INTRODUCTION
This study examines the technical efficiency across high schools in Niğde
Province of Turkey, using common methodology of Data Envelopment Analysis
(DEA) and presents evidence on efficiency rankings of schools and possible
efficiency improvements in educational institutions. The subject is obviously
important, once it is recognized that a strong educational system is a
driving force of economic prosperity in the face of highly competitive
world markets and resources allocated to education are scarce. As shown
in the recent literature on endogenous growth, a significant part of the
longrun economic growth can be attributed to human capital accumulation
which is closely related to the performance of educational institutions.
In addition, considering the fact that budgetary conditions in most countries
allow the transfer of only a limited amount of resources to education,
it can be argued that those countries which use available resources in
education efficiently will have higher human capital accumulation and
hence higher longrun growth rates.
The efficient allocation of resources is especially important for developing
countries, such as Turkey, in where resources are scarce, the rate of
growth of population is high and therefore the share of funds allocated
to education is inadequate to achieve satisfactory level of education.
Departing from these observations, the Turkish government has launched
restructuring program in public sector including educational institutions,
which focused on achieving efficiency in public sector. It is apparent
that the success of this reform is closely related to the empirical evidence
provided on the measurement of efficiency in implementation, monitoring
and evaluation stages of the program.
Although, there is fast growing literature on school efficiency in developed
countries, studies on developing countries, including Turkey, are almost
nonexistent. In this study, we investigated the level of efficiency in
high schools and reported on possible improvements to make inefficient
schools efficient.
In recent years, public and professional interest in educational institutions
has increased tremendously and schools are more and more the subject of
analysis. A large number of empirical studies have already undertaken
to measure inefficiencies in educational institutions employing the mathematical
programming techniques. These studies focused on identifying efficient
educational institutions which produce the highest levels of achievement
given their inputs and compare them with inefficient institutions. This
is evidently important because once inefficiencies in education are identified
and quantified; policy can be constructed so as to maximize school achievements.
In addition, the measurement of efficiency also provides valuable information
for policy makers in implementing, monitoring and evaluating the reforms
in education.
The empirical study on education economics is concentrated on the empirical
analysis of the technical relationship between inputs and outputs of education.
In this study, schools are considered as production units which turn educational
inputs into educational outputs. Although, there is no consensus over the selection
of input and output variables, those variables which are under the control of
the educational institutions are in general, taken as the inputs of education
production function such as the number of teachers and variables related to
teaching environment and outputs are represented with exam scores (Worthington,
2001). One of the most cited and the oldest study on efficiency in education
is carried out by Bessent et al. (1982). The
present study attempted to determine technical efficiency levels of schools
in Houston using the DEA analysis. Since then, a large number of empirical studies
have investigated the efficiency in education in developed countries. Some of
these studies are Jesson et al. (1987), Fare
et al. (1989), Mancebon and Molinero (2000),
Mancebon and Bandres (1999), Johnes
(2006) and Waldo (2007).
Considering the fact that the exact form of the functional relationship between
inputs and outputs is not known, some of the researchers in the study, stressed
the importance of the assumed technology in the measurement of technical efficiency
(Banker, 1984; Zhu and Shen, 1995;
Engert, 1996; Pritchett and Filmer,
1999). In other words, the level of efficiency is closely related to the
assumptions about the definition of technology. Fare et
al. (1989), Duncombe et al. (1997), Bates
(1997) Ray (1991), Engert (1996)
and Ganley and Cubbin (1992) have employed both the constant
returns and increasing returns technologies in their calculations of efficiency
and found that the inefficiencies decrease when increasing returns technology
is assumed implying the importance of scale economies in education.
Although, there is an extensive literature on efficiency in education for developed
countries, the number of studies on developing countries is very limited. This
is also a case for Turkey. To this best knowledge, there are only two studies
investigated the level of efficiency in Turkish schools mainly for two reasons.
The first one is related to the data restrictions and the second one is that
the importance of efficiency in education has not been recognized yet in Turkey.
