Scientific research to assess efficiency has its roots in the study of Charnes et al. (1978), who in their initial study approached the notion of Decision Making Units (DMUs) with the non-parametric Data Envelopment Analysis (DEA). Since then, for the next forty years to date, there has been rapid and continuous growth in the field. As a result, a considerable amount of published research has appeared, with a significant portion focused on DEA applications of efficiency and productivity in both public and private sector activities (Emrouznejad, Parker, & Tavares, 2008). The purpose of such scientific articles is to assess the efficiency of educational units and organizations in order to identify the factors that influence it while also providing particularly useful information for decision-makers related to educational policy. Furthermore, when the research takes place in countries where the school education system is public (like it is in Greece), important information on input and output prices are usually missing. Consequently, the measurement of efficiency in education is a complicated and controversial process, while in some cases there is no clear consensus on what the ‘real’ outputs are and how they should be measured, a problem that also occurs for the schooling inputs. In addition, some of the school inputs are not controllable by schooling institutions even though their influence on outputs is evident (Kirjavainen, 2009). Despite these difficulties, what emerges from the literature review (D.Sutherland, R.Price, I.Joumard, C.Nicq, 2007), is that the basic types of factors that can affect student performance and therefore the efficiency of a school are two: The first type refers to "direct" inputs, which are under the supervision of the school system and the second type refers to the so-called "indirect" or "environmental" inputs. This paper investigates and evaluates the effectiveness and the Technical Efficiency of secondary education units in the region of Western Macedonia in Greece and data analysis is divided in two stages. First stage analysis is assessing the effectiveness of the educational system in Greece, with focus in the secondary education, using DEA. In this study the inputs chosen are: the teacher student ratio, the staff student ratio and the computer student ratio of each educational unit. The output (student performance) refers to the student’s achievement in the national exams during the school years of 2014 – 15 and 2015 – 16. In this first stage analysis, output efficiency scores were estimated by solving a standard DEA (output - oriented VRS) problem with school units DMUs. In the second stage analysis, these efficiency scores, derived from the first stage analysis, were explained in a regression with the environmental variables as independent variables. The independent variables chosen were divided in two categories: the variables from the direct school environment (school size, teacher’s experience, teacher’s qualifications and per student expenses) and variables from the wider social environment in which each school operates (GDP per capita, unemployment rate and educational level of each school’s area). In the present study, all upper secondary education units in Western Macedonia were invited to participate. In a total of thirty-eight (38) units, twenty-nine (29) responded to the research process, (response rate of 76.31%. One of the most important factors in the selection of the Region of Western Macedonia as an area of analysis of the technical efficiency of the secondary schools is the particular characteristics of the area (high unemployment rate, high GDP per capita and low educational level of each school’s area).

The analysis of this study is divided in two stages. In the first stage the efficiency level of each school is measured and the efficient and inefficient schools are defined. The method used in this first stage is the Data Envelopment Analysis (DEA). DEA is a nonparametric method that allows measurement of efficiency in cases where multiple inputs produce multiple outputs. The methodology of DEA was developed based on the model of Charnes, Cooper & Rhodes (1978). Charnes, in his study, describes the method of DEA as a mathematical programming model which is applied to empirical data and provides a new way of obtaining empirical estimates of relations, such as production functions, which are the cornerstones of modern finance. For the second stage analysis, the technique of linear regression with the method of the Ordinary Least Squares (OLS) were used. The study uses official school data and self collected questionnaires answered by school principals of upper secondary schools in the region of Western Macedonia. The questionnaire was designed based on literature (Kirjavainen & Loikkanen, 1998 -Afonso & Aubyn, 2006 - Bradley, Johnes & Millington, 2001) and modified to the Greek educational system. The questionnaire consisted of questions, in five different categories. The first category referred to the general characteristics of the school unit, such as school size, class size and the number of teachers who provided educational services in during the school years 2014-15 and 2015-16. The second, referred to the teachers’ experience, teachers’ qualifications, and the number of people working as supportive staff (School Counselors, Secretarial Support etc). The third and fourth categories were related to the school unit’s facilities and available equipment for educational process. The fifth, concerned the operating costs of the school unit. The school output (student performance) which referred to the student’s achievement in the national exams during the school years of 2014–15 and 2015–16, was estimated using data by the School Directors and by the Secondary Education Offices of Western Macedonia. For the data referring to the environmental variables of each school unit (GDP per capita, unemployment rate and educational level of each school’s area) data from the Hellenic Statistical Authority (ELSTAT), Eurostat and the Ministry of Education, Research and Religious Affairs of Greece was analyzed. The research took place between November 2016 and February 2017 and in a total of thirty-eight (38) units, twenty-nine (29) responded to the research process, (response rate 76.31%).

Results from the first stage analysis show that 4 out of the 29 educational units in each of the 5 DEA models were characterized as technical efficient units. These units became benchmarks for all the others with lower efficiency. Furthermore, for each model, information on the possible slacks of the inputs and the possible projection of the outputs was analyzed. In the second stage analysis, results from regression analysis show that from the independent variables, from the direct school environment, teachers’ experience significantly affects school efficiency while teacher’s qualifications, school size and per student expenses do not affect school efficiency of secondary education units in the region of Western Macedonia. Concerning the variables from the wider social environment, GDP per capita, unemployment rate and educational level in each school’s area didn’t show a statistically significant effect on the technical efficiency of the educational units. The findings of the present study conclude that the average technical efficiency of Western Macedonia's secondary education units is quite high. Also, results show that there are opportunities for enhancement of the efficiency level, without neglecting the fact that there are key factors, affecting the technical efficiency of the school units, which are not under the school unit’s control. Another important element that emerges from the present study is that the model tests, of DEA, have shown that it is particularly important to use the limitations and empirical rules in the DEA models in order for all variables to contribute to the final result and the efficiency’s estimation.

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