ASSESSMENT OF UNIVERSITIES EFFICIENCY USING DATA ENVELOPMENT ANALYSIS: WEIGHTS RESTRICTIONS AND SUPER-EFFICIENCY MEASURE Sourour Ramzi, PhD student Mohamed Ayadi, PhD, Professor Higher School of Management University of Tunis, Tunisia 40

Introduction In order to occupy their place on the labor market, individuals must possess technical, theoretical and relational skills adequate to skills required by the job and corresponding to socio-economic needs of the country. Unfortunately, higher education in Tunisia has undergone over the past decade several changes and reforms that led to a loss of efficiency overlooked the socio-economic needs of the country. With an unemployment share of university graduates over 30% of the total number of unemployed in Tunisia, the higher education has become a mass education system and not a selective one. This deterioration in the quality of higher education has made our universities less competitive at international level. It is then important to assess the efficiency of these universities, to detect their shortcomings and propose solutions for the improvement. DEA models have been widely used to evaluate the efficiency of higher education. They represent a linear programming models proposed by Farrell (1957) and developed by Charnes et al. (1978). In this paper we evaluate the efficiency of 11 homogenous Tunisian universities in 2009, 2012 and 2013 using two input variables “the number of students enrolled in Letter and Human Sciences” and “the number of students enrolled in Computer Sciences, Media and Telecom”. The output variable describing research activity is the number of research units and laboratories. Teaching activity is measured by the number of graduates from Fundamental and Applied Licence. We have introduced in the analysis two fields of DEA development “weights restrictions and super-efficiency measure” to evaluate the performance of universities and to distinguish between efficient and inefficient DMUs. To study the importance of each input and output variables in the efficiency of universities, we have conducted different DEA model specifications. The main results show that the application of DEA in higher education has motivated the use of weights restrictions to avoid the complete freedom of weights’ variation allowed by the original DEA model. The introduction of weights restrictions into DEA model in order to analyze the efficiency of universities increases the discrimination of estimated results. The super-efficiency measure reveals its usefulness for the ranking of efficient universities by attributing to them scores greater than one. The estimation of the different specifications models demonstrate the significant effect of the input variable, the number of students enrolled in Computer sciences media and telecom and the output variable, the number of graduates from Fundamental and Applied science on the efficiency of Tunisian higher education. This paper is organized as follows: in next section we present a description of the general characteristics of higher education in Tunisia. Following section presents the literature review on the related existing literature on the evaluation of the efficiency of

higher education using DEA approach with weights restrictions and super-efficiency analysis. Than we present the methodology applied in our analysis. In next section we describe the data collection, variables selection and results estimated. Finally, last section provides the conclusion.

Higher Education in Tunisia Since 1959, the Tunisian education has experienced an important progress. The

Tunisian government was interested in its development in order to produce a strong 41 human capital able to deal with the change of a nation. Several measures have been set to reduce the centralized government control and bureaucracy, to increase the university’ autonomy and to enhance the employability of higher education graduates. Other specific measures were focused on the vocational training of graduates. Several reforms have been pursued to improve the quality of higher education in Tunisia and to ensure the scientific value of Tunisian diplomas and all they overlap like skills. The principal reform that experienced the higher education is the adoption of the LMD (Licence-Master-Doctorate) system and the technical accreditation that must emanate from an independent organization and address the required quality criteria. The objective of this reform is to adopt the educational system to European Standards. The adoption of the LMD system by the Tunisian authorities was performed 7 years after France and 4 years after Morocco did it. The first wave of academic institutions has adopted the LMD system in 2006-2007 and the second wave was in 2007-2008. It was known under the name of BAC+3+5+8 which means the apportionment of the university cycles. The first cycle is a Licence that lasts 3 years and it includes 180 credits, spread over two semesters; the second cycle consists on a research or professional master degree with duration of 2 years (120 credits). Finally the doctoral degree takes three years. However, Engineering, medicine and architecture studies are not concerned with the LMD reform. The diplomas from old regime such as the “maîtrise” have continued to be awarded provisionally. The graduates from LMD system have passed from 2063 for fundamental Licence and 6128 for Applied Licence in 2009 to 19925 and 32597 respectively in 2011, while graduates from old system have decreased by 99% between 2009 and 2011. Several initiatives have been introduced to train a pool of Tunisian university teachers and professors in the quality-based approach to improve the quality of teaching activity ensured within universities. Tempus, through many projects has contributed to enhance the internal quality assurance and to introduce certification procedures in the Tunisian higher education system. In 2011, the Ministry of Higher education prepared a quality assurance program PAQ (programme d’appui à la qualite) in the objective of enhancing the teaching standards and introducing a new decentralized system. Higher education in Tunisia is provided by Universities, Higher Institutions of Technological Studies (ISET) and Higher Institutes of Teachers Training (IGH). During last years, the number of public universities and the number of university institutions have been increased despite a decrease in enrollment students in Higher education (Figure 1, 2 and 3).

