reality, but also can be used as further basis for benchmarking the most successful practices from better performing institutions according to a ranking.

However, such a method of assessing the university performance has a significant drawback, which it also generates. Researchers themselves in their work studied the dependence of the choice of school by students on publications in the mass media of the ratings of these educational institutions. Using mathematical tools (regression models), scientists have shown that the position of the school in a ranking is an important factor for students and their parents while making a decision about future university to apply to and, accordingly, study at. This leads to the fact that more students want to be enrolled in universities that are higher in a ranking, which increases the competition for one place among entrants. Thus, educational institutions with better reputation have the opportunity to select the most talented and gifted students, which, in turn, affects the rating of this university. This is an artificial improvement in the quality indicators of some universities and the deterioration of others.

Luis C. Nunes with his colleagues from the Lisbon School of Business and Economics Nova came to a similar conclusion in their study [36]. In 2015, they also assessed the impact of public information on the ranking of schools in Portugal on the attractiveness of these schools in the eyes of students and their families and also confirmed an existence of this connection. It is also notable, that they also mentioned that school ratings are compiled based on students' results in national graduation exams, and in this case, rankings are not an actual valid source of data on school performance in terms of adding value to student knowledge. Thus, universities, driven by their aspiration to get better students, have their own understanding of efficiency, dissimilar to that of the students. For them efficiency can be measured through different rankings. Among them the following ones are the most influential and respected in a world:

· Quacquarelli Symonds (QS) World University Rankings

· Times Higher Education (THE) World University Rankings

· Shanghai Academic Ranking of World Universities (ARWU)

These three rankings are based on different approaches to calculate and determine, which metrics are the most important in a final score and, accordingly, have to have greater weight, as much as different ways to collect the database for subsequent measures.

First of them is constructed as a combination of 6 metrics weighted by their contribution to the final efficiency according to their importance for university from a ranking creators' perspective. Their methodology [59] is presented in Table 2.

Table 2

QS World University Rankings Methodology

Metric	Weight, %	Criteria
Academic reputation	40	Reputation survey of 94 000 experts from the industry regarding teaching and research quality
Faculty/Student Ratio	20	Teacher per student ratio
Citations per faculty	20	Citations per paper within 6 years period, normalized by a scientific field
Employer reputation	10	Employer survey of 45 000 experts from companies
International faculty ratio	5	Not specified
International student ratio	5	Not specified

Source: QS World University Rankings website

Based on their methodology, it is obvious, that QS ranking system accentuates the educational role of universities, assigning 70% of the weight in the final performance indicator to the criteria related to this. Only 20% of the efficiency, according to a given approach, is determined by a scientific performance of the university, while international activities are the least influential in ranking's framework. In this case, it creates a clear artificial improvement of universities with a better reputation. At the same time, achievements and advances of students or researchers, on the contrary, are of relatively smaller importance. Moreover, almost all the measures are based on someone's judgements instead of objective facts or even numbers. Reasoning from this fact, the ranking system, as a whole, leads to further misrepresentation of the real university efficiency from an additional value of education to a question of prestige of certain university.

The second ranking among listed before - Times Higher Education (THE) World University Rankings [62] - has a different approach to a determination of the more and less efficient universities. Generally, they assumed that the efficiency score in their scale consists of five universal dimensions of university:

1. Teaching (the learning environment)

2. Research (volume, income and reputation)

3. Citations (research influence)

4. International outlook (staff, students, research)

5. Industry income (knowledge transfer)

Hereby, all the indicators included in the study were designed to assess the performance of universities in each of the identified categories and then included in the final score with their contribution ratio. Aiming to enhance the quality of the ranking, those universities with poor research performance (less than 1 000 papers in five years) and imbalanced in terms of research subject areas (the share of research in one of the areas should not exceed 80%) were excluded from the scope.



Table 3

THE World University Rankings methodology

Metric	Weight, %	Criteria
Teaching	30	- Reputation survey of university prestige among 20 000 respondents - Staff-to-student ratio - Doctorate-to-bachelor's ratio normalized by discipline - Doctorates awarded-to-academic staff ratio - Institutional income scaled against academic staff
Research	30	- Reputation survey - Research income - Research productivity
Citations	30	- Average number of citations per paper within 5 years most recent period (excluding those exceeding 1 000 authors)
International outlook	7,5	- Proportion of international students - Proportion of international staff - International collaboration
Industry income	2,5	- Research income per person from academic staff

Source: THE World University Rankings

This ranking uses both factual numbers and survey results likewise the one mentioned above, nevertheless, a huge difference between them lies in distribution of the contribution weights of education and research activities' roles in university's position in this ranking For instance, education makes only 30% of a university performance, from THE perspective, whilst QS claims it's 70%.

