EVALUATION AND RE-DESIGN OF PUBLIC EDUCATION …

1

EVALUATION AND RE-DESIGN OF PUBLIC

EDUCATION NETWORKS: A CENTRALIZED

ANALYSIS1

Laura López-Torres

Diego Prior2

ABSTRACT

The vast number of studies on school efficiency confirms that it is a topic of interest

for researchers. While existing literature has focused on determining the features of

educational centers and environmental factors that influence students’ results, this

study aims to assess and re-design a sample of schools in the public education

network in Catalonia (north-eastern Spain) based on post-New Public Management,

through the use of a specific non-parametric frontier technique. This stream has

received less attention in the research of the field and evaluates the overall efficiency

of a set of units controlled by a central authority. The approach proposed in this study

involves the creation of an internal performance-based scheme that encourages an

effective level of accountability and efficiency for state schools. In this regard, three

theoretical models are proposed in order to improve the efficiency of the network: 1)

the expansion of the results for those state schools whose students’ grades could be

improved; 2) the constraint of the expenses for some state center without lowering the

quality, and 3) a mixture of the previous models. Obviously, the specific orientation to

follow is dependent on the strategies pursued by the government. The results indicate

the network could be improved to redistribute optimally the resources devoted to

education. The study also provides useful information for accountability and decision

making, regarding the implementation of improvement programs in state schools.

Therefore, this paper contributes significantly to the current literature as it uses a

pioneering theoretical approach to analyze school efficiency.

KEY WORDS: Education network, centralization, efficiency, Data Envelopment

Analysis (DEA), reallocation.

JEL CLASIFICATION: C61, D24, I21

1 We are grateful for the helpful comments by Manuel Muñiz, Javier Salinas and other participants at

the 20th Public Economics Meeting (Sevilla, February 2013) and also to the Consell Superior

d’Avaluació del Sistema Educatiu de Catalunya for providing us the data. The authors acknowledge the

financial support of Ministerio de Ciencia e Innovación (ECO2010-18967/ECON). 2 Business Department. Universitat Autònoma de Barcelona. [email protected] and

[email protected].

mailto:[email protected]

mailto:[email protected]

2

1. INTRODUCTION

In recent decades, interest in school efficiency has increased, from both practitioner

and academic points of view (Goldstein and Woodhouse, 2000). From the practical

side, one of the reasons for the emergence of such studies is the increasing importance

of the education sector in the economy3. This sector has provided intellectual training

for the population and better human capital and labor productivity (Blau, 1996).

Likewise, education is considered an essential tool for achieving higher economic

growth (Krueger and Lindahl, 2001).

The Spanish economic reality is currently at the center of a social and political debate.

In the public sector, the pressure to increase the performance implies that any action

to improve efficiency becomes a priority of economic policy so that under current

budget constraints, the continuity of organizations is a decision variable (Bel, Fageda

and Warner, 2010). In particular, to rationalize spending on education, the Spanish

government made budget cuts of 11% and passed the Royal Decree of Urgent

Measures (Real Decreto Ley de Medidas Urgentes). This Royal Decree managed to

save 3,000 million euros by implementing certain measures at the regional level, such

as increasing the students per classroom ratio, expanding the range of increases in

university fees, and delaying the replacement of teachers. However, despite the cuts,

the current system does not encourage schools to work effectively. For that to occur,

we need a reorganization that will motivate them to efficiently achieve good results.

The approach proposed in this study is to create an internal performance-based

scheme that encourages an effective level of performance and accountability for state

schools. In this respect, the optimal size of the network is first determined and, then,

in order to reach this size, the changes required in the allocation of the budget can be

imposed. The introduction of incentives would help the centers to be more efficient

and would allow them to be sustained over time (Burgess and Rato, 2003; Heinrich

and Marschke, 2009). In short, we introduce a number of rules into the field of public

education in the same way as have been done in other public service organizations

such as hospitals (Hafsteinsdottir and Siciliani, 2012) and local authorities (Balaguer-

Coll and Prior, 2009; Zafra-Gómez, Prior, Plata and López-Hernández, 2012; Zafra-

Gómez, Rodríguez and Alcaide, 2012).

3 In the case of Spain, the percentage share of this sector in the level of public spending relative to GDP

has increased by 2% on average from the 1990s (INE, 2011).

3

It should be noted that this process would guarantee the performance of students and

optimize the educational network’s functioning without losing its quality or public

benefits. To summarize, Figure 1 shows the sequence of the scheme proposed in this

paper.

[Insert Figure 1 here]

To develop the scheme, we first designed a management model that would encourage

good educational practices and penalize unsatisfactory results (part A of Figure 1).

Secondly, the rules would be applied to schools that had unsatisfactory results (part B

of Figure 1). Ultimately, we would re-design the public education network through

the application of incentive management (part C of Figure 1).

From the academic point of view, theoretical and methodological literature on school

efficiency is increasing (Coleman, Campbell and Hobson, 1966; Mar-Molinero, Prior,

Segovia and Portillo, 2012). The central hypothesis of school efficiency states that

certain school features and the environment affect the results achieved by students

(Thieme, Prior and Tortosa-Ausina, 2013). This study proposes that research be

conducted on improving school efficiency (ISE). There has been notable progress in

this line owing to, among other factors, the development of new methodological

applications that have improved the conceptualization and measurement of the

reasons that explain the results of students and schools (Johnson and Ruggiero, 2011).

Thus, the Data Envelopment Analysis (DEA) method that appeared in the seminal

work of Charnes, Cooper and Rhodes (1978) has become one of the most commonly

used techniques in the literature (Smith and Mayston, 1987; Thieme et al., 2013;

among others). This paper uses a specific stream of the DEA literature based on the

centralization. This focus has received less attention in the research of the field and

evaluates the overall efficiency of a set of units controlled by a central authority

(decision maker).

Through this framework, this paper addresses the following research questions: What

is the level of efficiency in the public education network? Is it possible to optimize its

performance?

This study is based on the concept of technical efficiency, proposed in the Theory of

Production (Farrell, 1957), and the principles of post-New Public Management (post-

NPM) (Walker and Boyne, 2006; Zafra-Gómez et al., 2012(1); Zafra-Gómez et al.,

4

2012(2)). It aims to evaluate the technical efficiency of a sample of schools in the

public education network in Catalonia (northeastern Spain), by using frontier

techniques. It also seeks possible reallocations that bring about improvements in the

performance of the network.

The results show that efficiency can be improved without losing outputs or inputs, but

this depends on the government’s objectives. The actions to achieve better results are

determined by three approaches: 1) the expansion of the results for those state schools

whose students’ grades could be improved; 2) the reduction of expenses for some

state centers without lowering the quality, and 3) a mix of the two previous actions.

The method proposed in this study has a direct and very important practical

application. It establishes the necessary actions to optimize the network through the

budgets’ reallocation. It also provides valuable information for the decision making

by public authorities. It facilitates the implementation of improvement programs in

schools and their accountability, which contributes to higher levels of quality,

motivation, and fairness within the system4. Therefore, this paper contributes

significantly to the current literature as it uses a pioneering theoretical approach to

analyze school efficiency focusing on the optimizations of the network outcomes.

Following this introduction, Section 2 describes the theoretical framework used in this

research. The third Section reviews the literature on school efficiency. Then, Section 4

details the proposed methodological approach. In Section 5, we comment on and

discuss the results. Finally, in Section 6, we establish the main conclusions and

implications of the study.

4 These topics are fully in line with the objectives of the proposed new Law for the Improvement of

Educational Quality announced in Spain in 2012 (Ley Orgánica para la Mejora de la Calidad

Educativa, LOMCE).