42

Figure 1. Evolution of the Number of Tunisian Public Universities Source: Ministry of Higher education

Figure 2. Evolution of the Number of University Institutions Source: Ministry of Higher Education

Figure 3. Evolution of Enrolled Students in Higher Education Source: Ministry of Higher Education

Figure 4. Expenditure on Higher Education as Percentage of 43 Government Expenditure Source: Institute for Statistics, UNESCO

Figure 5. Government Expenditure per Student as % of GDP per capita Source: Institute for Statistics, UNESCO

Figure 6. Evolution of the Government Expenditure per Student in PPP$ Source: Institute for Statistics, UNESCO

The resources allocated to higher education are mostly budgetary. The Tunisian government spends the equivalent of 1.7% of national GDP for the financing of higher education. This confirms the strong commitment and the high priority accorded by the Tunisian Government on the funding of education (Figure 4). Public spending is to a large extent devoted to operating expenses and mainly the payment of salaries of functionary, whose share in the expenses increased by 74% in 2003 to over 79% in 2012. The evolution of the educational expenditure per student

44 shows the limits of public financing deal with the “massification” of universities (Figures 5 and 6).

Literature Review In recent years, several studies have evaluated the efficiency of higher educational institutions using DEA approach. From one study to another, decision making units (DMUs), variables and types of DEA models differ depending on the objective of the research aimed by the authors and the availability of data. Original DEA models (constant returns to scale, variable returns to scale, input oriented and output oriented DEA models) were used to measure the relative efficiency scores attributed to Universities, departments, etc. Abbott and Doucouliagous (2003) apply this approach to evaluate technical and scale efficiency of the population composed by 36 Australian government universities in 1995. For teaching activity, the authors used the number of equivalent full time students, number of post-graduate and under-graduate degrees enrolled, the number of post-graduate conferred and the number of under-graduate degrees conferred. Research activity is measured by Research Quantum Allocation that each university receives as well as medical and non-medical research income. The input variables used are the total number of academic and non-academic staff and expenditure used on energy, non-salary academic and administration service. The results show that the relative efficiency scores estimated indicated a high level of technical efficiency in Australian universities but this doesn’t neglect the presence of margin for improvement in several inefficient universities. Some other studies have focused on increasing the distinction between efficient DMUs with Data Envelopment Analysis. Two types of methods can be used to achieve this goal. Those that require a priori information provided by the decision maker or analyst on the importance of variables used such as weights restrictions; preference structure and value efficiency analysis to evaluate the efficiency of organizations. The second group of methods doesn’t exact a priori information to perform the ranking of DMUs. It serves to avoid or to minimize the intervention of the expert and to increase the discrimination in DEA such as super-efficiency measure. Thompson et al. (1986) were the first authors that have introduced the technique of weights restrictions in the analysis of DMUs ‘efficiency using DEA model. They aimed to solve a choice problem with the imposition of acceptable bounds on ratios of weights. Sarrico and Dyson (2004) used a method of discrimination in DEA of the first group for assessing the performance of 89 UK universities. They introduced weighs restrictions to restrain the freedom variation of weights authorized by the original DEA model. They conclude that allowing the total flexibility weights can generate weights that are often in contradiction with prior information and views under the estimation of

unrestricted DEA model. The incorporation of virtual weights restrictions curbs the overestimation of efficiency and increases the discrimination of results estimated from the application of DEA model in concrete situations. They argue that the use of virtual inputs and outputs of a DMU identifies the relative contribution of each variable (input and output) to its efficiency score and they distinguish between strong and weak level of DMUs’ performance. They conclude that the applicability of the different categories of weights restrictions is required to determine the preference structures in the area of

higher education. 45 Athanassopoulos and Shale (1997) evaluated the cost and outcome efficiency of higher educational institutions in the UK considering that principal outputs of the education system are first and higher degrees and research activity. They use DEA model with the incorporation of value judgments to increase the discrimination of the analysis on the performance of HE. The results show that applying value judgments reduces the number of efficient universities compared to unrestricted model. The targets estimated for inefficient universities indicated that the main factor of inefficiency is the low quality of research activities. Deficiency can be corrected by reducing the research income and increasing the research output. Many inefficient DMUs are considered as over-resourced in the field of research activity. Chaparro et al. (1997) examined the role ensured by weights restrictions in DEA model. They argue that the traditional DEA does not apply constraints on weights and then giving the opportunity for each DMU to use the most favorable weight that maximizes the efficiency level. They recommend the adoption of virtual weights in the assessment of DMUs with DEA model because it required a little prior information from the expert or the analyst. They conclude that the introduction of weights restrictions involves value judgment. However, the use of the unrestricted model itself involves an implicit value judgment (factors that have less favorable impact on the DMU are eliminated from the efficiency evaluation of this DMU). A review on the evolution, development and future research directions on the introduction of weights restrictions and value judgments in Data Envelopment Analysis was provided by Allen et al. (1997). They present the different methods for incorporating value judgment in DEA and they focus on analyzing the result of incorporating weights restrictions on the efficiency scores, targets and peers of inefficient DMUs. They consider that the approach based on the introduction of weights restrictions attributed to input and output variables is one of the fields of DEA development motivated by the real-life applications. Thanassoulis and Allen (1998) introduced a new approach for capturing and applying value judgments in DEA assessment using unobserved DMU. They found that the capture of value judgments in DEA via unobserved DMU is useful to capture local and nonlinear marginal rates of substitution between input and / or outputs. Other alternatives can be used to incorporate decision maker’s preferences into the evaluation of DMUs with DEA measure. In this context, Halme et al. (1999) developed a novel procedure for incorporating preference information in the efficiency evaluation of DMUs. The methodology begins by aiding the Decision Maker in searching the most preferred combination of inputs and outputs of efficient DMU. Efficiency scores are then calculated for each DMU by comparing the difference in value between the unit under evaluation and the most preferred solution. Charnes et al. (1990) suggested another approach based on transforming input