However, both approaches can be considered as more or less alike. Shanghai ranking methodology [60], on the contrary, is built in a completely different way, and points out only two major dimensions of university performance: academic and research efforts. The rating also pays considerable attention to the academic achievements of professors, taking into account the internationally recognized awards obtained, such as the Nobel Prize.



Table 4

Shanghai ARWU methodology

Metric	Weight, %	Criteria
Quality of Education	10	Number of the alumni having Nobel Prizes and other subject medals on an international level in total
Quality of Faculty	20	Number of the professors, awarded by Nobel Prizes in total
	20	Total number of highly cited researches (21 subject areas)
Research Output	20	Papers published in Nature and Science considering the author affiliations in the most recent 5 years period
	20	Papers indexed in Science Citation Index (Social and expanded)
Per Capita Performance	10	Weighted scores of five indicators mentioned above per one full-time academic employee

Source: Shanghai Academic Ranking of World Universities

Hereby, ARWU considered that education and research activities are highly interrelated so that they directly associate the quality of education and, therefore, efficiency of a university, with its contribution to a worldwide science.

All of the above rating systems give preference to various criteria of university efficiency. In turn, ratings are an important tool for attracting students, investment, as well as creating scientific and business reputation. To achieve high positions in each of these ratings, university management must rely on different values and focus on the development of certain aspects of their activities. In addition, Angela Yung Chi Hou [49] and colleagues in 2012 identified not only this fact, but also developed the approach whereby some ratings are suitable for achieving short-term goals, and high positions in some of the results are the mid-term (QS, THE) and long-term (ARWU) planning and require the investment of time.

Thus, efficiency for universities is not so much an increment of the value of each student as a future employee, but rather a comprehensive indicator of their performance in general. At the same time, students are only a part of their activities, but not the main focus, as international rankings show.

There are also several world rankings of universities, which has particular impact locally in their country of origin. For United States one of the most notable and large-scale rankings is U.S. News & World Report (USNWR). Some scientists (R. Green, F. Baskind, A. Fassler, A. Jordan, 2006) [25] tend to assume that university top lists in the world, and in particular in the USA, are “not only unreliable, but also commercialized and dirty". In their opinion, when compiling ratings, manipulating various parameters in a certain direction can tip the scales in favor of one or another educational institution.

Therefore, they, in turn, evaluated the world ratings 2004. In the course of that research, a survey of 1516 respondents was conducted, among which were deans, professors and students from various universities, according to the results of which universities were assessed for quality, professors' publications, as well as how durable and sustainable the program is. The results showed that most of the data obtained by the researchers agreed with the USNWR data, which, from this point of view, indicates that rankings as a whole are quite far advanced in developing a high-quality and relevant methodologies for assessment and comparison of educational institutions.

However, this scientific publication cannot be considered worthy of unambiguous trust. T. Singer, dean of the University of Louisville (USA), noted [42] that the study had some significant shortcomings. Many of the variables that did not agree with the checked rating were ignored, the questions were not aligned correctly, the respondents were guided by their own personal preferences, but not by objective knowledge, and the estimated parameters without justification of the reasons were implemented into the model with equal weights.

Despite this, rating system continue to be a relevant source of reputational appeal for applicants.

Government is also an essential and decisive stakeholder of educational system in a country. Universities are, in turn, a part of public sector of national economy and, thus, are objects to a public management. From the state's point of view, educational institution is efficient when it meets the requirements of two aspects. On the one hand, universities, as well as schools, colleges, etc., have to bring value to a society through providing people with high-quality education. It is well-known and proven fact that education has a positive correlation with a living standard, and its impact can't be underestimated. According to the UNESCO research [56], the quality and the amount of education are matter not only at a level of income, but also shapes a person's social life, patterns and lifestyle. On the other hand, in a most countries all around the globe government plays a supporter role for universities. Therefore, in the context of limited resources, the financial efficiency of educational institutions has one of the most important roles.

