Educational systems efficiency in European Union countries

Studies in Educational Evaluation 37 (2011) 108–122

Educational systems efficiency in European Union countries§

Francesca Giambona, Erasmo Vassallo *, Elli Vassiliadis

Dipartimento di Contabilita Nazionale e Analisi dei Processi Sociali, University of Palermo, Viale delle Scienze, Ed.2, Parco d’Orleans, 90128 PA, Italy

A R T I C L E I N F O

Article history:

Received 27 August 2010

Received in revised form 16 April 2011

Accepted 12 May 2011

Available online 16 June 2011

JEL classification:

I21

N30

C14

Keywords:

PISA

Educational achievement

Efficiency analysis

A B S T R A C T

We use the PISA 2006 results to analyse students’ proficiency in EU countries with regard to two indexes

that represent the home background, viz the educational resources available at home and the family

background of students. However, many factors affect proficiency and therefore, using a DEA-bootstrap,

we intend to measure the efficiency of the European educational systems as capability to ensure high

students’ competencies despite adverse conditions about the educational resources available at home

and the family background. Results show an unexpected differentiation among EU countries. In

particular, the most developed countries often show disappointing students’ proficiency despite good

levels of home background. In this case, an important role is played by the social and economic context.

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1. Introduction

In literature, as the innate ability cannot be measured, the studentbackground has been considered the most decisive factor inexplaining student performances. The background includes personalcharacteristics and information on parents’ origin, or education andnumber of books at home and so on (Hanushek & Luque, 2003;Woßmann, 2003). In this paper, we explore the students’ competen-cies allowing for some educational resources available at students’home and some components of students’ family background. Inparticular, we say that the educational system will be more efficientif, with equal family conditions, it achieves a higher students’proficiency. Hence, the greater efficiency can be explained by otherfactors, for example school resources or institutional context.

Through the students’ scholastic competencies in mathematics,reading and science, we use the PISA 2006 data to represent humancapital in the following European Union countries: Austria, Belgium,Bulgaria, Czech Republic, Denmark, Estonia, Finland, France,Germany, Greece, Hungary, Ireland, Italy, Lithuania, Luxembourg,Netherlands, Poland, Portugal, Romania, Slovak Republic, Slovenia,Spain, Sweden, United Kingdom.1 If greater competencies denotegreater human capital, then the effectiveness and the efficiency of

§ The authors thank the editor and two anonymous referees for their helpful

comments and suggestions on a previous version of the paper. Any errors and

omissions are the responsibility of the authors.

* Corresponding author. Tel.: +39 91 6561 518; fax: +39 91 6561 501.

E-mail address: [email protected] (E. Vassallo).1 PISA 2006 involves 57 countries with 30 OECD members. In the paper, we

choose 24 countries in the European Union: Cyprus and Malta are not participants

in PISA 2006 and Latvia has many missing data.

0191-491X/$ – see front matter � 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.stueduc.2011.05.001

the educational system become a basic target, although economicand social contexts where students live and study have the main role(Currie & Moretti, 2003; Lam & Duryea, 1999; Martin, 2004).

Therefore, the purpose of this paper is to connect the students’competencies in mathematics, reading and science to a measure ofeducational resources available at home and a measure of familybackground as proxy of socio-economic students’ conditions. Tothis aim, we have constructed two specific indexes named IAR(educational resources available at home) and IFB (familybackground) while, for the efficiency score, we have applied abootstrap version of Data Envelopment Analysis (DEA).

The paper is divided into five sections. Section 2 presents a briefliterature review. Section 3 illustrates the construction and somepeculiarities of the IAR and IFB indexes and exposes a concisedescription of the DEA-bootstrap technique. Section 4 presents theDEA efficiency scores where IAR and IFB are inputs of the educationalprocess and the competencies in mathematics, reading and scienceare outputs. In the same section, for a better interpretation of theefficiency scores, a cluster analysis is done to assay the presence ofheterogeneous groups of countries in relation to the inputs andoutputs. Section 5 concludes the paper with a discussion of the mainfindings. Finally, Appendix includes some useful tables and figures.