and output variables to stimulate weights restrictions, where DMUs are evaluated using the input and output data of pre-selected DMUs considered as efficient by experts. Regarding the second technique applied in this paper to enhance the performance analysis of universities, the ‘super-efficiency” measure is considered also as a field of DEA development based on the ranking of efficient DMUs. Several studies have made use to the super-efficiency method to compare efficient DMUs operating in different domain and especially in education sector.

46 In the sub-sector of higher education, Agha et al. (2011) evaluated the efficiency of academic departments in Islamic University in Gaza during 2004-2006 using CCR (Charnes et al., 1978) and BCC input oriented DEA model. They estimated the super- efficiency scores attributing to efficient departments. The input variables used on their analysis are: expenses, credit hours and training resources. While the output variables are the number of graduates, promotions, and public service activities. The results of CCR model show that on average, the efficiency score of the entire departments is about 68.5%. To reach the efficiency frontier, the departments in the faculty of sciences, engineering and information technology should reduce their laboratory expenses whereas the department of economics and finance has the highest super- efficiency score compared to the other efficient departments. The super-efficiency analysis is then beneficial for efficient and inefficient departments by following the more efficient ones. Zhu (2001) discussed and examined the use of super-efficiency measure in DEA sensitivity analysis. He aimed to develop a new approach for the sensitivity analysis models based on the use of different super-efficiency DEA models characterized by the non-inclusion of test DMU in the reference set. He noted that the super-efficiency measure is especially used in specific situation where simultaneous proportional change is supposed in all inputs and outputs for the DMU under evaluation. The author concluded that the sensitivity analysis of DEA efficiency classification can be easily achieved by applying super-efficiency DEA measure. Andersen and Petersen (1993) developed a modified version of DEA model based on the comparison of efficient DMUs relative to a reference technology covered by all other units. They conducted a procedure for ranking efficient DMUs by comparing the unit under evaluation with a linear combination of all other DMUs in the sample. A score greater than one is attributed to efficient DMU and reflects that this unit is able to increase its inputs proportionally while remaining efficient. Xue and Harker (2002) argued the usefulness of the application of Super- efficiency DEA models in practice. They showed that in the case of infeasible problems in super-efficiency DEA models estimated under alternate RTS (Returns to scale) assumption other than CRS, it is possible to obtain a full ranking of the entire observation. According to the authors, it is possible to perform a full ranking of the whole set of DMUs even with infeasibilities in super-efficiency DEA models. Therefore, the current study uses the two field of DEA development (weights restrictions and super-efficiency measure) to perform the ranking of Tunisian universities. The application of DEA model in education sector was more performed in developed countries (USA, Australia, England, Portugal, etc). In the case of Tunisia, it is considered to be the first study of efficiency measurement of Tunisian universities with DEA model.

The Methodology The methodology used to evaluate the efficiency of Tunisian universities in 1999-2012 and 2013 consists on the application of an input-oriented DEA model estimated under constant returns to scale (CRS) assumption. We have employed an input oriented DEA model at the university environment, because it is easier to control the quantity of inputs used in the production process rather than the outputs produced. In order to increase discrimination in the assessment of teaching and research

activities’ efficiency within universities, we have introduced in the analysis two fields 47 of DEA envelopment, weights restrictions and super-efficiency technique. Three types of weights restrictions can be incorporated into DEA models to perform the analysis of efficiency and to avoid the freedom flexibility of weights (Table1). Table 1. Categories of Weights Restrictions Assurance regions of type II Absolute weights Assurance regions of type I (ARI) (ARII) restrictions -Introduce the link between the input or the -Introduce the link between -Consist of output’s weights. input and outputs’ weights. varying the value -Charnes et al. (1990) and Thompson et al. (1986) -Produce the same of the variable highlight that incorporating ARI into the analysis efficiency score either in the within a given of DEA model provides at least one efficient unit case of input or output interval. and produces identical efficiency scores whether orientation. the output or the input orientation is used.

The restricted input-oriented DEA CCR model (Charnes et al., 1978) and the super-efficiency measure used to evaluate the efficiency of Tunisian universities are conducted with MES (Measurement Efficiency System) software version 1.3.0 developed by Holger Scheel (Scheel, 2000). The super-efficiency measure was introduced by Anderson and Peterson (1993) as a method to distinguish between efficient DMUs. It gives the opportunity to rank efficient DMUs characterized by identical relative efficiency scores equal to unity under the estimation of the original DEA model. It enables the decision maker to examine the maximum radial changes in inputs and/or outputs for an observation to remain on the efficiency frontier. It consists on attributing efficient universities a score greater than one by removing the constraint of virtual output lower than virtual input from the basic DEA model. For this reason, the technique of super-efficiency measure is known as “deleted domain”. It affects only efficient units by allocating to them scores higher or equal to 100% to become super-efficient. Efficiency scores of inefficient universities remain unchangeable since they are by definition smaller than unity. A super-efficiency DEA model used to identify the classification of efficient decision making units can be written as in Goncharuk (2007).