In contrast to the understanding of the efficiency of education from the point of view of pedagogy, given earlier, for the government, efficiency is determined not only by the degree of achievement of the educational purpose. From a perspective of a public sector management [27], efficiency consists of a following aspects and has to satisfy at an acceptable level them all:

· Effectiveness as meeting the existing demand, so that in total educational institutions must be able to accept anyone who wants to;

· Quality that is, the provision of education at a sufficiently relevant and modern level;

· Equity and equality as an access to education for everyone, expressed in terms of accessibility and feasibility of education in different countries;

· Efficiency itself as achieving the best performance on the previous three criteria in a resource-constrained environment.

Thus, the term of efficiency for such a stakeholder of global education as government is interpreted in a completely different way with an undeniable dependence from a financial issue. At that point the problem of an efficiency measurement comes. And further within this research the efficiency will be defined from the position of government, that is, as a best possible performance combined with adding value to a student knowledge, subject to limited resources.

According to a review by Y. V. Fedotov [21] of approaches to evaluating efficiency, such interpretation of this term is most often used precisely in the context of correlating costs with the results obtained. In many respects, for Russia, an assessment how efficient an educational institution has the particular relevance due to the fact that the majority of educational institutions at all levels are state-owned. Therefore, it is important to understand which of them are the most efficient and provide the highest quality of educational services not only to depict the general situation in the country's education, but also to efficiently manage the development of this area of society and plan the distribution of the state budget.

Thus, in this context, the term efficiency implies all the following components: quality, productivity, and effectiveness of the educational process, that is, an indicator of how successfully, using the available tools and methods, the initial degree of students' knowledge transfers into a qualitatively higher layer at a given level of limited resources.

1.2 The impact of university scale on various aspects of its efficiency

From the management perspective, the purpose of studying the efficiency of a university consists, first of all, of finding the sources of inefficiency, if there are any, as well as shaping ways to overcome it. This circumstance determines the presence of research interest in the study of the influence of various characteristics of universities on their efficiency, both in general and in particular, in certain aspects of their activities.

Avkiran N. K., a researcher from Australia, in 2001 was studying [5] the technical and scale efficiency of 36 universities for the purpose of deeper investigation of gaps and weaknesses of these universities. He studied universities' return to scale in terms of technical and scale efficiency of their performance so that researcher discovered that majority of universities were operating with a decreasing return to scale even if they had relatively high rates of technical efficiency. Based on this, it is reasonable to conclude that the potential for efficiency increase for these universities is lying in a reduction of university scale in order to optimize the performance. Thus, Avkiran N.K. asserts that the efficiency of a university depends to some extend on its scale, and this dependence is not linear.

This raises the question can a university be efficient in terms of its academic and scientific activities, while remaining small? What aspects of a university's activities are affected by its scale and how? Should a university invest in growth (attract students, professors), will it lead to an increase in quality?

The microeconomics economies of scale [38] concept asserts that costs and size of business entities are not linearly dependent. Starting from a certain point, the costs of the subject for the production of an additional unit of a product, service or information becomes smaller compared to the first units. Furthermore, this effect is also applicable at a plant and even organizational level. In general, economies of scale occurs in a situation with simultaneous outcome increase and average costs decrease. Hereby, achieving economies of scale benefits companies with larger capacity, but only to a certain extend. After passing the economies of scale limits, costs begin to increase often due to a raw material local limits or saturation of a market. Thus, the achievement of the optimal volume by an enterprise can be considered one of the dimensions of its efficiency. So, companies that have more significant economies of scale will be considered the most efficient.

As for universities, understanding of efficiency for them is expressed not only through economic optimality, however, being one of the key components of the work of universities, the financial side of their activity can affect efficiency in general.

For instance, according to a Spanish research [7], educational institutions which have better economies of scale, tend to perform higher levels of efficiency in general.

Traditionally, university scale in respect to efficiency was studied as a successful conduct of financial activities, profit from educational and scientific activities. However, university has a purpose different from that of a business unit, so its efficiency can't be shortened to only profitability. Speaking about educational institutions, investigation of the economies of scale could mislead researches to an assessment effectiveness of a unit whilst quality of education, research performance and education accessibility plays much more important roles. That is the reason why researchers (Carayol N. and Matt M.) [14] traditionally emphasized the scale influence on the recruitment process and, as a consequence, on creation of an intellectual environment. Furthermore, other researchers [28], H. Horta and T. A. Lacy, stated that larger universities tend to be more advantageous in creating their network. The combination of these two factors creates a better position for quality development and efficiency of large universities compared to small ones.