One of these studies is undertaken by Baysal and Toklu (2001),
in where the authors examine the level of efficiency for 11 high schools in
Konya province. In this study, the number of teachers and salaries to personnel
are used as input variables and the number of students won university entrance
exams are used as output variables. The present study reports that only two
of the 11 high schools are efficient and the level of efficiency ranges between
11.5 and 100% averaging 54%. In other words, providing that inefficient schools
become efficient, it is possible to improve input usage about 46%.
In another study, Atan et al. (2002) found that
schools in Ankara province differ significantly in terms of the level of efficiency.
They measured efficiency for 22 Anatolian High Schools (a class of high schools
offering quality education) using DEA analysis and data for 2001 using the number
of students, teachers, classes, laboratories and computers as inputs and the
number of graduates, pass university entrance exams as outputs. They reports
that only 8 out of 22 Anatolian high schools are efficient and if inefficient
schools become efficient, the outputs will increase about 21% with the available
inputs.
Although, these studies provide some evidence on the level of efficiency
in schools in Turkey, the coverage of schools employed in these studies
is very limited and analysis is carried out using constant returns technology
only. For this reason, we will investigate the technical efficiency of
all high schools in Niğde Province assuming both constant returns
and increasing returns technology in empirical educational production
function.
MATERIALS AND METHODS
Efficiency in education examines the ability of schools to turn the inputs
of education into outputs. Given the production technology, if a school
cannot reduce its inputs without causing a reduction in its outputs it
is called efficient school. However, if a school achieves the current
performance using higher number of inputs than other similar schools,
this indicates that the school does not use its resources efficiently.
These inefficiencies may be arising from mismanagement, inappropriate
sizes of schools and external factors.
The main aim of the empirical studies on efficiency measurement is to
construct empirical production frontiers to evaluate the performance across
schools. Production frontier represents the highest possible performance
that can be achieved using available technology. Each Decision Making
Unit’s (DMU) efficiency, in this case a school, is measured by comparing
the efficiency score of this unit with schools that constructs the frontier.
Although, there are different alternative methods to determine production
frontier (parametric and nonparametric), most of the previous empirical
studies in education employed the DEA method.
Figure 1 provides a simple example of measuring efficiency
using DEA and shows the meaning of efficiency.

Fig. 1: 
Efficiency frontier curve 
To simplify the presentation,
it is assumed that schools use only one input to produce one output. In Fig. 1AE represent schools in the input (X)output
(Y) plane. Under the assumption of constant returns to scale, the most
efficient school is the one that has the highest outputinput ratio in
the case of one input and one output. In the figure, constant returns
to scale is shown with a linear line stems from the origin. According
to Fig. 1, the most efficient school is the school B
since the slope of OH line has the highest value at point B. Thus, efficient
production technology is determined by the OH line that goes through point
B. All other points are inefficient because they are under this line.
After determining efficient frontier in this way, at the second stage, the
efficiency scores for inefficient schools are calculated as follows. Assuming
that the observation on the efficiency line (in present example this is shown
by point B) is efficient, efficiency score corresponding to this point is one
(or 100%). Schools which are under the efficiency line are inefficient and the
level of inefficiency of these schools is related to the distance to line H.
Efficiency score for school E, is determined by the ratio of X_{G}/X_{E}.
Although, it is easy to measure efficiency level for one input and one output,
when the number of inputs and outputs are greater than one it becomes very difficult
to measure efficiency scores. In such cases, the linear programming methods
are employed to measure the efficiency scores. DEA model allows the measurement
of efficiency when there are more than one input and output is developed by
Charnes et al. (1978). DEA, is a nonparametric
technique that is used in construction of empirical production frontier and
evaluation of performances of homogenous DMU’s. In this analysis, DMU’s
are schools which use more than one input to produce multiple outputs. In the
analysis, assuming that the number of DMU’s is n and each of these units
use m inputs and s output, the mathematical representation of DEA model can
be written as (Lovell, 1993):
DEA model:
where, c, represent the DMU that its efficiency level will be evaluated,
y_{rj} is the school j’s rth output, x_{ij} is school
j’s ith input, u_{r} and v_{i} are the weights that
will be obtained from solving the model corresponding to input r’s
and output i’s, respectively. Model 1, involves the maximisation
of objective function h_{c}’s, DMU c’s weighted output
to weighted inputs ratio, including itself under the restriction of no
one DMU ratio is greater than one. The weights of u_{r} and v_{i}
in the model is obtained with optimisation. To solve the optimisation
problem given in model 1, we equate h_{c}’s denominator to
one thereby turning the problem into linear programming. Corresponding
model suitable to linear programming can be written as:
In model 2, it is assumed that constant returns technology is employed
in the optimisation problem. In addition, as seen from the model 2, the
weighted average of inputs is equal to one and outputs are maximised.