Data Collection and Variables Data collection Data used in this paper is composed of 11 public Tunisian universities, multidisciplinary and homogeneous: Universities of Tunis, Tunis Manar, 7 November of Carthage, Manouba, Sousse, Monastir, Sfax, Gabes, Kairouan, Jendouba and Gafsa. They grant academic degrees in varied specialties and provide undergraduate and

postgraduate education in different disciplines: Humanities, Sciences, Education and Mathematics, etc. The estimation of DEA models requires some characteristics specific to the variables and data used in the estimation such as the homogeneity of DMUs evaluated and the selection of the input and output variables used in the analysis and weights attached to them (Sarrico and Dyson, 2004). In our example, we have chosen 11 public universities with similar study domain (letter, social sciences, behavior, physical

48 sciences and mathematics, etc). They used identical school resources during their production process (equipment and raw materials, laboratories, teaching and administrative staff, financial resources, etc) to produce both teaching and research activities. We have excluded the University of Ezzitouna, Higher Institutes of Technological Studies (ISET) and virtual University from the sample because they are heterogeneous from other universities. The University of Ezzitouna is specialized in religious teaching particularly Arabic and Islamic civilization. Health studies like medicine, dental medicine, biology, sciences of life, mathematics and statistics are not included in its study program which is not the case of other universities. Higher Institutes of Technological Studies (ISET) and virtual university are excluded from our sample because of their teaching pedagogy. The later one is based on the formation of only senior technicians. The length of study in ISET is set at 3 years of teaching, so the opportunity of a student to pursue postgraduate studies in these institutions is not possible. The virtual university develops courses and university curricula online so it provides an educational pedagogy different from that provided by other universities. The regional classification of the 11 public Tunisian universities is presented below in Table 2.

Table 2. Regional Distribution of Public Tunisian Universities North Center South -University of Manouba - - -University of Tunis - -University of Gabes -University of Carthage - - -

Variable selection The selection of input and output variables for evaluating the efficiency of universities using DEA model has been discussed in many studies. To ensure meaningful efficiency scores, the number of universities must be at least twice the number of inputs and outputs (Golany and Roll, 1989). Dyson et al. (2001) suggested that a total of two times the product of the number of input and output variables should be considered. For this reason, in the analysis, we have limited to use two input variables, number of enrolled students in Letter and number of enrolled students in Computer sciences media and telecom and two output variables, number of laboratories and research units and number of graduates from Fundamental and Applied Licence. The rule which requires that the number of DMUs (universities) >= 2*m*s=8 was considered which is less than the number of 11 DMUs used in this paper. All the input and the output variables are extracted from the statistics published

by the office of studies, planning and programming under the Ministry of higher education and scientific research in 2009, 2012 and 2013. Descriptive statistics of variables used in the evaluation of universities are displayed in Table 3.

Table 3. Descriptive Statistics for Variables and Weights Restrictions 2009 2012 2013

Inputs Mean 5156 4021 3739 49 Number of students enrolled in Letter Median 5069 3751 3303 StDev 1751 1307 1340 Mean 4197 3421 3084 Number of students enrolled in Computer Sciences Median 4210 3871 3514 Media and Telecom StDev 1608 1309 1265 Outputs Mean 55 26 37 Number of research units and laboratories Median 45 17 31 StDev 56 25 37 Mean 723 3986 3478 Number of graduates from Fundamental and Median 634 3601 3352 Applied License StDev 432 1238 1097 (ARI) Weights restrictions (ARII)

:-weight attributed to the input variable: number of student enrolled in Letter; -weight attributed to the input variable, the number of student enrolled in Computer sciences Media and telecom; - weight attributed to the output variable, number of graduates from Fundamental and Applied Licence.

From Table 3, it is clearly shown a decrease on the mean, median and standard deviation of the two input variables, the number of students enrolled in Letter and the number of students enrolled in Computer sciences media and telecom from 2009 to 2013. While the descriptive statistics of the output variable “the number of graduates from fundamental and applied license” varied in a reverse direction. Whereas, the number of research units and laboratories describing the research activity within universities has been reduced from 2009 to 2013. We have introduced in this study two types of weights restrictions to analyze the efficiency of universities. The first one is an assurance region type I (ARI). It reflects the fact that the weights attributed to the number of students enrolled in Letter should be greater than the weights attributed to the input variable describing the number of students enrolled in Computer, sciences, media and telecom. The second restriction is an assurance region type II (ARII) that links the input’s weights to the output’s weights. It reflects the fact that the weights attributed to the two input variables, number of students enrolled in Letter and the number of students enrolled in computer, sciences media and telecom should be greater than the weights attributed to the output variable, the number of graduates from Fundamental and Applied Licence.