2. Research problem in context

Many papers in the economic field address some aspects of theeducational process and factors that directly or indirectly influenceit (for example, Bramanti & Odifreddi, 2006; Brunello & Checchi,2005; Coleman, 1966; Putnam & Helliwell, 1999; Putnam, 1993).This is a relevant issue for the sustainable development of the

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F. Giambona et al. / Studies in Educational Evaluation 37 (2011) 108–122 109

modern economies and an important key to promote developmentin all nations of the world (Sen, 1999; De La Fuente & Ciccone, 2002).The first major scientific contributions of Mincer (1958), Schultz(1961) and Becker (1964) on the education economics haveencouraged studies about the relationship between human capitaland productivity, the distribution of wealth and, more generally, theeconomic and social development of countries (Romer, 1990). Briefly,more education and then more human capital generate economicand social well-being and ensure economic and social progress(Nelson & Phelps, 1966). In human capital theory the education ofpopulation is highly instrumental and necessary to improve theproduction (Psacharopoulos & Woodhall, 1997; Sakamota & Powers,1995; Schultz, 1971). Essentially, human capital theorists argue thatan educated population is a productive population because a higherhuman capital and, so, a higher cognitive stock of workers withhigher income, promotes the adoption of new technologiesincreasing productivity and generating economic growth and socialprogress (Harmon, Walker, & Westergaard-Nielsen, 2001; Mankiw,Romer, & Weil, 1992). Thus, the formal education is a productiveinvestment in human capital considered as important as physicalcapital (Temple, 1999). The training success of a population impliesa better educated population, more skilled and competent workers,and it determines, in fact, the success of the scholastic educationalsystem whose main purpose is human capital accumulation.

Generally, human capital is measured through the participationrate of the population in education and through the number ofyears of schooling (Barro, 2001; Barro & Lee, 1993), but the simpleconsideration that a year of study and training may not have thesame value in all countries, has brought to consider also measuresof human capital quality (Hanushek & Kim, 1995). Indeed, a largepart of the investment in human capital is aimed at increasing theintellectual ability and the cognitive skills which, however, dependon the family background too (Coleman, 1966; Cutillo et al., 2004;Fagerlind & Saha, 1997). In particular, Hanushek and Kimko (2000)underline that the differences of growth among countries aresignificantly affected by human capital and its quality is influencedby cultural, racial, family and scholastic conditions.

The role of human capital in economic and social development ofa country is not a trivial issue. Although the theory is clear, theempirical evidence is less clear and sometimes discordant (Cohen &Soto, 2007; Krueger & Lindahl, 2001). The unavailability of statisticalsources and the difficulty to build good variables make everythingmore uncertain (Barro, 2001). For this reason, among the useful toolsto measure human capital, the surveys about skills, capabilities andcompetencies appear relevant (Tyler, Murnane, & Willett, 2000).Specifically, it is useful to measure human capital through thescholastic competency of students (the future workers) even if thisdoes not capture completely their attitudes and motivations.Anyhow, the results could provide some important evidences aboutlevel and quality of human capital in some countries (Afonso &Aubyn, 2005).

The first question is: how can we represent students’ skills?Many important surveys measure knowledge, students’ skills andabilities from a number of countries, i.e.: the International AdultLiteracy Survey (IALS) carried out in three editions (1994, 1996 and1998) by OECD and Statistics Canada; the Trends in Maths andScience Study (TIMSS) (in 1995, 1999, 2003 and 2007) and theProgress in International Reading Literacy Study (PIRLS) (in 2001and 2006), both conducted by the International Association for theEvaluation of Educational Achievement (IEA) through its Interna-tional Study Center at Boston College.2 Finally, the Program forInternational Student Assessment (PISA), conducted every three