As for Chinese government [33], the question of a scale is not the aim itself, but the strategic way to make educational system more efficient through development. Attraction international student to increase a scope is a part of their strategy for “The National Outline for Medium- and Long-Term Educational Reform and Development (2010-2020)”. Thus, they believe that expansion of scope will lead to a reputation and infrastructure benefits so that it will positively impact on a development of national educational system.

Australian researchers R. Carrington, C. O'Donnell and D. S. Prasada Rao [15] also insist that economies of scale and, consequently, university scale itself is one of the most important implications of an overall efficiency. This opinion is also shared by Australian government. Thus, in this country economies of scale is proposed to become a factor to assess an efficiency while allocating state funds. To obtain relatively high level of it, universities were provided with following options: apply focusing strategies as specialized courses, intensify research activity or simply grow.

In 2015, the study of the statistical significance of scale in the efficiency of European universities resulted in the article by C. Daraio et al [11]. These authors also made a deep analysis to gather the data of previous research on this topic. To do so, they turned to a literature review made by Brinkman and Leslie in 1986 as much as to an article by Cohn and Cooper (2004). They tested a hypothesis of an impact significance of university size and specialization on its efficiency. In process of the study, based on the model of multiple inputs and outputs integrated with bibliometric data, it was determined that both factors significantly affect the overall efficiency.

Couple of years before, these authors also examined [10] an impact of tested factors on a research efficiency of 401 universities from 19 European countries and came up to a partly discordant result as expected. Having a significant impact on efficiency, scale is generally a negative factor for a research activity of best performers and those who provide lower productivity, while specialization has a positive impact on efficiency.

Thus, the results of this study suggest that larger universities tend to be less able to cope with scientific activities. This may be due in part to the more complex administrative management system, as well as, obviously, to the greater concentration of resources on studying process. In addition, the research efficiency should be evaluated in relation to the number of students potentially able to be engaged in research activities. Considering that in larger universities the number of students who will not be engaged in this type of activity is higher, it becomes reasonable that the research activity of large universities is less concentrated than in smaller ones.

Nevertheless, it is impossible to study the economic efficiency of a university, ignoring the question of the effectiveness of its costs. In order to keep the main purpose of a university to translate knowledge and create new ones, Tsu-Tan Fua with colleagues [24], all from Taiwan, expressed the average costs of a university as a function depending on the number of students and such a compound variable as the quality of education. While the relationship between the number of students and the costs of a university is more or less obvious and linear, the authors assumed that a university is required to spend more for a provision the higher quality of functioning.

Researchers discovered the positive relation between university quality and its optimal scale, but the relationship between them was due to the dependence of the optimal scale of a university on the level of quality it would like to achieve. This statement means that despite the obvious impact that one variable has on another one, this dependence is observed only within the scale group, and a university could be efficient regardless its scale.

A comparison of the efficiency by the parameter of the quality of education and the graduates to entrant ratio was carried out by L. Russel [40] in Georgia (country) in virtue of five mergers of universities. As an outcome of this comparison, it was shown that the result has a synergistic effect. In addition to an increase in the scale of universities and a relatively small increase in costs, the number of students successfully completing a year of study increased by 1.7 percentage points per annum and the number of graduates by 4 percentage points.

Notwithstanding the positive effect of the one-time significant increase in the scale of the five universities in Georgia, it cannot be defined how sustainable the effect is, and whether it is a consequence of the increase in scale, since it has not been studied how efficient these universities were before the merger. At the same time, it is a fact that an increase in a university scale can lead to an increase in efficiency with regard to its quality.

Despite the absence of a retrospective data on the efficiency of universities in Georgia before the merge, the positive effect of the scale growth can be partially explained by the results of the study provided by J. Nemoto and N. Furumatsu [35] on the example of Japanese universities. They found that economies of scale were not only common in large universities, but also in small ones. Scientists, in turn, recommend that universities take advantage of economies of scale in order to grow. At the same time, they also argue that another extremely important factor for the development of a university is its specialization, so the most optimal way to develop and increase the scale without losing specialization is a merger with another university, which could be the case of Georgian universities.