This formulation of the DEA model is called input oriented efficiency
measurement and indicates that schools try to minimise inputs given the
outputs. The dual of the Primal Linear Programming Model given in model
2, can be written by defining the input weights of schools as θ_{c}
and output weights as λ_{j}:
Dual model:
The values of θ_{c} scores obtained solving the model is
equal to one and the slacks s_{i}^{+} and s_{i}¯
is equal to zero, school c is called efficient. The efficiency school
implies that it is impossible for the school to achieve the given output
level with using less inputs. If θ_{c} is smaller than one,
these schools are called less efficient than the benchmark reference schools
and the value of θ_{c} indicates the extent that school c
needs to reduce input usage to reach efficient frontier. For inefficient
schools reference schools are obtained using the optimum values of λ_{j}’s.
To consider the Variable Returns to Scale (VRS) in the production, an
extra restriction of
needs to be added to the model 3 (Banker et al.,
1984).
Jackknifing method: As explained in the previous section, efficiency
scores for schools are measured with the distance from the empirical production
frontier. The empirical production frontier is determined by the schools which
have the highest output level per inputs and efficiency scores for other schools
are measured with respect to efficient schools. For this reason, it is very
important for the reliability of results that the efficiency scores of those
firms that constructs frontier are not outliers. This is because if the schools,
which construct the frontier, are very different from the others in the province,
when these schools are removed from the sample the efficiency level of the remaining
schools will change. To determine whether outliers affects frontier and hence
efficiency scores the Jackknifing method was employed. The other studies that
employed jackknifing technique are as: Fare et al.
(1989), Ray (1991), Ganley and
Cubbin (1992), Bates (1997) and Engert
(1996). Jackknifing method is a method that is used to test the consistency
of the DEA results in case that a school with outlier observation is included
in the analysis. Briefly, this method, involves measuring the efficiency scores
by removing the reference schools one at a time from the DEA analysis and then
testing changes in the efficiency rankings of schools and average efficiency
values. To determine whether the efficiency rankings of schools change, the
Spearman Rank Correlation coefficient is used and whether the average efficiency
scores change when efficient schools dropped from the sample one at a time is
tested using the Ftest.
RESULTS AND DISCUSSION
Data on inputs and outputs were collected for 35 high schools in Niğde
during the 20042005 school years. The data is obtained mainly from Niğde
Provincial Directorate for National Education and the Student Selection
and Placement Centre (ÖSYM) publication of 2005 Student Selection
Exam Results by Education Institutions. In the empirical analysis we employed
three outputs and four inputs. The selection of the input and output variables
is carried out in line with the existing empirical literature. Output
variables involve students’ university exam scores on science (ÖSSSAY),
social science (ÖSSSÖZ) and weighted average of Turkish and
mathematics (ÖSSEA). Input variables are the number of science teachers
per student, the number of social science teachers per student, the number
of classrooms per student and the number of laboratories per student.
Here, presents the empirical results of the study. In presenting DEA
results, we measure and interpret efficiency scores assuming both constant
returns to scale and variable returns to scale and assuming that output
given so that the deviation of scores from one (or 100%) indicates savings
possibilities in the use of inputs. Table 1 provides
evidence on the stability of DEA results for efficient schools obtained
from the Jackknifing method. The examination of the table shows that Spearman
rank correlation coefficients ranges between 0.866 and 1.000 implying
that the removal of efficient schools did not change the efficiency ranking
of schools. It is also evident from the Ftest results that once the efficient
schools are dropped from the analysis the average efficiency scores do
not show any statistically significantly difference.