2 There are other less important and less known surveys. They are not cited since

carried out on a smaller number of countries or carried out with strong discontinuity;

for example, Adult Literacy and Lifeskills (or ALL) (Smyth & Lane, 2009).

years and organized by OECD in 2000, 2003, 2006 and 2009 (OECD,2006, 2007a, 2009a). The PISA OECD project aims to measure 15-year-old students’ skills on mathematics, reading and scienceliteracy scales and to monitor the trends over time. PISA 2006 is thethird PISA assessment and the last available survey at time ofwriting this paper. We note that the choice of 15-year-old studentsis not accidental in PISA, since it marks for many countries thetransition from a basic education to a more specific instruction orprofessional training.

Compared to the IEA surveys, the PISA project shows somedifferences, particularly: (a) the target population, for example inTIMSS 2007, is fourth grade and eighth grade students, while in PISA isthe 15-year-old students; (b) PISA is not constrained by the need ofhaving comparable contents of the school programme among theparticipating countries, the knowledge is not defined in terms of acommon school curriculum but in terms of skills that are consideredessential for students’ future life. Indeed, OECD assesses: ‘‘theknowledge, skills, competencies and other attributes embodied inindividuals [. . .] are relevant to personal, social and economic well-being’’ (OECD, 2001, p. 18). In this paper, we prefer to use the PISAsurvey as: (a) it collects information on all three areas of competencies(mathematics, reading and science), unlike the IEA surveys collectinformation in reading literacy (PIRLS) and mathematics and scienceliteracy (TIMSS) separately; (b) it is carried out every 3 years whilePIRLS and TIMSS every 5 and 4 years respectively; (c) it considers the15-year-old students and therefore it allows to compare the compe-tency level, useful for labour market inclusion. In general terms, PISAis useful for our goal as it is a comprehensive survey that analysesthe disparities of students’ proficiencies among countries and itallows us to easily explore the students’ socio-demographic charac-teristics (Bratti et al., 2007; Checchi, 2004; Checchi & Flabbi, 2006).

Then, the second question is: how can we represent the contextand the conditions in which students live? To this aim, we haveconstructed two specific indexes named IAR (educationalresources available at home) and IFB (family background). Besides,to highlight some sources of heterogeneity, the students aresubdivided by gender (male and female), school management(public and private), school size (small, medium and large), andcommunity size (village, town and city).

In this way, we build an efficiency rank of the educationalsystems giving a greater value to those systems where thecompetencies are high despite an unfavorable context of theeducational resources available at home and the family back-ground (Cunha, Heckman, Lochner, & Masterov, 2006).

As general rule, a high students’ skill with low resources athome and poor family background is translated in a high efficiencyscore assuming the positive presence of institutional factors, localand global school policy, school facilities, teachers’ expertise, etc.But, the inclusion of these elements in the analysis is affected bymeasurement difficulties or lack of data, rather they are treated asexplanatory factors of the efficiency scores. In brief, a greaterefficiency score represents the success of the educational system(Bishop & Woßmann, 2004).

In fact, higher values of IAR and IFB should be related to higherskills. So, it is interesting to underline the countries with low IARand IFB values and high competencies (high efficiency) and, viceversa, the countries with high IAR and IFB and low competencies(low efficiency). It should be noted immediately that we use microdata but, at the end, we are interested in a national framework and,therefore, a comparison of countries about the educational systemuseful for policy and to identify clearly the macro benchmarkamong the European Union countries.3

3 The micro level analysis allows for high detail at student level but it does not

allow to generalize at country level. Then, in the paper, we shift from a micro to a

macro approach.