The Results Weights restrictions Table 4 shows the efficiency scores, the reference set (s) (benchmarks), the rank of each DMU, in addition to the average score of all universities in each year estimated under the unrestricted DEA model. In 2009, only the Universities of Tunis El Manar, Monastir and Gabes are efficient. The two universities of Carthage and Gafsa have the worst level of efficiency and occupied the two last ranks of universities. The University

50 of Tunis has a score of 61%, which means that it should decrease its amount of inputs by 39% to become efficient.

Table 4. Efficiency Scores Estimated under Unrestricted DEA Model 2009 2012 2013 Universities Efficiency Ranks Benchmarks Efficiency Ranks Benchmarks Efficiency Ranks Benchmarks scores scores scores 2 (0,2) 2 (0,2) 1- Tunis 0,61 6 0,92 2 1 1 0 7 (0,1) 11 (0,8) 2-Tunis El 1 1 3 1 1 3 1 1 1 Manar 3-7 Novembre 7 (1,3) 0,35 9 2 (0,4) 1 1 4 0,85 3 of Carthage 11 (0,3) 2 (0,0) 7 (0,2) 7 (0,5) 4-Manouba 0,97 2 0,41 8 3 (0,4) 0,52 6 11 (1,0) 11 (0,7) 11 (0,2) 3 (0,3) 7 (0,4) 5-Jendouba 0,83 4 11 (0,5) 0,79 5 0,73 5 11 (0,4) 11 (0,5) 7 (0,6) 3 (0,7) 7 (1,0) 6-Sousse 0,69 5 0,85 4 0,79 4 11 (0,0) 11 (0,3) 11 (0,6) 7-Monastir 1 1 5 1 1 2 1 1 7 11 7 (0,1) 8-Kairouan 0,90 3 0,78 6 11 (0,9) 0,66 7 (0,5) 11 (0,8) 2 (0,5) 2 (0,1) 2 (0,4) 9-Sfax 0,56 7 0,90 3 0,99 2 7 (0,2) 7 (1,3) 7 (1,0) 3 (0,5) 7 (0,9) 10-Gabes 1 1 5 0,72 7 0,70 6 7 (0,1) 11 (0,2) 7 (0,0) 11-Gafsa 0.52 8 1 1 5 1 1 6 11 (0,3) Mean 0.77 0.85 0.84

All inefficient DMUs have reference set(s), called benchmarks. The utility of the reference universities is to learn inefficient DMUs how to transform their inputs into outputs to become efficient. In addition, inefficient units should adopt the similar strategy, technique and policies of their benchmarks during their production process. For example, as shown in Table 4, the reference sets of the Universities of Sousse and Manouba are both the universities of Monastir and Gabes. On average, the efficiency score of all universities is 77% which explains, that on average, all the universities are required to decrease their inputs by 23% to reach the efficiency score. In 2012, the universities of Tunis El Manar, 7 November of Carthage, Monsatir and Gafsa are considered as efficient with efficiency score equal to unity. The last score of 41% is attributed the University of Manouba. In order to reach the efficiency frontier, this university should reduce its inputs by 59% and follow its reference sets, the universities of Tunis El Manar, Carthage and Gafsa with weights of (0,0), (0,2) and (0,4) respectively. The row weights assigned to peer units when solving the DEA optimization problem. Further, it is observed that DMU11 (the university of Gafsa) is the most recurring benchmarks. It was referenced for 5 times, which explains that there

are five inefficient universities which could follow it to become efficient. Despite the average efficiency score of all universities in 2012 has been increased by 10.4% compared to 2009, it remains insufficient to reach the efficiency frontier. In 2013, the four universities of Tunis, Tunis El Manar, Monastir and Gafsa reached the efficiency frontier with efficiency score equal to unity. The University of Kairoun has occupied the lowest rank with an efficiency score of 66% which means that it should reduce its inputs by 34% to become efficient. The University of Tunis El

Manar constitutes a reference only for the University of Sfax while the University of 51 Tunis does not represent any reference for inefficient DMUs, it is then considered as efficient by default. The University of Monastir is the most recurring benchmark. It was referenced 7 times by the universities of Carthage, Manouba, Jendouba, Sousse, Kairouan, Sfax and Gabes. The average efficiency score for all universities in 2013 is about 84%, which means that on average, all the universities are advised to reduce their inputs by 16% to become efficient. Table 5 summarizes the distribution of input-output slacks for the 11 Tunisian universities in 2013. The calculation of slacks is needed to prompt DMU to reach the efficiency frontier. Input-output slacks exist only for inefficient DMUs to help them to become efficient. It is important to find enhancement strategies for inefficient units either by reducing the amount of inputs used during the production process (input slacks) or by increasing the amount of outputs produced (output-slacks).