A similar viewpoint was also shared by authorities in Poland in the 1980s and 1990s as much as Australia [48]. Researches Seliga R., Sulkowski L. and Wozniak A. from Poland [41] explained a universities intention to merge and become bigger by costs optimization of the university activities and the whole organization in general, which is still questionable at least because nowadays there is not only one university exist.

Italian universities have also been tested [13] by Cantele S., Guerrini A. and Campedelli B. for their efficiency with regards to following drivers: size, location, staff composition as much as ownership. Authors stated that the significant change in university performance was occur due to a different management approach to run higher education institutions. For instance, because of the pressure of an international competition and a tendency by government to reduce state funding, university authorities switched to manage it like a business unit rather than a professional organization. Notably, as an outcome of this study was the conclusion that the size is the only one controllable variable of a university that should be administered by its board to reach efficiency. But at the same time, article also provides a fact, that it could be a 35% variation in efficiency within one scale group, which brings doubts about the impact of university scale on its efficiency.

Thus, on the one hand, with the growth of the university, its quality should also increase, especially teaching, due to a creation the university infrastructure and positive impact on its reputation through better recruitment policy and international cooperation opportunities. Government of many countries assume that the size growth is an instrument of resource management optimization and, in obedience to their conviction, larger scale could trigger the educational system development.

On the other hand, scale growth negatively affects research efficiency. In addition to this, there is also a financial side, because higher-quality universities require more investment, which would seem to be easier for large universities, but, according to the theory, from some point the economies of scale can be negative and the financing ineffective. All this leads to a strong dependence of the effectiveness of the university in all aspects on its scale.

However, there is a set of studies claiming that university efficiency depends only on the economies of scale in terms of costs and even a relatively small university can be efficient since it reaches an optimal scale of performance. At the same time, this leads to an issue of limits of such efficiency. Another words, to what extend small university is efficient and at which dimensions it could be improved.

All this creates a research interest in investigation whether a dependence between university scale and its efficiency exists or not.



2. Development of an approach to assess the efficiency of universities

2.1 Retrospective review of approaches to assessing the efficiency of educational institutions

Among the modern approaches to evaluate the performance of universities is one which involves the measurement of the efficiency of the public sector units from the point of view of the distribution of finance in meeting the requirements set by the state. This approach was developed for the healthcare sector at Yale University (first implemented in 1983 as a part of US Medicare Program) and called Diagnosis-Related Groups (DRG) system [22]. This system is used in one form or another in almost all developed countries. According to that system, hospitals are funded according to their activities, namely: the number of patients of each specific group of diagnoses. Consequently, hospitals with better services, which are usually has more patients, gets more funds. All the money saved at the end of a financial period hospital can spend for purposes of further development. As a result, state avoids excess expenditure and reward the most efficient hospitals, ideally. Factually, that system has its own weaknesses, but still it was a huge step for public management to monetary reward the efficiency.

European government in 8 countries employed a model of competitive funding with the aim of motivating universities to show better performance. According to the research (T. Bolli, M. Olivares, A. Bonaccorsi, C. Daraio, A. G. Aracil, B. Lepori) [9] that was tested that system, competition for funding between European universities can be considered useful for creation of an elite tier of universities in higher education.

The process of evaluating the efficiency is complicated, according to K. Euske and M. Lebas [32], by the very nature of this concept. The definition of efficiency is situational and depends on the inner beliefs of the person using the term, as well as on the context. That is why the reduction of the method of evaluating the efficiency to a single universal standard becomes much more complicated, since each approach contributes its own value, which results in multiple discrepancies in this matter.

The topic of the measurement of efficiency of educational institutions is covered by researchers in a wide range of scientific fields, which, in addition to economics and management, also include psychology, sociology, and pedagogy.

From the purpose of psychology (G. E. Gunko) [26], the concept of the efficiency of educational activities is reduced to only the definition of effectiveness. Its evaluation is related not so much to how successfully students master the curriculum, but to what personal qualities pupils acquire in the learning process, which is especially critical for higher education. In a more or less explicit form, this point of view is also supported by many modern Russian universities, which draw attention to the fact that the knowledge that students receive during their studies is as much important as the problem-solving skills, ability to analyze a large amount of unstructured information, and so on.