F. Giambona et al. / Studies in Educational Evaluation 37 (2011) 108–122110

The final question is: how can we get these efficiency scores? Theefficiency score is obtained through the statistical technical efficiencyapproach with a nonparametric method based on a DEA-bootstrapalgorithm. This method can be applied with a few of data, it correctsthe typical bias of the classical DEA estimates and avoids the curse ofdimensionality. The score varies from 0 (worse state) to 1 (betterstate) and represents a measure of the ability of a country to stimulatebetter students’ skills despite unfavorable socio-economic condi-tions. It represents the success of the educational system.4

3. Research approach and methods

3.1. Home background indexes

In order to evaluate the differences between countries, we haveconsidered the three students’ competencies in mathematics,reading and science and two indexes representing the students’conditions from PISA 2006.5 In particular, we have considered: (1)the educational resources available for the student at home(named IAR); (2) some features related to the family background(named IFB). The role of the students’ conditions and, in particular,the dimensions represented in the two indexes have a significantrelationship with the students’ skills (Acemoglu & Angrist, 2000;Currie & Thomas, 2001; Feinstein, 2004; Fuchs & Woßmann, 2004;Moretti, 2004; OECD, 2007b; Schulz, 2005).

The two indexes must be constructed from micro data and,therefore, to maintain consistency in the analysis and to provide adetailed study of the skills by subgroups, we need the proficiencyvalues for each student.6

In order to represent the educational resources available at homewhich are useful for the student training, following the literatureindicated in this and in the previous section, we have selected the

4 In literature, both nonparametric DEA methods and classical parametric

frontier models are utilized to analyse the educational process and to measure its

statistical efficiency (Cooper & Cohn, 1997; Johnes, 2006; Soares de Mello et al.,

2006). But, a robust nonparametric DEA approach is here preferable.5 The PISA target population consists of 15-year-old students attending schools in

grades 7 and higher. In PISA 2006 the target population could be defined as all students

born in 1990 attending a school or other educational institution. It is almost impossible

to examine the whole population and, so, taking advantage of the statistic theory, it is

opportune to use a representative subset of the population. The sample is collected

(sampling) following a specific design and statistics are calculated from the sample so

that one can make inferences from the sample to the population. In all but one country,

the sampling design is a two-stage stratified sample. The first-stage units are schools

with 15-year-old students with sampling probabilities proportional to size. The

second-stage units are students within sampled schools. In one country, a three-stage

design is used: the first-stage units are geographical areas, the second-stage units are

schools and the third-stage units are students. A minimum of 150 schools are selected

in each country and, within each school, a prearranged number of students, usually 35,

is randomly selected with equal probability. Prior to sampling, schools are stratified.

The stratification operation classifies units into groups according to some stratification

variables; it is useful, i.e., to improve the statistical characteristics of the sample or to

ensure adequate representation of all parts of a population. The students included in

the sample for a given country are chosen randomly, but the selection probabilities of

the students vary. Therefore, some weights are incorporated into the analysis to ensure

that each sampled student represents the correct number of students in the PISA

population. More details are in OECD (2009a).6 We use the five Plausible Values (or PV) for each of the three competencies in

reading, mathematics and science. Plausible values were first developed for the

analyses of National Assessment of Educational Progress data by Mislevy, Sheehan,

Beaton and Johnson, based on Rubin’s work on multiple imputations. Plausible

values were used in all subsequent NAEP surveys, TIMSS and PISA. The simplest way

to describe plausible values is to say that they are some kind of student ability

estimates (Wu, 2004). In our paper, the five PV are kept separate throughout the

analysis and they are aggregated (by means) just at the end when at country level

the bias effects became irrelevant. This method is not the usual technique to

aggregate PV but it is simply a summary measure of students’ competencies. It is an

obvious simplification, but since we are interested in aggregated data for the whole

country, the results are not biased; in fact, when available, they are equal to official

data published by OECD (2007a). It should be noted that for all computations, for

data aggregations and indexes construction, we weight the micro data by the final

students’ weights and the final schools’ weights according to circumstances.

possession (value 1) or not (value 0) of some relevant goods from thequestion nr. 13 in the student questionnaire (OECD, 2005):

1. desk to study,2. quiet place to study,3. computer to use for school work,4. educational software,5. link to the internet,6. own calculator,7. books to help with school work,8. dictionary.