Table 5. Summary of Input and Outputs Slacks (2013) Input slacks Output slacks Number of Number of students Number of Number of graduates students enrolled in Computer research units from Fundamental enrolled in Sciences Media and and and Applied License Letter Telecom laboratories 1- Tunis - - - - 2-Tunis El Manar - - - - 3-7 Novembre of 0 0 3,77 0 Carthage 4-Manouba 0 0 1,22 0 5-Jendouba 0 0 14,25 0 6-Sousse 0 0 12,66 0 7-Monastir - - - - 8-Kairouan 0 0 2,65 0 9-Sfax 0 1072,11 0 0 10-Gabes 0 0 24,67 0 11-Gafsa - - - -

From the Table 5, it is noticed that the four efficient universities of Tunis, Tunis El Manar, Monastir and Gafsa have neither input nor output slacks. The rest of universities are considered as inefficient and need to improve their efficiency level. For example, the University of Sfax is required to reduce its number of students enrolled in Computer sciences media and telecom by 1072 students to become efficient which is the only input slacks proposed by the model. Regarding the output slacks, they exist only for the output variable, number of research units and laboratories. They reflect the universities in which their inefficiency can be related to a low quality of research activity. For example, the University of Carthage is required to increase its number of research units and laboratories by 3

units, while the universities of Jendouba and Sousse have to increase them by 14 and 12 respectively to reach the efficiency frontier. The highest number of research units and laboratories to be increased exists in the University of Gabes (24 research units and laboratories). Table 6 shows the efficiency scores, the reference set (s) (benchmarks), the rank of each DMU, in addition to the average score of all universities estimated under restricted DEA model during the period of analysis. The results demonstrate that the

52 introduction of ARI and ARII into the analysis of universities’ efficiency reduced both the efficiency scores and the number of efficient DMUs in each year.

Table 6. Efficiency Scores Estimated under Restricted DEA Model 2009 2012 2013 Universities Efficiency Efficiency Efficiency Ranks Benchmarks Ranks Benchmarks Ranks Benchmarks scores scores scores 1- Tunis 0,22 8 2 (0,3) 0,53 9 7 (0,9) 0,47 8 7 (0,9) 2-Tunis El 1,00 1 10 1,00 1 1 1,00 1 1 Manar 3-7 Novembre 0,26 7 2 (0,4) 0,96 2 7 (1,8) 0,80 3 7 (1,5) of Carthage 4-Manouba 0,34 5 2 (0,2) 0,39 10 7 (0,9) 0,43 9 7 (1,0) 5-Jendouba 0,19 9 2 (0,0) 0,72 6 7 (0,8) 0,60 7 7 (0,7) 6-Sousse 0,35 4 2 (0,3) 0,80 5 7 (1,4) 0,70 4 7 (1,3) 7-Monastir 0,98 2 2 (0,5) 1,00 1 9 1,00 1 9 8-Kairouan 0,17 10 2 (0,0) 0,60 8 7 (0,8) 0,47 8 7 (0,6) 2 (0,1) 2 (0,4) 9-Sfax 0,48 3 2 (0,6) 0,90 3 0,99 2 7 (1,3) 7 (1,0) 10-Gabes 0,31 6 2 (0,0) 0,69 7 7 (1,1) 0,66 6 7 (1,0) 11-Gafsa 0,12 11 2 (0,1) 0,84 4 7 (0,8) 0,69 5 7 (0,7) Mean 0.4 0.77 0.71

In 2009, the relative efficiency scores of all universities have been reduced except the University of Tunis El Manar, which is the only efficient DMU in 2009. The University of Gafsa turned out to be the university with the lowest performance of 12%. This means that it should decrease its inputs by 88% while keeping the same level of output produced to become efficient. Moreover, the average CCR score of the 11 universities is 40% which means that on average, the universities should decrease their level of inputs consumed by 60% to become efficient. In 2012, two universities (Tunis El Manar and Monastir) of 11 universities under evaluation are best performers with the estimation of restricted input-oriented DEA model. The efficiency score of the remaining universities have been reduced compared to unrestricted DEA model. The efficiency scores of the universities of Tunis, Sfax and Manouba have been reduced by 64%, 14.3% and 65% respectively. The lowest efficiency score of 39% is attributed to the University of Manouba which is referenced by the University Monastir with weight of 0,9. To become efficient the University of Manouba should adopt its benchmark’s policies and techniques. The University of Monastir is considered as the most recurring benchmark with its reference member. It was referenced for 9 times, which means that there are 9 inefficient universities that could learn from it best practices and strategies to become efficient. However, the University of Tunis El Manar is considered as peer only for the University of Sfax with weight of 0,1. The average efficiency score estimated under restricted DEA model in 2012 has been decreased by 9.4% compared to unrestricted model.

In 2013, two universities of Tunis El Manar and Monastir remain efficient with the incorporation of weights restrictions, while the two universities of Gafsa and Tunis become inefficient with efficiency scores of 69% and 47% respectively. To become efficient these universities should reduce their inputs by 31% and 53% respectively and adopt their benchmark’s practices, those of University of Monastir. The University of Sfax with an efficiency score of 99% can virtually become efficient by combining the two universities of Tunis El Manar and Monastir as peers, with weights of 0.4 and 1