5

2. THEORETICAL FRAMEWORK: POST-NEW PUBLIC MANAGEMENT

The theoretical framework that addresses the objectives of this study fits within post-

New Public Management (post-NPM) (Walker and Boyne, 2006; Zafra-Gómez et al.,

2012(1); Zafra-Gómez et al., 2012(2)). This type of public administration

management, born in reaction to the criticism of New Public Management (NPM),

emerged in the late 20th

century owing to, among other things, excessive

decentralization, poor vertical control, lack of coordination across organizational

units, the focus on results, and short-sightedness about the overall welfare of citizens

(Christensen and Lægreid 2007; Diefenbach, 2009; Zafra-Gómez et al., 2012(1)).

The aforementioned constraints of NPM have created a debate about a new approach

in public sector management based on the post-NPM (Christensen, Lie and Laegreid,

2007). There are some authors argue that this new approach could be seen as a new

type of reforms to public administration because it changes the main features of NPM,

but on the other hand others think that it is not a breakup with the NPM model (Zafra-

Gómez et al., 2012(2)).

The new model of public sector management introduced by post-NPM emphasizes

objectives shared across organizational boundaries, as opposed to working alone

within an organization (NPM model). The post-NPM philosophy, thus, encompasses

the design and delivery of a large variety of policies, programs, and services that cross

organizational boundaries. On the one hand, the main objective is the re-centralization

of public administration to achieve better coordination and greater accountability and

transparency between public organizations (Walker and Boyne, 2006). On the other,

this approach emphasizes reducing fragmentation through structural integration,

increasing centralization, improving coordination, and strengthening core capabilities

and administrative policies (Christensen and Lægreid, 2008; Pollitt, 2009; Kuhlmann,

2010).

Table 1 shows the main features of this new governance model. As can be seen, post-

NPM fosters structural reorganization of the administration. Public entities can

cooperate and work together to reinforce control and coordination both vertically and

horizontally, by combining structural and cultural elements, in order to provide an

integrated service to citizens and achieve cost reduction and efficiency improvement

(Zafra-Gómez et al., 2012(1)). This type of coordinated organizations may be more

6

efficient than a fragmented system, which is focusing mainly on efficiency in service

delivery (Christensen and Lægreid, 2008).

[Insert Table 1 here]

This new form of management can be applied in state schools. The objective is to

design incentives for working effectively, to professionalize their management by

introducing competition mechanisms, and to evaluate the overall system efficiency,

arguments fully in line with the previously mentioned characteristics of post-NPM.

From this point of view, schools are treated as public service organizations in which

knowledge transfer occurs. As we mentioned in the introduction, educational

institutions are fundamental to human capital formation and the country’s economic

growth (Blau, 1996; Krueger and Lindahl, 2001).

The current public education system in Spain is characterized as being bureaucratic,

regulated, and directed (Heckman, Heinrich and Smith, 1997). This model has some

limitations that were mitigated by first introducing competition mechanisms to

improve organizational incentives and then applying management techniques to

optimize individual incentives. In this situation, post-NPM integrates the principles of

NPM (characterized by decentralization and outsourcing) and the bureaucratic model

(which is more authoritarian and centralized), seeking a re-centralization and re-

coordination of public administration to achieve the benefits of reduced costs and

improved efficiency and quality.

The application of this theoretical approach to school efficiency constitutes an

important contribution to the literature because, currently, there are no references that

deal with this subject. The management model suggested by post-NPM has been

applied to local government reforms (Christensen and Laegreid, 2007(2); Kinder,

2012; Zafra-Gómez et al., 2012(1); Zafra-Gómez et al., 2012(2)) and public hospitals

(Dent, 2005) but not to state schools. Therefore, this theoretical approach has

significant practical application. It is in line with the new educational reform recently

announced by the Spanish Ministry of Education, which aims to increase the quality

of the system and reduce the drop-out rate. It also aims to maintain central control (of

the budget, with common content and periodic evaluation) while granting autonomy

to schools.

7

3. DETERMINANTS VARIABLES OF SCHOOL EFFICIENCY

A public entity’s efficiency is a condition for its future permanence. The extreme

difficulty of any assessment process is a major problem in the public sector, due to its

multidimensional structure and the complexity of precisely defining the objectives

assigned. The ISE line of research is based on empirical studies designed to estimate

the magnitude of the impact of the school’s results promoted by the internal and

external environmental factors.

Since its inception, this line of research has provided several findings that have

contributed to improving the knowledge and understanding of the educational

elements that affect the development of students, thus providing information for

decision making in the classroom, school, and educational system. In this regard, for

more than two decades, educational researchers, politicians, and teachers have been

concerned with what makes an efficient center, that is, the factors that contribute to

achieving higher than expected results in a particular context (Goldstein and

Woodhouse, 2000). Some studies have indicated that students’ educational and socio-

economic characteristics explain the differences in their educational level not only in

school but also between centers (Opdenakker and Van Damme, 2001; Elacqua,

Schneider and Buckley, 2006; Cervini, 2009; Thieme et al., 2013).

Despite the importance of measuring school efficiency and its many positive

externalities, researchers have not reached a consensus about the variables taken into

account in determining what makes an efficient center. In this sense, there are still

difficulties in properly defining and measuring a center’s output. There is no

consensus on the importance of school inputs in achieving results. The only area in

which there is more agreement is on the effect of the environmental inputs.

The ISE line of research can be considered classical in educational research. The

report by Coleman et al. (1966), focused on inequality problems in education,

constitutes the beginning of this line of knowledge. Since the report’s publication,

research on this topic has changed in terms of the models and analysis techniques

used, including the variables and instruments for data collection. Despite its

limitations, Coleman report led to an important research line known as “educational

production function” (Boussofiane, Dyson and Thanassoulis, 1991). Furthermore, this

8

work showed the importance of students’ socio-economic environment and its effect

on their academic performance.

Table 2 summarizes the variables used in the literature to evaluate school efficiency.

As can be seen, most papers used results from an aptitude test that was homogeneous

for all students, and this was assessed as output. Furthermore, most studies

distinguished between teachers’ qualities and schools’ physical conditions for school

inputs. Finally, the non-discretionary inputs may have different origins and can be

based on environmental factors (which include students’ personal characteristics or

their close family environment) and complexity factors (variables reflecting the

diversity in the school).


Based on the literature review and considering the theoretical approach followed, it is

possible to build a school efficiency assessment model that collects in detail all of the

variables considered. However, although it would be useful to consider all evaluable

dimensions, the model would be too complex for this study’s objective. For this

reason, we propose a simplified school efficiency assessment model that considers

only the variables used in this study (Figure 2).


As can be seen, the proposed model includes different variables in each category, and

the unit of analysis is the school. In this regard, it should be noted that this model is

descriptive and contains elements that constituted the school’s internal and external

context. Despite its approximate nature, this model could be useful for different target

audiences (teachers, researchers, or decision makers). It is important to highlight that

we do not have any data about the cost of the center and about the students' level. In

Catalonia it is very difficult to access data at this level of analysis, and the authorities

do not provide us with this kind of information.

Outputs are conditioned by different inputs, two of them are discretionary (number of

teachers and availability of teaching innovation projects) and the remainder are non-

discretionary. Through this procedure, we do not sacrifice the education quality nor

did we modify the number of students that compose the current educational network.

The objective is to determine the overall efficiency and the possible inefficiency of

the system.

9

Likewise, outputs are measured by three indicators that are considered at the same

level. However, in the reality of a school, there is a trade-off between the number of

approved students and the average final grade. As we have no indication of which

goal is more desirable, we define them at the same level, although some centers value

one more than the other. The variable “number of students with special educational

needs” is an indicator of output complexity. In this sense, we assume that these

students require more resources and attention from the teachers.

It is also important to highlight some aspects about the inputs. Firstly, the variable

“availability of teaching innovation projects” is an input rather than an output. This

indicator expresses the existence of valuable human capital and refers to the internal

consistency among teachers of the center. It is an indicator of the quality of inputs. It

gives us an idea of the teachers’ involvement in the school. Being a binary variable,

when the value is the unity, it indicated that teachers are more involved in school

management, set goals, and initiate an improvement project. In this regard, it is

important to underline the nature of this variable. Although it is binary, it does not

divide the sample into two groups. We follow Banker and Morey’s (1986) proposal

on how to introduce categorical variables in DEA models. Once this approach is

applied we perform a lenient assessment with those schools that do not have a

teaching innovation project. These types of center are compared with similar schools.