This researcher believes that in the modern psychology, the most important for evaluating the efficiency and, accordingly, the quality of education is to determine the magnitude of the personal progress of each student and the personal focus on a given result. As a rule, this assessment is carried out either by personal monitoring of a staff psychologist in educational institutions, or, more commonly, from the point of view of formalization and simplicity of collecting and processing large amounts of information, by testing knowledge and personality traits, as well as their changes over time.

As in the case of the psychological approach, pedagogy places the highest value in assessing the efficiency of education on the personal approach. In his article, K. P. Fedorov [23] provides a method for calculating efficiency through a mathematical formula based on four groups of parameters. At the same time, the difficulty in using these parameters comes down to the need to select objective assessment scales that consider the personal characteristics of each student. He also points out to the necessity to consider the dynamics of the performance indicator over time in order to compare the current values with general characteristics of this system.

Thus, within the framework of the understanding of the problem of evaluating the efficiency of education from the point of view of psychology and pedagogy, it is impossible to strictly formalize this process because of its complexity and subjectivity: the effectiveness of training is evaluated individually for each student, starting from his personality, and the assessment is done by some outside observers (for example, teachers), which a priori for an objective assessment is not able to sufficiently know each students' personality. All this leads to the fact that it becomes impossible to compare educational institutions according to the criteria of efficiency and quality of the services provided, using a personal approach.

In turn, the study of the efficiency of education also refers to the interests of public authorities. There is a wide range of studies on interstate comparisons of educational approaches.

Traditionally, the quality of education and, accordingly, its efficiency is measured for different countries with help of the PISA [58] (Programme for International Student Assessment) students' skills assessment program, developed by OECD countries. This universal test is designed to evaluate the knowledge and ability of students in mathematics, reading, science as well as their soft skills like problem solving.

This test shows how the quality of education in schools meets the current requirements of scientific and professional realities. For instance, according to a study in 2015, Russian schoolchildren were ranked 4^th in the world in financial literacy field, but in reading, mathematics and the natural sciences were in 20-30^th places, which is below the average level. This means that the knowledge that is given to schoolchildren is either not properly absorbed, or not useful in future.

The weak point of this method of evaluation and ranking of educational programs and abilities of students from different countries is the fact that the test results are not dissociated from the regional and cultural characteristics of each country. Therefore, the mentality of the population of some countries can significantly affect the development of what competencies pupils will be most inclined to. This test ignores this assumption.

The Organization for Economic Development and Cooperation (OECD) annually initiates many studies in this field. In their research [53] of 2011, employees of this organization analyzed the efficiency of school education in Greece compared to other OECD member countries in terms of factors that ensure the quality of education, such as: the provision of schools with a staff of teachers, teacher motivation tools (salary and other benefits), level of school independence in decision making, student characteristics. From their perspective of view, these factors have a direct effect on the quality of the learning process in schools. In general, the Greek education system is characterized by comparing these indicators, and recommendations are developed after evaluating each of the indicators based on benchmarking the experience of those countries that show better results.

This assessment method as a whole is not incorrect, since it avoids the formation of any single grade, which would require waging the contribution of each of the factors to the final efficiency grade and could also lead to a distortion of the actual situation. However, breaking a single system into its constituent elements, the researchers ignore the peculiarities of the education system in each country, its background. And they also omit the influence of the interrelationships formed between the factors, which themselves can determine the educational system in Greece, thus the risk to miss out some important factors is relatively high.

Numerous Russian researches in the field economics and sociology, concerning the question of the efficiency of certain schools or universities, link the criterion of quality and efficiency with how successfully these educational institutions achieve the objectives set by the state. For instance, in his article L. Popov [39] cites as such criteria ranking the higher educational institution as worlds' TOP 200 as well as the average age of teaching staff, the contribution of the university to the share of Russian scientific researches in the Web of Science system and so on. That is, the evaluation of the efficiency of universities and their further ranking is carried out through its formal conformity with certain set of criteria created by state.

G. A. Tsukerman in her article “Efficiency of A Domestic Education” [46] points out that the educational system in general has a high level of uncertainty and heterogeneity due to different social level of applied students, school funds equipment and other reasons. Accordingly, in the purpose of assess the potential efficiency of educational system as a whole she intentionally excluded from the scope schools with unfavorable background, thus reaching the accuracy and validity of the experiment. The quality of education on the given schools was measured through the PISA test. As a result of experiment, there was determined that in terms of applied educational methods, schools with experimental teaching forms most likely to become efficient.

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