The index of the educational resources available at student’shome (IAR) is obtained by the sum of the possession values (1 = yesor 0 = no); so, it varies from 0 (none availability) to 8 (wholeavailability). Finally, the country value is the mean for thecorresponding students.7

The second index represents the students’ family background.Specifically, in the student questionnaire we consider:

the possession of the goods (b) and (m) from the question nr. 131. own room,2. dishwasher;

the possession of two or more of the goods (a), (b), (c) and (d)from question nr. 14:

3. cellular phone,4. television,5. computer,6. car;

from question nr. 15:7. possession of 100 books or more; from question nrs. 7 and 10:8. a level 4 in the ISCED qualification of at least one parent; from

question nrs. 5 and 8:9. at least one parent legislator, senior official, manager, profes-

sional, technician or associate professional according to the ISCOclassification.

The index of students’ family background (IFB), obtained by thesum of the possession values (1 = yes or 0 = no), varies from aminimum of 0 (no possession) to a maximum of 9 (wholepossession). The country value is the mean for the correspondingstudents.8

As mentioned earlier, the student’s skills are influenced bymany factors including the quality of teachers and the facilitiesavailable in schools (also, Gundlach, Woßmann, & Gmelin, 2001;Hanushek, 2003). These factors are not explicitly considered in thepaper but they affect the competencies values and, then, influencethe efficiency score of the educational system, so that they willhelp us in explaining differences in performance (Bishop, 1997;Jacob, 2005; West & Peterson, 2006).

Table 1 shows the three competencies, the IAR and IFB valuesfor the EU countries.9

7 The index is similar to HEDRES (home educational resources index) proposed by

OECD (2009b); in particular, we have also included in IAR the possession of ‘‘link to

the internet’’ as very useful resource for the study at home.8 IFB is similar to WEALTH (family wealth possession index) proposed by OECD

(2009b) with some differences: the OECD variables related to the possession of

certain goods (cellular phone, television, computer and car) are dichotomised to

‘‘possession of not more than one’’ and ‘‘more than one’’; also it includes the

possession of books (<100 and �100) and the level of parental education and

parental occupation.9 The IAR and IFB indexes are built by aggregating discrete values, but now they

are considered in a continuous scale. This is not a problem because the two indexes

are meant to represent a general level of possession for some items. The cultural

roots of the 24 European Union countries are sufficiently common to assume similar

cultural context in which the possession of goods considered for calculating both

indexes has the same meaning across the nations (OECD, 2009c); moreover, the

variability of possession is never too high across the 24 countries.

Fig. 1. IAR and IFB overall values.

Table 1IAR, IFB and PV overall values.