The schools with teaching innovation projects are compared with the entire sample.

Secondly, we considered a group of variables representing the internal complexity of

the center. This set of items is designed as non-discretionary because the school

cannot influence them. As we had 14 variables for this group, we decided to reduce

their number by performing a Principal Components Analysis (PCA) and we obtain

the six factors included in Figure 2. Likewise, we had 17 variables representing the

environmental context. As previously mentioned, we applied another PCA to reduce

the variables. Finally, we obtain three factors which are related to the socio-economic

and family educational level, unemployment and the student complexity5.

5 We do not show the tables of the two PCAs carried out for spaces’ reason. This data may be obtained

from the authors upon request.

10

4. METHODOLOGY

4.1. Variables, Sample, and Data Collection

Based on the literature review, we identified a number of variables that were related to

the ISE approach (Table 3). We developed our own database with interesting

variables for the study because it was difficult to find a secondary database that

contained all of the variables considered in previous theoretical reviews. We

contacted the Consell d'Avaluació del Sistema Educatiu de la Generalitat de

Catalunya to create a more complete database.


After several consultations, we developed a database with 1,695 centers for the

academic year 2009–2010. This figure represented almost all of the centers that

existed in Catalonia. We excluded the centers that only offered special education.

Once we obtained the database, we proceeded to externally validate it through the

Inspectors d’Educació de la Generalitat de Catalunya and an internal evaluation in

which the researchers analyzed each observation. This database allowed us to achieve

the primary objective of this study.

Secondly, the education network analysis through the DEA method required a new

database that detailed the distance between schools. To do this, we again contacted the

Consell d’Avaluació. Once we had carried out the same process described above, we

obtained a matrix of distances between centers (km) composed through 5,576

observations. This database allowed us to undertake the process of reallocating the

inputs in order to establish improvement solutions.

Both databases covered a large range. It was therefore considered that the best

approach for the study’s proposed objective was to choose a specific territorial area.

This was the first approximation for the centralized evaluation. Specifically, the study

of school efficiency was applied to the centers located within the territorial area of

Vallès Occidental, which constituted a sample of 132 centers.

11

4.2. Methodological Procedure

Even though the DEA method for measuring school efficiency is extensive, most

approaches separately consider decision-making units (DMUs), which provide a

relative efficiency index for each unit against the rest. However, few studies have

applied an approach in which they studied the units together and simultaneously

projected to the efficiency frontier with an overall objective (Table 4).


There are situations in which the DMUs operate under a common centralized

direction. This type of scenario is common when all units belong to the same

organization that provides the resources needed to achieve results, as can be the case

with bank branches, hospitals, universities, schools6, or police stations. The central

authority, despite being interested in the efficiency of each unit, is also concerned

with the total consumption of inputs by different DMUs and the overall production of

outputs.

Therefore, to develop this study’s objective, we carried out an analysis of allocation

inputs that projected the units together onto the efficiency frontier. This involved

applying a particular approach called “centralized DEA” (Lozano and Villa, 2004). In

the literature, some previous approaches have considered the DMUs together. These

centralized evaluation approaches have taken different perspectives, more or less

centralized, as shown in Appendix 1. This paper extends Mar-Molinero et al.’s (2012)

approach, which was initially proposed by Lozano and Villa (2004).

This centralized DEA has different orientations depending on the pursued objective.

For example, if we want to improve the results, the correct orientation is to increase

the output. However, if we have to reduce the budget we will have to use an input

orientation. There is also another approach, known as Directional Distance Function

(DDF) (Chambers, Chung and Färe, 1996). This approach is focused on increasing the

output and reducing the input at the same time. The results of this approach are

between the extremes of the two previous approaches. The most suitable approach

depends on the specific objectives of the decision maker.

6 If we take the example of schools, we may wonder why a teacher should be valued differently in two

different schools when doing the same job in the same manner and for the same education authority. It

would be more reasonable to impose the same model on all units operating under centralized direction

(Mar-Molinero et al., 2012).

12

Let us define the three approaches. Before starting the process, it is necessary to

clarify the meaning of the sub-index that appears in the analytical development: j, r =

1, 2, ..., n: sub-index for each DMU; i = 1, 2, ..., m: sub-index for each input; k = 1, 2,

..., p: sub-index for each output; xij = amount of input i consumed by DMUj; ykj =

amount of output produced by the DMUj; θ = technical efficiency ratio; (λ1r, λ2r, ...,

λnr) = intensity vector of the inputs and outputs of each DMUr; di symbolizes the

discretionary inputs (di = 1, ..., q); while ndi represents the non-discretionary inputs

(ndi = 1, ..., s).

This process contained several stages: first, we determined the efficiency of the

current educational network of Vallès Occidental with its total number of available

centers (n = 132). We then contrasted the possibilities for optimizing the network’s

efficiency. To do this, we found the optimum number of centers that the system

should comprise for it to be efficient (n = n*). These phases were developed through a

centralized DEA program based on that proposed by Lozano and Villa (2004), which

was simplified by Mar-Molinero et al.’s (2012) approach.

In this paper, firstly we develop the original output and input models of Lozano and

Villa (2004) and then we simplify these models using the Mar-Molinero et al., (2012)

approach. Finally, we present a specific proposal of the DDF models, the proportional

DDF model (Briec, 1997).

Model phase 1/radial/output-oriented/dual (Lozano and Villa, 2004)

.,0

,,...,1,1

,...,,1,

,,...,1,

,,...,1,

:..

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1

1 1 1

1 1 1

1 1 1

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n

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ndijndijjr

n

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ijijjr

(Program 1A)

13

Model phase 1/radial/input-oriented/dual (Lozano and Villa, 2004)

.,0

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:..

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1

1 1 1

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n

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ndijndijjr

n

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ijijjr

(Program 1B)

These models determined the network efficiency while maintaining the total number

of operational centers. The number of unknowns in these formulas was n2+1 since

each unit created n lambdas, and the overall efficiency θ was also unknown. The

number of estimated unknowns increased as a quadratic function of the number of

units. This would lead to problems if it was a relatively small sample (Mar-Molinero

et al., 2012). In this case, Mar-Molinero et al. (2012) proposed the following

simplification.

Model phase 1/radial/output-oriented/dual (Mar-Molinero et al., 2012)

.,0

,

,,...,1,

,,...,1,

,,...,1,

:..

,.max

1

11

1 1

1 1

free

n

pkyy

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n

j

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n

j

j

n

j

kjj

n

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ndijndijj

n

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dijdijj

(Program 2A)

14

Model phase 1/radial/input-oriented/dual (Mar-Molinero et al., 2012)

.,0

,

,,...,1,

,,...,1,

,,...,1,

:..

:.min

1

11

1 1

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j

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ndijndijj

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(Program 2B)

In these models, we left the number of centers variable (by deleting the restriction

n

j

j n1

), which modifies the proposal of Lozano and Villa (2004). Model (2A)

indicated the optimal number of centers that must operate (n*) to maintain the current

level of fixed inputs. Likewise, Model (2B) indicated the optimal number of centers

that must operate (n*) to maintain the current level of fixed outputs. These programs

contained n+1 unknown decision variables and λj y θ. This was a major simplification

of model (1A and 1B).

Finally, the proportional DDF is defined as follow:

.,0

,

,,...,1,)1(

,,...,1,

,,...,1,)1(

:..

:.max

1

11

1 1

1 1

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In the following section, we present the results of the programs 1A, 1B, 2A, 2B and 3.