Table 1: 
The stability of DEA results for efficient schools 

*Shows that the null hypothesis of equal means could
not be rejected at 1% level of significance 
Table 2: 
Efficiency scores and savings possibilities in the use
of inputs for high schools in Niğde (Assuming constant returns
to scale) 

Values in parenthesis indicates the number of times
the efficient school became references to inefficient schools. Sct,
Sst, Class, Lab are the inputs variables employed in the empirical
analysis and represent the number of science teachers, social science
teachers classes and laboratories per student, respectively 
Taken together the
evidence provided by both of the tests, it seems that the DEA results
are consistent.
The results obtained from the DEA model given in Eq. 3
are provided in Table 2 and 3. Table
2 and 3 includes efficiency scores and potential
improvements to achieve efficiency for inefficient schools. We calculated
the inefficiency ratings for 35 high schools in Niğde Province of
Turkey. An efficiency value of unity represents efficient performance
indicating that the school is operating at a point on the frontier of
the technology. Measures less than unity reflect the inefficient performance.
Subtracting one from the measure yields the percent by which all inputs
could be decreased proportionally given outputs and best practice technology.
Mean efficiency estimated is equal to 0.617 assuming constant returns
to scale implying that total inefficiency is about 38%.
Table 3: 
Efficiency scores and savings possibilities in the use
of inputs for high schools in Niğde (Assuming variable returns
to scale) 

Values in parenthesis indicates the number of times
the efficient school became references to inefficient schools. Sct,
Sst, Class, Lab are the inputs variables employed in the empirical
analysis and represent the number of science teachers, social science
teachers classes and laboratories per student, respectively 
The second column
in Table 2 contains the efficiency measures for each
school in the reference technology of constant returns to scale. Of the
35 schools, about 89 (31%) were found to be inefficient. The efficiency
scores ranges from 0.165 to 1. The minimum efficiency score found was
16.5%. Only four of the 35 schools (schools 2, 10, 28, 33) were found
efficient and these four schools appeared frequently in the reference
set of inefficient schools. School 2 appeared 21 times, schools 10, 28,
33 appeared 17, 13, 10 times, respectively. Possible changes in inputs
need to be undertaken to make inefficient schools as efficient is presented
in the columns of 3 to 6 in Table 2. It is clear from Table 2 that inefficient schools uses too much inputs
to achieve their level of output. For example, the least efficient school,
school 8 employs almost 80% higher inputs to produce its output compared
to the reference schools.
Table 3 provides the efficiency scores and potential improvements
to achieve efficiency for inefficient schools assuming variable returns to scale
technology in educational production function. As seen from the table, the number
of efficient schools increased to nine. The calculated mean efficiency increased
only slightly to 0.686 indicating the presence of about 31% inefficiency in
input usage in education. The examination of the second column in Table
3 shows that only about 26 (9%) of the schools are efficient and the efficiency
scores ranges from 0.167 to 1. The schools that were found efficient assuming
constant returns are found to be efficient using variable returns technology
and they still appeared frequently in the reference set of inefficient schools.
This finding is consistent with the findings of the earlier studies of Fare
et al. (1989), Duncombe et al. (1997),
Bates (1997) Ray (1991), Engert
(1996) and Gonley and Cubbin (1992) which shows that the inefficiencies
decrease when increasing returns technology is assumed implying the importance
of scale economies in education.
CONCLUSION
In this study, we investigated the technical efficiency across high schools
in Niğde and provided evidence on potential improvements to achieve
efficiency for inefficient schools. The results imply that all these schools
appear to have had adequate resources, if fully utilized. When we employed
constant returns technology, the total inefficiency is about 38% and out
of the 35 schools, about 89 (31%) were found to be inefficient. The corresponding
values are 31%, 74 (26%) under variable returns to scale technology. These
values indicate that schools differ significantly in terms of inefficiencies
in input usage and if they began to utilize their resources fully they
would be able to increase their achievement about 35 %. In addition, the
results have shown that the number of efficient schools has increased
when variable returns technology is employed without affecting the efficiency
scores of highly inefficient schools. This also indicates that scale economies
are important in education and the use of increasing returns technology
in education production function is more appropriate. These findings also
show the importance of applied studies on the subject for policy purposes.
Identification and quantification of inefficiencies will definitely provide
valuable information for policy makers in their efforts to construct,
monitor and evaluate the policies aimed to maximize school achievement.