Country IAR IFB PV

mathematics

PV

reading

PV

science

Austria 6.99 6.59 505.48 490.19 510.84

Belgium 7.15 6.32 520.35 500.90 510.36

Bulgaria 5.90 4.75 413.45 401.93 434.08

Czech Republic 6.92 5.45 509.86 482.72 512.86

Denmark 7.16 6.88 513.03 494.48 495.89

Estonia 6.96 5.33 514.58 500.75 531.39

Finland 6.94 6.68 548.36 546.87 563.32

France 6.82 6.04 495.54 487.71 495.22

Germany 7.21 6.46 503.79 494.94 515.65

Greece 5.85 5.78 459.20 459.71 473.38

Hungary 6.51 5.62 490.94 482.37 503.93

Ireland 6.86 6.33 501.47 517.31 508.33

Italy 6.91 5.67 461.69 468.52 475.40

Lithuania 6.56 4.97 486.42 470.07 487.96

Luxembourg 7.11 6.64 490.00 479.37 486.32

Netherlands 7.09 6.50 530.65 506.75 524.86

Poland 6.74 4.64 495.43 507.64 497.81

Portugal 6.81 5.10 466.16 472.30 474.31

Romania 5.48 4.07 414.80 395.93 418.39

Slovak Republic 6.29 4.71 492.11 466.35 488.43

Slovenia 7.37 6.19 504.46 494.41 518.82

Spain 6.81 5.70 479.96 460.83 488.42

Sweden 6.97 7.08 480.35 507.31 503.33

United Kingdom 7.13 6.48 495.44 495.08 514.77

Median 6.92 5.91 495.44 488.95 500.57

Mean 6.77 5.83 490.56 482.69 497.25


With reference to IAR, the average value for all the 24 countriesis 6.77 and the median is 6.92. The minimum is in Romania (5.48)and the maximum is in Slovenia (7.37). For IFB, the average valuefor all the 24 countries is 5.83 and the median is 5.91. Theminimum is in Romania (4.07) and the maximum is in Sweden(7.08).10

Fig. 1 crosses the IAR and IFB values. The graph is divided in fourquadrants by the median of the two indexes. The countries arealong the main bisector showing a close relationship among thetwo indexes. In particular, among the countries with lower valuesthan the median value, we note Greece and Poland. Greece has IARmuch lower than the median and IFB just below its median. Polandhas the opposite position. Among the countries with higher valuesthan the median, we find Slovenia and Sweden showing,respectively, the highest IAR and the highest IFB.

To verify if there are interesting differences among the 24 EUcountries about students’ proficiencies and students’ conditions,we use the five variables previously described (the threecompetencies – mathematics, reading and science – and the twoIAR and IFB indexes), and we analyse them by student’s gender(male/female), school management (public/private), communitysize (three categories, village and small town – named village – /town/city and large city – named city) and school size (small/medium/large, with reference to the first 1/3, the second and thelast 1/3 of the distribution of the students number for eachcountry). With reference to student’s gender and mathematicscompetencies, we note that males have slightly higher scores thanfemales, except for Bulgaria. On the contrary, reading competen-cies show a better value for female. The differences are more

10 With regard to the average level of availability of the eight IAR components in

percentage terms, we see a smaller variability among the 24 countries with respect

to ‘‘a desk to study’’ (range equal to 12.9), ‘‘a quiet place to study’’ (14.2) and ‘‘a

dictionary’’ (13.9), and a higher variability with respect to ‘‘a link to the internet’’

(64.6) and ‘‘your own calculator’’ (45.4). About the average level of availability of

the nine IFB components, we note a smaller variability among the countries with

respect to ‘‘two or more cellular phones’’ (26.0), ‘‘two or more televisions’’ (28.8),

‘‘more than 100 books’’ (26.9), while a higher variability is in ‘‘a dishwasher’’ (75.4)

and ‘‘two or more computers’’ (72.0).

balanced for science competencies. Obviously, we have notanalysed the differences between IAR and IFB by gender sincethe relationship between the two indexes with the male or femalefeature is senseless. The analysis for public and private manage-ment presents higher scores in all the three competencies forprivate schools in many countries except Italy, Luxembourg,Austria, Finland and partially Czech Republic, where there areslightly higher scores for public schools. Basically, Italian publicschools have higher educational standards than private schoolswhereas the opposite happens in other countries, for example inthe United States (Brunello & Rocco, 2008). With reference to thetwo indexes, we note a higher IAR for private schools in manycountries, although in Finland, Estonia, Austria, Netherlands,Luxembourg, Denmark and Germany the public and private valuesare very similar. Also, the IFB values are higher in private schoolsthan in public schools except Netherlands, Austria, Luxembourgand Finland where public and private schools have very similarvalues. Since the IAR and IFB indexes represent the educationalresources available at home and the family background, it isobvious that higher values, indicating better conditions, arepresent more easily for students in private schools. Besides, theIAR and IFB indexes and the three competencies are as higher as thecommunity size is bigger. Likewise, the two indexes and the threecompetencies improve according to the school size.11

3.2. Brief description of the DEA-bootstrap algorithm

The traditional view of the Farrell-efficiency concept corre-sponds to the relationship between inputs and outputs. In theproduction analysis, for example in a firm, the production isconstrained by the technical possibilities denoted, for a given atechnology, by the production set