However, it is worth pointing out the Catalonian Government’s objective. In the

current Spanish context of budget constraints, a maximum reduction of costs was

demanded. This meant that the more inefficient units could be closed. More

(Program 3)

15

specifically, in September 2012, the Catalan Government revealed the required cut to

be applied in the educational budget. In the present academic year Catalonia has

30,000 more students and 3,000 less teachers. The budget of the department of

education of Catalonia is 4,335 million euros. This figure reduces educational

spending to the level it was at in 2007. Because the government’s objective is to cut

the budget for education, the most appropriate model to reflect this target is program

2B. This model tells us the optimum number of centers that should make up the

education network in order to reduce costs and become more efficient.

Once established the optimal number of centers, according to the government's

objective the next step was to reallocate the inputs from closing centers to surviving

schools that have a similar environment. In order to do this, we carried out a standard

(decentralized), input-oriented variable returns to scale DEA with the total units (n =

132). The relative efficiency index for each unit indicated which centers were less

efficient and, therefore, which would have problems to continue if the reallocation

process is decided. Analytically:

.,0

,...,1,1

,,...,1,

,,...,1,

,,...,1,

:..

.min

1

1

1

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free

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qdixx

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n

j

jr

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ndindijj

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didijj

(Program 4)

At this point, it was worth pointing out the social cost caused by the reallocation of

inputs by closing less efficient centers. This cost referred first to the reallocation of

the teachers to surviving centers7 and second, to the student reallocation between the

schools that would continue to operate. Having into account theses costs, extra effort

7 We performed a detailed analysis of the types of teaching contracts. The savings in teacher numbers

and costs were determined by eliminating the non-permanent contracts.

16

was applied to minimize these side effects, attempting to minimize the possible

associated transportation costs.

The proposed reallocation process was conducted as follows. First, we proceeded to

compare each school that would survive with a more efficient peer. Once identified

the best performing center, we calculated the differences in terms of students and

teachers with respect to benchmark for each center that would still be operational.

From this procedure, we knew the reception capacity of students and teachers for each

school that would comprise the new network. Then, we calculated the distance

between each inefficient center and the rest of the sample. Subsequently, we listed the

distances in ascending order to reallocate students and teachers in the closest centers

possible.

The direction of the reallocation differed for students and teachers. In the case of the

students, this was performed in order of efficiency, that is, we reallocated the students

of the lowest inefficient centers first. In the case of the teachers, those who had to be

reallocated were moved to the nearest and most unbalanced center. The process was

the same for each center that was to close. This was an iterative and dynamic process,

so after the reallocation of the inputs of each inefficient center, we proceeded to

recalculate the reception capacity of other schools. This process is shown graphically

in the following diagram (Figure 3).


The development of the above techniques was performed through specific routines

using the optimization package, GAMS (General Algebraic Modeling System).

5. RESULTS AND DISCUSSION

Table 5 summarizes the results of all the programs. As can be observed, the columns

indicate the program for each case. If we take the output orientation models, the

network’s inefficiency level is higher in the case of program 2A than in 1A. In the

former, outputs can be increased by 16.24 % without consuming more inputs, while in

the latter the required output increase is 15.93 %. These figures mean that the network

is not operating efficiently, so the students’ results can be increased without

consuming more inputs. By looking at these results in more detail, it can be seen that,

17

in order to minimize the cost per center, it is more efficient to copy the best schools.

The cloned centers were the peers in terms of size and socio-economic environment.

In this regard, the units cloned in program 1A are unit 19 (75 times) and unit 31 (57

times). On the other hand, the unit cloned in program 2A is only unit 19 (127 times).

So in this last program, the network should include only 127 schools instead of 132.

This situation would mean that five centers have to be closed.

If we move to the input oriented assessment, we find similar results. The network is

not efficient. In program 1B, the efficiency of the network is 0.8795, that is, it showed

that we could obtain the same system outputs even saving 12.05% of the discretionary

inputs. Otherwise, in the Mar-Molinero et al. (2012) program (2B) the network

operates with 86.03% efficiency. Later on we will go into more detail about this

program and the peer to be cloned.

Finally, the last option to obtain better results in the network is to maximize the output

and at the same time minimize the inputs. This alternative is represented by the DDF

model. If we look at the model 3A, keeping the number of centers constant, it is

possible to increase the outputs and reduce the inputs both by 6.89 %. However, if we

want to optimize the network’s overall efficiency we should keep the number of units

free. In this case, we can increase the outputs and reduce the inputs both by 7.51 %.

Once explained the results of the different programs, and following the Catalonia

government’s strategy, we expand now the specific results for the application of

programs 1B and 2B (Table 6). The columns indicate the number of centers for each

case. The most important columns are columns 4 and 6. When we applied program

(1B), we obtained the result in column 6. As we said before, the overall efficiency of

the group was 0.8795, that is, it showed that we could obtain the same system outputs

even if we saved 12.05 % of the controllable inputs.


However, as indicated above, this model included an unjustified restriction. It sought

to minimize the controllable input while keeping the total number of centers. Mar-

Molinero et al. (2012) suggested that there are situations in which the central

authority can change the inputs’ assignment by closing the most inefficient units or

opening new units. In the current context of budget constraints, the Catalonian

Government was requested that the maximum reduction of costs be achieved so the

18

more inefficient units could be closed. To do this, we ran program (2B) by changing

the value of n each time (range from n = (0.7)n to n = (1.8)n). Feasible solutions did

not exist for n < (0.7)n, and n > (1.8)n. This meant that it would be impossible to

obtain the current output level with less than 93 centers.

Although n = 132 was a feasible solution, it was possible to improve the results if we

reduced the number of operational centers. The global minimum (θ = 0.8603) was

reached when n = 109 centers (the cloned unit was unit 19 (109 times) (column 4 of

Table 6)). Thus, we can say that unit 19 was an ideal center for the system, and it

should be taken as the benchmark.

If we examine the main features of the center 19, we can observe that it is a big school

that obtains very good marks, despite the significant number of students with special

educational needs. Furthermore, the families' socio-economic level is high. However

the unemployment level is also high. Observing the internal features of the center, we

can describe the typology of the students and teachers. Specifically, the students'

complexity level is low, as we find few foreign students and students with special

economic needs. Likewise, it is a center with a low student mobility level. The student

and teacher absenteeism level is also low. Finally, it is a relatively new center. In its

seven years of operation, it has only had one change in the management team, so it

can be described as a stable center.

We obtained an important finding from this result: when we reallocated the excess

inputs of the 23 centers that closed, enlarging the remaining centers, we demonstrated

the existence of increasing returns to scale. That is, the 109 operating centers received

students and teachers. We achieved a result with schools with more students per

teacher ratio but without altering the results obtained by the students. This result is in

line with the strategy announced by the Catalonian Department of Education.

However, the proposed model is selective with the redirection of the budget.

Indiscriminate cuts are not performed to all network centers, we only penalize those

who perform worse.

From the methodological point of view, we found that the existence of variable

returns to scale (VRS) was demonstrated by observing the result compared to the

inefficient units. Analytically, we left the Σλ restriction free and not equal to 1

19

(Lozano and Villa, 2004) or n (Mar-Molinero et al., 2012): Σλ = n variable, where 0 ≤

n ≤ ∞.

In short, the method for optimizing the efficiency of the education network in the area

of Vallès Occidental is to increase the centers’ size. This management mechanism

would introduce internal competition between schools, and those that did not achieve

good results would be penalized. Through this process, we have created a

performance-based scheme of regulation that introduces incentives and motivates the

effective performance of schools. In turn, it achieves better coordination between

public entities and greater accountability and transparency between them (Walker and

Boyne, 2006). As can be seen, the results link with post-NPM. We would achieve an

administrative structural reorganization. The schools would improve their

performance in order to reduce costs, budget allocations and improve efficiency

(Zafra-Gómez et al., 2012). Figure 4 shows the solutions presented in Table 6. The

vertical line represents the current number of schools that make up the network. As

can be seen, the maximum saving on inputs occur when there are 109 operational

centers.