respectively. The lowest efficiency score of 43% is attributed to the University of 53 Manouba, which is referenced by University of Monastir to become efficient. An average, the efficiency score is about 71%; it means that an average, the universities should decrease their inputs by 29% to become efficient. Table 7 summarized the input-output slacks of the 11 Tunisian universities in 2013 estimated with restricted DEA model. The results show that they concern only the input variable” number of students enrolled in Computer sciences media and telecom” and the output variable “number of graduates from Fundamental and Applied Licence” (the same results of unrestricted DEA model). From the Table 7, it is noticed that the two efficient universities of Tunis El Manar and Monastir have neither input nor output slacks. On the contrary, all inefficient DMUs necessitate improving their level of efficiency, either by increasing their outputs’ production or by decreasing their inputs’ use. Table 7. Summary of Input and Output Slacks (2013) Input slacks Output slacks Number of Number of students Number of Number of students enrolled in research units graduates from enrolled in Computer Sciences and Fundamental and Letter Media and Telecom laboratories Applied License 1- Tunis 0 0 7,42 0 2-Tunis El Manar - - - - 3-7 Novembre of Carthage 0 0 12,38 0 4-Manouba 0 0 20,3 0 5-Jendouba 0 0 27,15 0 6-Sousse 0 0 27,28 0 7-Monastir - - - - 8-Kairouan 0 0 23,15 0 9-Sfax 0 1072,11 0 0 10-Gabes 0 0 30,65 0 11-Gafsa 0 0 26,06 0

The University of Sfax is the only university that is required to decrease the input variable “number of students enrolled in Computer sciences media” to become efficient. All other inefficient DMUs have to adopt the improvement strategy based on increasing the number of research units and laboratories in order to reach the efficiency frontier. The universities of Tunis, Carthage and Manouba should increase their number of research units and laboratories by 7, 12 and 20 respectively to become efficient. The highest number of research units and laboratories to be increased appears in the University of Gabes (32 units and laboratories). In general way, we remark that the output slacks estimated with restricted DEA model are higher than those estimated under unrestricted model. This result can be explained by the fact that the introduction of weights restrictions into the DEA model reduced the relative efficiency scores attributed to DMUs. In consequence, the missing quantities of inputs and/or the excess quantities of inputs increased to improve the

efficiency level of universities. Super-efficiency analysis As we have mentioned above, traditional DEA model performs the calculation of the relative efficiency scores of DMUs, but does not allow the ranking of efficient DMUs, because the efficiency scores are upper bounded at one. Therefore, and for efficient universities, this study is useful to evaluate their super-efficiency by attributing to them scores greater than one. Table 8 shows the super-efficiency results.

54 Efficiency scores attributed to inefficient DMUs remain unchanged because they are less than unity. Table 8. Super-Efficiency Scores 2009 2012 2013 Super- Super- Super- University efficiency Rank efficiency Rank efficiency Rank score score score 1- Tunis 0,61 8 0,92 5 1,12 4 2-Tunis El Manar 1,55 2 1,44 1 1,66 1 3-7 Novembre of Carthage 0,35 11 1,03 4 0,85 6 4-Manouba 0,97 4 0,41 11 0,52 11 5-Jendouba 0,83 6 0,79 8 0,73 8 6-Sousse 0,69 7 0,85 7 0,79 7 7-Monastir 1,88 1 1,07 3 1,23 2 8-Kairouan 0,90 5 0,78 9 0,66 10 9-Sfax 0,56 9 0,90 6 0,99 5 10-Gabes 1,01 3 0,72 10 0,70 9 11-Gafsa 0,52 10 1,30 2 1,18 3 Mean 0,9 0,93 0,95

It is noticed that the University of Monastir has the highest super-efficiency scores of 1.88 in 2009, which explains that it can increase its inputs by 88% without becoming inefficient. In 2012 the University of Tunis El Manar was ranked the first with a super-efficiency score of 1.44 which means that it can increase its quantity of inputs used by 44% without leaving the efficiency frontier. The other efficient universities have a super-efficiency scores ranging from 1.03 to 1.3. In 2013, the University of Tunis El Manar remained at the first rank with a super-efficiency score of 1.66. The University of Tunis was ranked fourth with a super- efficiency score of 1.12, which explains, that it is able to increase its inputs by 12% without becoming inefficient.

Importance of inputs and outputs on the efficiency of universities In order to help universities prioritize their objective and to focus on the significant variables to become efficient, we estimated different models specifications by subtracting/adding each time every input and output variables based on the averaging data between 2009, 2012 and 2013. Then, we compared the efficiency estimates of the different models specification by using the non-parametric test of Mann-Whitney. The results presented in Table 9 show that the input variable, number of students enrolled in Computer sciences media and telecom and the output variable, number of graduates from Fundamental and Applied Licence have a significant effect on the Universities’ efficiency (P-Value <0.05). The efficiency level of Tunisian universities depends on the number of students enrolled in computer sciences media and telecom and graduates students from Fundamental and Applied Licence. The number of students enrolled in Letter and the

Number of research units and laboratories don’t have a significant contribution to efficiency scores of universities.