C ¼ fðx; yÞ 2 Rpþqþ jx can produce yg (1)

11 For the sake of brevity, we do not include the corresponding tables and figures

in the paper. All documents are available on request from the authors.


where x 2 Rpþ represents a matrix of inputs and y 2 R

qþ one of

outputs. If

8 y 2 C ; XðyÞ ¼ fx 2 Rpþjðx; yÞ 2 Cg (2)

then the radial input-oriented efficient frontier is

@XðyÞ ¼ fxjx 2 XðyÞ; ux =2 XðyÞ 8 0 < u < 1g (3)

Consequently, the Farrell input-oriented technical efficiency for ageneric point (x, y) is

uðx; yÞ ¼ inffujux 2 XðyÞg (4)

Therefore, a production unit is technically efficient when itminimises the input levels for a given level of output. It is easy totranspose this analysis to the output-oriented case: then, a unit istechnically efficient when it is able to maximise output for a givenlevel of input.

In this paper, the units are the 24 EU countries, but theproduction process is virtual because we consider the two indexesIAR and IFB as inputs and the three proficiencies in mathematics,reading and science as outputs.

The production possibilities set C is unknown and only thecombinations (x, y) of the effectively observed units are know.Therefore, it will be necessary to estimate in some way C, X(y),@X(x) and u(x, y) for the input orientation, or with a similarreasoning, Y(x), @Y(x) and f(x,y) for the output orientation. Amongall the alternatives, the estimates obtained using DEA (DataEnvelopment Analysis) are the most common (Førsund &Sarafoglou, 2005).

For an input-oriented DEA, we have the following estimator

udeaðx0; y0Þ ¼ inffujðux0; y0Þ 2 Cdeað@nÞg (5)

and

Cdeað@nÞ ¼�ðx; yÞ 2 R

pþqþ jy �

Xn

i¼1

g iyi; x �Xn

i¼1

g ixi;

Xn

i¼1

g i ¼ 1; g i� 0 8 i ¼ 1; . . . ; n

�(6)

where @n = {(xi, yi), i = 1, . . ., n} and with

Cdea� C and uðx0; y0Þ � udeaðx0; y0Þ � 1 (7)

It is immediate to translate this in output-oriented terms,where

8 x 2 C ; YðxÞ ¼ fy 2 Rqþjðx; yÞ 2 Cg;

@YðxÞ ¼ fyjy 2 YðxÞ; fy =2 YðxÞ 8 f > 1g;fðx; yÞ ¼ supffjfy 2 YðxÞg (8)

In the paper, we have chosen the output orientation. Therefore,a country has higher efficiency score of the educational system if,for given inputs (educational resources available at home andfamily background), its students have higher proficiencies inmathematics, reading and science.

Besides, since the Farrell output-oriented efficiency score variesfrom 1 to infinite, we use the reciprocal 1/f that varies from 0 to 1as in the Shephard representation.

The classic DEA approach has considerable advantages and itdoes not demand a specific, often unjustifiable, mathematicalform between inputs and outputs, but it has also somedrawbacks not wholly negligible at times. In particular, theDEA scores show a bias (see formula (7)) yet a correction ispossible. The absence of theoretical information about the DEAestimates suggests a bootstrap procedure to simulate the DataGenerating Process (DGP) (Simar & Wilson, 1998, 2000a, 2000b).Following the Simar–Wilson approach, it is possible to obtain

bootstrap samples so that from each sample we have oneefficiency score for each specific country and, consequently, tostudy the statistical characteristics of the efficiency values and,so, to correct the bias.