The next step was to reallocate the students and teachers of the 23 centers that were to

close. A total of 8,263 students were reallocated from nearby schools considering that

no student should have to walk, in mean, more than four kilometers. Meanwhile, the

total number of teachers in the Vallès Occidental area was 3,789. Program (2B)

established that it was possible to save 13.97% of the controllable input without losing

outputs. This percentage represented 529 teachers. The total number of teachers from

the 23 centers that were to close was 675, 146 of whom were reallocated to nearby

and unbalanced schools, because the remaining teachers were non-permanent and near

retirement age. Appendix 2 summarizes the reassignment process that considered the

shortest distance of each inefficient center from the rest of the sample.

Despite the efficiency of this form of education system reorganization, it was still

restrictive. It forced the closure of the worst performing schools. It should be noted

that there are other forms of management that could improve the results of the current

educational network without any center needing to close. A viable alternative would

20

be decentralization, which is more in line with NPM (Behn, 2003), that is, giving

freedom and information to economic agents (the parents) to choose schools.

The way to allow this choice lies in transparency and accountability. For example, if

the Spanish centers were to provide more information to parents, they could make

better decisions8. An example, already implemented in the United States, is the

publication of the inspectors’ evaluation reports (Roderick, Jacob and Bryk, 2002). A

further example is in the United Kingdom where the Office for Standards in

Education (OFSTED) publishes the inspection reports annually9. This mechanism

introduces competence and motivates the centers to work effectively without

penalizing them. The publication of such reports disciplines the centers, because they

are aware of the consequences of poor performance (parents do not choose them, and

they cannot be sustained in the future).

Notwithstanding the importance of this issue, the limitations of the Spanish education

system (its scoring and distance systems) and the objective of this study prevented us

from addressing it more deeply. For this reason, this issue will be analyzed in

subsequent extensions of this study.

6. CONCLUSIONS, IMPLICATIONS, AND LIMITATIONS

This paper answers the question about the efficiency level of a specific public

education network in Spain and, if necessary, how to optimize its performance

through a new methodological approach. As we have seen, the DEA method (Charnes

et al., 1978) has become one of the most widely used techniques for measuring school

efficiency (Smith and Mayston, 1987; Thieme et al., 2013); however, centralized

DEA is comparatively less popular among researchers.

In this line of research, Lozano and Villa (2004) made a significant contribution. They

designed a centralized DEA model that equally valued all the inputs and outputs

regardless of the units that were used or produced. Subsequently, Mar-Molinero et al.

(2012) showed that this DEA model could be considerably simplified. This paper

8 However, the public education system in Spain is highly regulated by scoring and distance systems

(the latter measuring the distance from the students’ place of registration). 9 For further information, the reader can visit OFSTED’s website: http://www.ofsted.gov.uk/

http://www.ofsted.gov.uk/

21

applied such a simplification and went a step further, that is, it found the existence of

VRE by observing the result compared to the inefficient units (Σλ free).

We present different approaches in order to obtain efficiency improves inside the

network. However, if we take the Catalonia government strategy, the better option is

to follow an input orientation. This approach allows reduce inputs without lose

outputs. The results for this type of program indicate that, for the analyzed sample, the

current educational network is inefficient. Specifically, without modifying the results

obtained by the students, the school system could save 12.05% of its inputs. To

improve efficiency without losing outputs, the system should comprise by 109

centers, which would mean a saving of 13.97% of the inputs. This excess could be

distributed to centers with the capacity for more students and teachers, considering the

distance constraints between them. Therefore, the best option for improving

educational efficiency in this area is to create larger centers.

These conclusions have important implications for management practices. They

establish the actions that would be necessary in order optimize the network and to

optimally redistribute the budget available. Thus, the central authority would have an

objective justification for strengthening the efficient units and negative incentives for

supporting less efficient units. This study goes beyond a methodological application

of a data set: it is a proposed implementation involving a real case, so the applicability

of the results is very illustrative.

As indicated in the introduction, the current Spanish system does not encourage

schools to work effectively, so we need a reorganization that would motivate them to

efficiently achieve good results. The proposed approach would create a performance-

based scheme of regulation that would introduce a number of rules and encourage

effective functioning. In turn, it would achieve better coordination between state

schools and greater accountability and transparency (Walker and Boyne, 2006). As

can be seen, the results are in line with the strategy being followed by Catalonia and

the theoretical principles of post-NPM. We would obtain a structural reorganization of

the administration so schools could improve their performance in order to reduce

costs and improve their efficiency. The introduction of these incentives would help

the centers to be more efficient and would allow them to survive over time (Burgess

and Rato, 2003; Heinrich and Marschke, 2009). In this regard, this paper presents an

22

important theoretical contribution to the literature because, to date, we have not found

any papers that have addressed the study of school efficiency under this framework.

Despite the theoretical and practical implications, the paper has some limitations that

should be noted. First, the unit of analysis was a school. Thus, it would be very

interesting to have student-level data and, when possible, the distance walked by the

students from their residence to their school. We could then clearly outline the process

of reallocation. Moreover, we considered data for only one annual session of the

school. For further applications, it would be very fruitful to undertake a longitudinal

analysis of various academic years. We could carry out an evaluation of the added

value for schools.

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Zafra-Gómez, J. L., Prior, D., Plata, A. M. and López-Hernández, A. M. (2012) (1),

“Reducing costs in times of crisis: delivery forms in small and medium sized

local governments’ waste management services”, Public Administration,

forthcoming DOI: 10.1111/j.1467-9299.2011.02012.x.

Zafra-Gómez, J. L.; Rodríguez, M. P. and Alcaide, L. (2012) (2), Contrasting New

Public Management (NPM) Versus Post-NPM through Financial Performance:

A Cross-Sectional Analysis of Spanish Local Governments, Administration and

Society, DOI: 10.1177/0095399711433696.

28

Appendix 1. Resources reallocation and centralized DEA studies

AUTHORS METHODOLOGY VARIABLES

Golany, B., Phillips, F. Y. and Rousseau, J. J. (1993)

Input-oriented linear program for reallocation. From solving a DEA additive, they create a model to achieve an overall efficiency index. They use the efficiency index series and the

average productivity of each DMU to see the change in system performance.

Numerical example with two inputs, two outputs and 10 units.

Golany, B. and Tamir, E.

(1995)

Output-oriented DEA program for reallocation. Model for achieving overall efficiency index

by setting a restriction on the upper limit of available resources. The model allows variations

on the limits.

Numerical example with two inputs, two outputs and

20 units.

Li, S. K. and Ng, Y. Ch.

(1995)

They use a centralized DEA. The inputs and outputs reallocation are introduced in all units.

The number of DMUs remains constant.

They compared the results in two different samples:

20 public hospitals in Hong Kong and 26 public

textile companies.

Athanassopoulos, A. D. (1995) He uses a centralized DEA combined with Goal Programming (GoDEA). The inputs and outputs reallocation is introduced in all units. The number of DMUs remains constant. He

uses a sample of 62 local authorities in Greece.

Three discretional inputs (salary costs, maintenance and loans) and three discretional outputs (local taxes

and charges, investment expenditure and service

delivery).

Färe, R., Grabowski, R.,

Grosskopf, S. and Kraft, S.

(1997)

Output-oriented DEA Model with two steps. The model allows the reallocation of a fixed

amount of shared inputs.

The authors reallocated types of land for different

crops.

Kumar, D. K. and Sinha, B. K.

(1999)

Two DEA programs (one input-oriented and one output-oriented) for a multi-period model of

production that considers each time period as a DMU. The objective function is presented as

the period’s average efficiency.

Numerical example with two inputs, two outputs and

five DMUs (time periods).

Ito, R., Namatame, T. and

Yamaguchi, T. (1999)

Firstly, they measure the efficiency of the current activity of each DMU. Then, they estimate

the management resources to reallocate to maximize results. They take into account the

current activity of the DMU, where it is assumed that the DEA’s efficient frontier is a mutually-exclusive proposal for each DMU.