Table 9. Effect of Input and Output Variables on the Efficiency of Universities Input variables Output variables (-) (-) (+) (-) (+) (+) Number of Number Number Number Number (-) (+) Number of graduates of of of student of student Number of Number of graduates from student student enrolled enrolled research research from Fundamental enrolled enrolled in in units and units and Fundamental 55 and in in Computer Computer laboratories laboratories and Applied Applied Letter Letter sciences sciences License License 1-Tunis 1,00 1,00 0,23 1,00 0,90 1,00 0,53 1,00 2-Tunis El Manar 1,00 1,00 1,00 1,00 0,88 1,00 1,00 1,00 3-7 Novembre of 0,80 0,88 0,60 0,88 0,88 0,88 0,41 0,88 Carthage 4-Manouba 0,53 0,57 0,31 0,57 0,57 0,57 0,18 0,57 5-Jendouba 0,79 0,88 0,43 0,88 0,88 0,88 0,04 0,88 6-Sousse 0,88 0,94 0,50 0,94 0,94 0,94 0,34 0,94 7-Monastir 0,97 1,00 1,00 1,00 1,00 1,00 0,69 1,00 8-Kairouan 0,82 0,82 0,30 0,82 0,82 0,82 0,03 0,82 9-Sfax 0,76 0,78 0,75 0,78 0,76 0,78 0,57 0,78 10-Gabes 0,69 0,81 0,54 0,81 0,81 0,81 0,11 0,81 11-Gafsa 1,00 1,00 0,36 1,00 1,00 1,00 0,08 1,00 Mean 0.84 0.88 0.55 0.88 0.86 0.88 0.36 0.88 Mann-Whitney Test (Alpha:0.05) U 48,500 20,000 53,000 10,500 Esperance 60,500 60,500 60,500 60,500 Variance 223,929 227,202 224,190 229,036 P value <0,442 <0,008*** <0,640 <0,001*** Note: In this table we have used the averaging data between 1999-2012 and 2013

In Figure 7, we report the plot of a measure of efficiency scores and input/output variables used in the analysis. The results show that the input variable, number of students enrolled in Computer sciences, media and telecom influences negatively the efficiency scores of universities, this result can be explained by the fact, that increasing the number of student enrolled in this branch causes a high cost able to reduce the efficiency of universities. However, the output variable “number of graduates from Fundamental and Applied Licence” influences positively the efficiency scores of universities.

Conclusion This study used the input minimizing Data Envelopment Analysis model to estimate the technical efficiency of universities. The DMUs evaluated in this research are 11 Tunisian universities ensuring research and teaching activities. Years of study are 2009, 2012 and 2013. Two input variables describing the number of students enrolled in Letter and the number of students enrolled in Computer sciences media and telecom have been used in this analysis. The output variables selected to evaluate teaching and research activities within Tunisian universities are the number of graduates from Fundamental and Applied Licence and the number of research units and laboratories.

56

Figure 7. Scatter Plots of Efficiency Scores and Input/Output Variables

In order to increase discrimination in Data Envelopment Analysis approach, we have introduced weights restrictions into the estimation of input oriented DEA model. Efficiency scores estimated with restricted DEA models are 40%, 77% and 71% in 2009, 2012 and 2013 respectively. In 2009, only the University of Tunis El Manar was considered as efficient, while in 2012 and 2013, the two universities of Monastir and Tunis El Manar have reached the efficiency frontier with scores equal to unity. The super-efficiency measure was originally formulated to rank efficient universities by assigning to them scores greater than one. The University of Tunis El Manar has the highest super-efficiency scores of 1.44 and 1.66 in 2012 and 2013 respectively. This explains that it is able to increase its inputs by 44% and 66% respectively without becoming inefficient. Therefore efficient and inefficient universities can benefit from this research by learning and following the more efficient ones. The analysis of the importance of input and output variables on the efficiency of Tunisian universities demonstrate the significant effect of enrolled students in Computer sciences, media and telecom and the number of graduates from Fundamental and Applied Licence on the level of universities’ efficiency. Despite the overstaffing of students enrolled in literary branches, the input variable number of students enrolled in Letter does not have a significant effect on the efficiency of Tunisian universities. Literary branches are considered as branches, where job opportunities are low.

Improving the efficiency level of Tunisian universities can be attained by increasing the number of graduates from Fundamental and Applied Licence and by reducing the number of enrolled students in computer sciences, media and telecom.

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ASSESSMENT OF UNIVERSITIES EFFICIENCY USING DATA ENVELOPMENT ANALYSIS: WEIGHTS RESTRICTIONS AND SUPER-EFFICIENCY MEASURE Sourour Ramzi Mohamed Ayadi University of Tunis, Tunisia Abstract Higher education represents the spine of development and economic performance in any country. Evaluating the efficiency of this sector is necessary to detect its insufficiency and to develop strategies and policies to improve its productivity. In this paper we evaluate the efficiency of 11 public Universities in Tunisia in 2009, 2012 and 2013 using two fields of DEA development: weights restrictions and super-efficiency measure. We use two input variables: the number of students enrolled in Letter and human sciences and the number of students enrolled in Computer sciences, media and telecom. The two outputs describing research and teaching activities within universities are the number of research units and laboratories and the number of graduates from Fundamental and Applied License respectively. The results show that the application of DEA model with weights restrictions in the sub- sector of higher education increases the discrimination of efficiency results. The super- efficiency measure reveals its usefulness in the ranking of efficient DMUs by attributing to them efficiency scores greater than one. Keywords: higher education, weights restrictions, super-efficiency measure, non-parametric approach, DEA, Tunisia