The theoretical development is illustrated with

several hypothetical examples.

Färe, R., Grosskopf, S.,

Kerstens, K., Kirkley, J. E. and

Squires, D. (2000)

DEA with data panel (1987-1990) about the activity of nine boats. One output, two inputs (days at sea and man/days), a

fixed factor (boat characteristics) and an allocable

factor (stock abundance).

Beasley, J. E. (2003) Nonlinear reallocation model with the objective of maximizing the period average. The approach is based on the radial model and it requires specific upper limits over the total

number of inputs and outputs.

Theoretical examples with two inputs and one output.

Lozano, S., Villa, G. and

Adenso-Diaz, B. (2004)

They use a DEA in two stages: in the first, they maximize the added output (total of recycled

glass in all municipalities), while in the second they maximize the slack of the aggregate controllable input (number of containers). Alternatively, they develop a parallel model

wherein the objective function is to minimize the number (integer) of containers without

changing the total amount of recycled glass.

Glass recycling operations in 62 municipalities of

Asturias. The inputs are the number of glass containers assigned to each municipality and the

population and the number of bars and restaurants in

town. The number of containers is the discretional

factor, the other two are considered not controllable environmental.

29


Lozano, S. and Villa, G.

(2004)

Centralized DEA model (input orientation, primal and dual, radial and non-radial, in two

stages) and then, they propose an example obtained from the literature (Golany et al., 1993) with two inputs, two outputs, and 10 units.

XY problem: one input and one output, 7 DMUs.

XX1 problem: two inputs and one output, 7 DMUSs. Literature problem: two inputs and two outputs, 10

DMUs.

Lozano, S. and Villa, G.

(2005)

Centralized DEA models with possibility of downsizing (three stages) and then, they propose

an example from the literature (Golany et al., 1993) with two inputs, two outputs and 10 units.

Two inputs and two outputs, 10 DMUs. Once the

program is proposed, they apply the three explained models.

Giménez-García, V. M.,

Martínez-Parra, J. L. and

Buffa, F. P. (2007)

They use a centralized DEA model in three stages. The reallocation of inputs and outputs is

introduced in the efficient units. Number of DMUs remains constant. The sample consists of

54 fast food restaurants in Spain. The analysis period runs from October 2001 to May 2002.

Output variables: sales (millions of €) and the quality

index for each restaurant (0 to 100). Inputs that can

be reallocated: total number of waiters and kitchen staff. Non-reallocated inputs: the number of seats

and the number of server counters. The non-

controllable inputs: location, number of competitors

and ticket price paid by consumers. Nesterenko, V. and Zelenyuk

V. (2007)

They use a centralized DEA. The inputs and outputs reallocation is introduced in the efficient

units. They introduce non-transferable variables. The final number of units can vary.

The sample is composed of simulated data from 20

units with two inputs and two outputs (taken from a

previous study). The authors use two measures of

inputs (X1 and X2) and two outputs (Y1 and Y2).

Fang, L. and Zhang, C. Q. (2008)

Centralized DEA model. The proposed program solves two objective functions, one concerning the overall efficiency and the other concerning the individual DMU: multi-

objective programming.

Sample of 10 units (fire offices) with two outputs (proportion of lives saved over lives at risk and

number of emergency calls) and two inputs (number

of firefighters and amount of expenditure) obtained

from the fire department's network of China. Li, X. Y. and Cui, J. C. (2008) The authors construct a macro algorithm using complete DEA tools, including CCR and BCC

models, inverse DEA model, the common model of weights analysis, and the algorithm of

additional resources.

The authors provide a few simple examples of

different units, two inputs and two outputs to

illustrate the analytical development.

Lozano, S., Villa, G. and Brannlund, R. (2009)

They propose a three-stage model with different objectives: maximizing desirable aggregate production (phase 1), minimizing undesirable production (emissions) (phase 2), and

minimizing inputs used (phase 3). In turn, the authors contrast this alternative with a model in

two phases.

The model is applied to a sample of manufacturers of paper pulp from Sweden (41 units). The variables are

revenue, costs and profit. The number of units is

constant.

Asmild, M., Paradi, J. C. and Pastor, J. T. (2009)

They use a centralized DEA model. The inputs and outputs reallocation is introduced in the inefficient units. For this, the process requires a pre-phase (DEA additive) which is divided

into efficient units (p) and inefficient units (q). Next, the model applies the CRAI-DEA

program of reassignment. The number of DMUs remains constant. They introduce non-

transferable outputs and uncontrollable variables.

The sample is composed of 16 public service companies controlled by a central government. The

services can be divided into three different sets: sub-

model A has three outputs, one of which is

considered non-transferable and other uncontrollable. Sub-models B and C have three and two regular

outputs.

30


Lozano, S., Villa, G. and

Canca, D. (2011)

They propose six alternative models. There are two approaches: one maximizes the output

(Models I, II, V and VI) and the other minimizes the total cost (models III and IV). They present the models in pairs, one allows reallocation and the other does not allow it.

Sample of 28 Spanish ports. They used the port area

(in m2), the length of the pier, number of tugs and cranes as inputs. As output, they used the port traffic

in tons, the ship calls and the TEU (unit of

measurement of shipping container capacity). The

number of the ports at the end was the same, and none were closed.

Mar-Molinero, C., Prior, D.,

Segovia, M. M. and Portillo, F.

(2012)

Centralized DEA model (weak centralization, the number of DMUs after reallocation can

change). The sample consists of 54 secondary schools in Barcelona, Spain.

Three controllable inputs (hours/teacher week,

hours/special education teacher per week, capital

investment in the last decade. One uncontrollable input (enrollment). Two outputs (number of students

who pass the final test, number of students who

continue their studies at the end of the academic

year). Wu, J. and An, Q. X. (2012) Three integrated models for resource reallocation. The first minimizes the inputs, the second

maximizes the total outputs with current resources, and the third maximizes the overall results

with the resources planned for the next production season.

The authors illustrated the proposed model with a

numerical example of 25 supermarkets, two inputs

and one output.

Source: Self devised

31

Appendix 2. Reallocation process

CENTER PEER

BEFORE

REALLOCATION RECEPTION CAPACITY REALLOCATION

AFTER

REALLOCATION

STUDENT TEACHER STUDENT TEACHER STUDENT TEACHER STUDENT TEACHER

2 19 432 31 -31 1 31 0 463 31

4 19 185 20 -278 -10 278 4 463 24

5 19 439 36 -24 6 24 0 463 36

6 19 457 33 -6 3 6 0 463 33

7 19 440 30 -23 0 23 0 463 30

8 19 422 32 -41 2 41 0 463 32

9 19 471 34 8 4 0 0 471 34

10 19 444 33 -19 3 19 0 463 33

11 19 223 17 -240 -13 240 8 463 25

12 19 219 19 -244 -11 244 6 463 25

13 19 69 8 -394 -22 17 0 86 8

15 19 391 33 -72 3 72 0 463 33

16 19 437 35 -26 5 26 0 463 35

17 19 321 24 -142 -6 142 0 463 24

18 19 446 32 -17 2 17 0 463 32

19 19 463 30 0 0 0 0 463 30

20 19 480 32 17 2 0 0 480 32

21 19 475 33 12 3 0 0 475 33

22 19 429 30 -34 0 34 0 463 30

24 19 488 33 25 3 0 0 488 33

25 19 475 32 12 2 0 0 475 32

26 19 390 26 -73 -4 73 0 463 26

27 19 604 42 141 12 0 0 604 42

28 19 240 24 -223 -6 223 0 463 24

29 19 225 18 -238 -12 238 7 463 25

31 19 415 27 -48 -3 48 0 463 27

32 19 234 18 -229 -12 229 6 463 24

33 19 477 32 14 2 0 0 477 32

34 19 466 32 3 2 0 0 466 32

35 19 496 34 33 4 0 0 496 34

36 19 391 28 -72 -2 72 0 463 28

37 19 233 17 -230 -13 230 7 463 24

38 19 407 33 -56 3 56 0 463 33

39 19 469 31 6 1 0 0 469 31

40 19 373 30 -90 0 90 0 463 30

42 19 443 30 -20 0 20 0 463 30

43 19 447 31 -16 1 16 0 463 31

45 19 266 19 -197 -11 197 5 463 24

47 19 451 30 -12 0 12 0 463 30

48 19 364 25 -99 -5 99 0 463 25

49 19 448 32 -15 2 15 0 463 32

50 19 497 32 34 2 0 0 497 32

51 19 479 34 16 4 0 0 479 34

52 19 452 30 -11 0 11 0 463 30

53 19 244 18 -219 -12 219 6 463 24

56 19 428 37 -35 7 35 0 463 37

57 19 430 30 -33 0 33 0 463 30

58 19 198 19 -265 -11 265 6 463 25

59 19 413 31 -50 1 50 0 463 31

61 19 441 33 -22 3 22 0 463 33

62 19 450 32 -13 2 13 0 463 32

63 19 401 33 -62 3 62 0 463 33

64 19 480 33 17 3 0 0 480 33

65 19 244 18 -219 -12 219 6 463 24

32

CENTER PEER BEFORE

REALLOCATION

RECEPTION

CAPACITY REALLOCATION

AFTER

REALLOCATION

STUDENT TEACHER STUDENT TEACHER STUDENT TEACHER STUDENT TEACHER

66 19 477 33 14 3 0 0 477 33

67 19 234 18 -229 -12 229 6 463 24

68 19 449 33 -14 3 14 0 463 33

69 19 421 29 -42 -1 42 0 463 29

70 19 232 18 -231 -12 231 6 463 24

71 19 196 17 -267 -13 267 8 463 25

72 19 279 21 -184 -9 184 3 463 24

73 19 445 32 -18 2 18 0 463 32

74 19 452 32 -11 2 11 0 463 32

75 19 457 32 -6 2 6 0 463 32

76 19 446 33 -17 3 17 0 463 33

77 19 459 31 -4 1 4 0 463 31

78 19 446 31 -17 1 17 0 463 31

79 19 488 33 25 3 0 0 488 33

80 19 601 43 138 13 0 0 601 43

81 19 226 17 -237 -13 237 7 463 24

82 19 379 36 -84 6 84 0 463 36

83 19 461 32 -2 2 2 0 463 32

84 19 490 34 27 4 0 0 490 34

85 19 454 31 -9 1 9 0 463 31

87 19 162 16 -301 -14 301 9 463 25

89 19 458 33 -5 3 5 0 463 33

90 19 441 31 -22 1 22 0 463 31

92 19 225 19 -238 -11 238 5 463 24

93 19 442 30 -21 0 21 0 463 30

94 19 449 31 -14 1 14 0 463 31

95 19 457 32 -6 2 6 0 463 32

96 19 471 35 8 5 0 0 471 35

97 19 453 31 -10 1 10 0 463 31

99 19 488 35 25 5 0 0 488 35

101 19 353 27 -110 -3 110 0 463 27

102 19 488 33 25 3 0 0 488 33

103 19 273 21 -190 -9 190 3 463 24

105 19 210 18 -253 -12 253 6 463 24

106 19 138 17 -325 -13 325 7 463 24

107 19 432 33 -31 3 31 0 463 33

108 19 210 19 -253 -11 253 5 463 24

109 19 227 17 -236 -13 236 7 463 24

110 19 476 34 13 4 0 0 476 34

111 19 454 31 -9 1 9 0 463 31

112 19 226 17 -237 -13 237 7 463 24

113 19 541 38 78 8 0 0 541 38

114 19 419 32 -44 2 44 0 463 32

115 19 495 34 32 4 0 0 495 34

116 19 450 32 -13 2 13 0 463 32

119 19 447 31 -16 1 16 0 463 31

120 19 173 18 -290 -12 290 6 463 24

121 19 491 34 28 4 0 0 491 34

122 19 413 29 -50 -1 50 0 463 29

123 19 443 32 -20 2 20 0 463 32

124 19 283 25 -180 -5 180 0 463 25

126 19 290 27 -173 -3 173 0 463 27

127 19 455 31 -8 1 8 0 463 31

130 19 406 29 -57 -1 57 0 463 29

132 19 445 30 -18 0 18 0 463 30


33

Table 1. Post-New Public Management (post-NPM) features

Configuration Re-centralization: vertical and horizontal coordination

Conception of the citizen Citizen orientation: responsibility, information and accountability

Regulation Administrative law: transparency

Processes Professionalization of management

Structure Networks

Evaluation Control and management evaluation

Personal Professionalization of the civil service

Source: Pérez et al. (2001:134).

Table 2. School efficiency studies revised

VARIABLE DESCRIPTION PAPERS

SCHOLAR

INPUTS (center

level)

Teachers’ qualities (personal

and educational, experience,

leadership role, assessment

policy, innovation projects,

teaching methodology).

Bessent and Bessent (1980); Bessent et al. (1982); Hanushek (1986);

Smith and Mayston (1987); Deller and Rudnicki (1993); Ehrenberg

and Bewer (1994); Ruggiero et al. (1995); Phillips (1997); Dewey,

Husted and Kenny (2000); Opdenakker and Van Damme (2001);

Silva-Portela and Thanassoulis (2001); Ouellette and Vierstraete

(2005); Ouellette and Vierstraete (2010); Johnson and Ruggiero

(2011); Mar-Molinero et al. (2012).

Schools’ physical conditions

(school size and environment,

school budget, sports

facilities, laboratories).

Hanushek (1986); Smith and Mayston (1987); Deller and Rudnicki

(1993); Phillips (1997); Dewey, Husted and Kenny (2000);

Opdenakker and Van Damme (2001); Silva-Portela and Thanassoulis

(2001); Ouellette and Vierstraete (2005); Ouellette and Vierstraete

(2010); Mar-Molinero et al. (2012).

ENVIRONMENT

AL INPUTS

(student and

context level)

Students’ personal

characteristics (personality,

motivation, academic

aspirations).

Bessent and Bessent (1980); Bacdayan (1997); Mancebón and Muñiz

(2008); Johnson and Ruggiero (2011).

Family environment

features (socio-economic and

educational family features,

family involvement, spill-over

effect).

Coleman et al. (1966); Hanushek (1971); Smith and Mayston (1987);

Thanassoulis and Dunstan (1994); Ruggiero et al. (1995); Pepin

(1999); Mancebón and Mar-Molinero (2000); Silva-Portela and

Thanassoulis (2001); Ouellette and Vierstraete (2005); Mancebón and

Muñiz (2008); Cordero, Pedraja and Salinas (2008).

OUTPUT

Academic performance

(homogeneous test results,

number of approved,

repeaters, students with

special needs).

Madaus, Kellaghan, Rakow and King (1979); Smith and Mayston

(1987); Ray (1991); Thanassoulis and Dunstan (1994); Ruggiero et al.

(1995); Mancebón and Mar-Molinero (2000); Silva-Portela and

Thanassoulis (2001); Ouellette and Vierstraete (2005); Mancebón and

Muñiz (2008); Ouellette and Vierstraete (2010); Johnson and

Ruggiero (2011); Mar-Molinero et al. (2012).


34

Table 3. Description of variables

VARIABLE VARIABLE

TYPE DESCRIPTION SOURCE

X1 Number of teachers Input Total number of teachers at the

school SIDEN

10

X2 Availability of teaching

innovation projects Input

Quality indicator. Availability

of Innovation Projects (0. No,

1.Yes)

Inspecció, Departament

d'Ensenyament

Xnd1 Student mobility level

Non-

discretional

Input

Factor representing the total

movement of school students

(newly incorporated students

and students leaving)


d'Ensenyament

Xnd2 Newly incorporated

students

Non-

discretional

Input

Factor representing the newly

incorporated children (at the

beginning of an academic year

or midway through the year)


d'Ensenyament

Xnd3 Teacher absenteeism Non-

discretional

Input

Factor representing the

teachers’ absences during the

academic year


d'Ensenyament

Xnd4 Student absenteeism Non-

discretional

Input


students’ absences during the

academic year (more than 75%

of the days)


d'Ensenyament

Xnd5 Newly incorporated

teachers

Non-

discretional

Input

Factor representing the newly

incorporated teachers


d'Ensenyament

Xnd6 Instability of the

management team

Non-

discretional

Input

Factor representing the changes

in the management team since

the center started operating


d'Ensenyament

Xnd7 Families’ socio-

economic level

Non-

discretional

Input

Factor representing the parents’

profession and education IDESCAT

11

Xnd8 Families’

unemployment level

Non-

discretional

Input


unemployment level of the

center's families


d'Ensenyament

Xnd9 Students’ complexity

level

Non-

discretional

Input


complexity of the classroom

(number of non-Spanish

students, number of grants)


d'Ensenyament

Y1 Number of students

approved Output

Total enrolled – repeaters –

absentee students (more than

75% of absences each quarter)


d'Ensenyament

Y2 Average test mark, 6th

Yr. Course Output

Measures the quality of

teaching. It defines the average

test mark obtained by the

center’s students in the general

test in sixth grade of primary

school

Consell d’Avaluació del

Sistema Educatiu,

Generalitat de Catalunya

Y3

Number of students

with special

educational needs

Output

Total of students with special

educational needs

(reinforcement classes)

SIDEN


10

SIDEN: Sistema de Información Estadística de Catalunya. 11 IDESCAT: Institut d’Estadística de Catalunya.

35

Table 4. School efficiency studies that applied DEA

FRONTIER METHODOLOGY: Non-parametric techniques

– DEA: Bessent and Bessent (1980); Bessent et al. (1982); Smith and Mayston (1987); Ruggiero et al.

(1995); Mancebón and Mar-Molinero (2000); Bifulco and Bretschneider (2001); Silva-Portela and

Thanassoulis (2001); Mizala et al. (2002); Ouellette and Vierstraete (2005).

– Multi-stage DEA: Ray (1991); Ruggiero (1998); Muñiz (2002); Muñiz, Paradi, Ruggiero and Yang

(2006); Cordero, Pedraja and Santín (2009), Cordero, Pedraja and Santín (2010).

– Multilevel DEA: Thanassoulis (1999); Silva-Portela and Thanassoulis (2001); Thanassoulis and Silva-

Portela (2002); Mancebón and Muñiz (2008); Cervini (2009); Silva-Portela and Camacho (2010); Thieme et

al. (2013).

– Centralized DEA: Athanassopoulos (1995); Lozano and Villa (2004, 2005); Lozano, Villa and Adenso-

Diaz (2004); Giménez-García, Martínez-Parra and Buffa (2007); Nesterenko and Zelenyuk (2007); Fang and

Zhang (2008); Asmild, Paradi and Pastor (2009); Lozano, Villa and Braennlund (2009); Oullette and

Vierstraete (2010); Lozano, Villa and Canca (2011); Mar-Molinero et al. (2012).

– Longitudinal DEA: Oullette and Vierstraete (2010); Johnson and Ruggiero (2011).

– Free Disposal Hull (FDH): De Witte, Thanassoulis, Simpson, Battisti and Charlesworth-May (2010).

– Simulated data: Thanassoulis (1993); Ruggiero (1998); Muñiz, Paradi, Ruggiero and Yang (2006);

Cordero, Pedraja and Santín (2009).


Table 5. Results of Programs

Program (1A) (2A) (1B) (2B) (3A) (3B)

Model

Lozano and

Villa, 2004

(OO)

Mar-

Molinero et

al., 2012

(OO)

Lozano and

Villa, 2004

(IO)

Mar-

Molinero et

al., 2012 (IO)

DDF (Briec,

1997)

DDF (Briec,

1997)

Centers n Optimum n* n Optimum n* n Optimum n*

Global

Efficiency

(θ) 1.1594 1.1625 0.8795 0.8602 0.069 0.0751

λ

19 75 126.3 23.7293 108.6517 38.7522 116.8130

31 57 0 78 0 78 0

37 0 0 30.2707 0 15.2478 0

Σλ 132 127 132 109 132 117


36

Table 6. Results of programs 1B and 2B (n = 132)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

Centers (0.7)n (0.8)n

Optimum

n* (0.9)n n (1.1)n (1.2)n (1.3)n (1.4)n (1.5)n (1.6)n (1.7)n (1.8)n

Global

Efficiency

(θ) 0.9259 0.8627 0.8602 0.8658 0.8795 0.8935 0.9080 0.9225 0.9370 0.9515 0.9660 0.9806 0.9952

λ

13 0 0 0 0 0 0 0 0 0 0 9.9979 33.3703 56.7427

19 21.8087 55.1377 108.6517 37.0026 23.7293 14.2859 11.1615 8.037 4.9124 1.7879 0 0 0

27 59.5117 0 0 0 0 0 0 0 0 0 0 0 0

31 0 0 0 78 78 73.1381 60.2548 47.372 34.4883 21.605 15.9939 20.1110 24.2281

37 0 0 0 3.7974 30.2707 57.7759 86.9837 116.19 145.399 174.61 185.2086 170.9186 156.6291

50 0 50.4623 0 0 0 0 0 0 0 0 0 0 0

95 11.0797 0 0 0 0 0 0 0 0 0 0 0 0

Σλ 92.4 105.6 108.6517 118.8 132 145.2 158.4 171.6 184.8 198 211.2 224.4 237.6


37

Figure 1. Working diagram sequence

A B C

Design of incentive

management model

Efficient centers

Centers more

efficient (new

operating features) Inefficient centers

Application of

the rules

Reallocation of

teachers

Reallocation of

students


Figure 2. School Efficiency Assessment Model


COMPLEXITY

INPUTS (non-

discretionary)

Student mobility level

Newly incorporated

students

Teachers absenteeism

Student absenteeism

Newly incorporated

teachers

Instability of the

management team

Xnd1

Xnd2

Xnd3

Xnd4

Xnd5

Xnd6

X1

X2

Y1

Y2

Y3

SCHOOL

MANAGERIAL

INPUTS

Number of teachers

Availability of teaching

innovation projects

OUTPUTS

Number of students

approved

Average test mark, 6th

Yr.

course

Number of students with

special educational needs

ENVIRONMENTAL

INPUTS (non-

discretionary)

Families’ socio-

economic level

Families’

unemployment level

Students’ complexity

level

Xnd7

Xnd8

Xnd9

38

Figure 3. Evaluation and reallocation process


Figure 4. Reallocation process results


Phase 1

•Centralized DEA (ϴ, n=132). Programs 1A and 1B.

Phase 2

•Centralized DEA (ϴ*, n*). Programs 2A and 2B.

Phase3 •Centralized DEA (ϴ*, n*). Program 3A and 3B.

Phase 4

•Decentralized IO, VRS DEA (ϴ0, n = 132). Program 4.

•DMUs with lower ϴ0, candidates to close.

Phase 5

•Reassignment process: social cost of reallocating inputs by closing inefficient centers.

•Reception capacity: comparison of each school with peers who survive Program 2B.

Phase 6

•Calculate the distance (km) of each center that is closed to the remainder of the centers that are similar in socio-economic environment.

Phase 7

•Reallocation of students to nearby schools.

•Reduction and reallocation of teachers.

0,85

0,86

0,87

0,88

0,89

0,9

0,91

0,92

0,93

0,94

0,95

0,96

0,97

0,98

0,99

1

92 106 109 119 132 145 158 172 185 198 211 224 238

Global Efficiency (ϴ)

Documents

EVALUATION AND RE-DESIGN OF PUBLIC EDUCATION …