If the data @n are from the process P(C, f(x, y)) where C is theunknown set and f is a suitable probability density function, fromthe same @n it is possible to derive an estimator of P, C and score u(or f). Let Pð@nÞ be a consistent estimator of the DGP P, thenPð@nÞ ¼ PðC ; fðx; yÞÞ. In a bootstrap way, a new dataset or pseudo-sample @�n ¼ fðx�i ; y�i Þ; i ¼ 1; . . . ; ng is drawn from P: An estimatorof C is now C

�ð@�nÞ; and so, for a fixed point (x0, y0), we have

u�deaðx0; y0Þ as estimator of udeaðx0; y0Þ: If the bootstrap is consistent,

then approximately

ðu�deaðx0; y0Þ � udeaðx0; y0ÞÞjPð@nÞ � ðudeaðx0; y0Þ � uðx0; y0ÞÞjP (9)

In theory, the sampling distribution of u�deaðx0; y0Þ is known but,

in practice, for impossibility of computation it is indispensable touse Monte Carlo simulations. Then, we use Pð@nÞ to generate B

samples, so we have @�n;b of size n with b = 1, . . ., B; consequently,we obtain B pseudo-estimates u

�dea;bðx0; y0Þ and their empirical

distribution provides an approximation of the sampling distribu-tion of u

�deaðx0; y0Þ. Evidently, the quality of the bootstrap procedure

is greater if B and n are big.Furthermore, (if some circumstances are verified) the bootstrap

procedure allows to correct the bias of the DEA estimators. It is

biasðudeaðx0; y0ÞÞ ¼ Eðudeaðx0; y0ÞÞ � uðx0; y0Þ (10)

and, then,

dbiasBðudeaðx0; y0ÞÞ ¼ 1

B

XB

b¼1

u�dea;bðx0; y0Þ � udeaðx0; y0Þ (11)

Consequently, confidence intervals obtained using Efron’spercentile method (the simplest and most straightforwardmethod) should be corrected by subtracting 2 times the estimatedbias from both the lower and upper bounds. Here, the problem isavoided following Simar and Wilson (2000b) by using Hallpercentile intervals based on differences.

4. Results

4.1. Efficiency of the educational systems

The previous sections show that mathematical, reading andscientific literacy of students may vary widely among countries.The reasons may be numerous: different family characteristics,high or low social and economic conditions, presence or absence ofspecific educational policies, and so on.

Therefore, we aim at looking at students’ proficiency in the 24countries taking into account the educational resources availableat home (IAR) and the family background (IFB) also consideringstudent’s gender, school management, school size and communi-ty size. With a high level of educational resources available athome and a good family background, we expect a high students’proficiency and, analogously, we expect low proficiency with pooravailable resources and poor family background (Acemoglu, 2001;Ryan, 1998). In an optimal combination, we could observe highstudents’ ability with low resources and poor background. So, thesuccess of an educational system in a country is as much evident ashigher is the proficiency score with given educational resourcesavailable at home and family background, where the positiveeffect of factors about schools, institutions, etc., explains higherperformances.

We are interested in this measurement, that is, we areinterested in the differences of performance (efficiency) of the

Table 2Efficiency scores, bias and confidence intervals: overall estimates.

Efficiency

rank

Countries Efficiency Bias Inf.

bound

Sup.

bound

1 Czech Republic 0.9742 0.0114 0.9583 0.9838

2 Estonia 0.9736 0.0264 0.9517 0.9983

3 Netherlands 0.9649 0.0108 0.9468 0.9749

4 Finland 0.9640 0.0360 0.9399 0.9987

5 Slovak Republic 0.9604 0.0396 0.9269 0.9982

6 Belgium 0.9562 0.0085 0.9421 0.9636

7 Hungary 0.9532 0.0207 0.9346 0.9726

8 Greece 0.9531 0.0469 0.9129 0.9984

9 Poland 0.9520 0.0480 0.9041 0.9987

10 Romania 0.9497 0.0503 0.9002 0.9984

11 Lithuania 0.9475 0.0222 0.9214 0.9683

12 Ireland 0.9427 0.0207 0.9203 0.9619

13 Slovenia 0.9254 0.0155 0.9064 0.9397

14 Denmark 0.9229 0.0126 0.9035 0.9348

15 Bulgaria 0.9186 0.0243 0.8894 0.9414

16 France 0.9154 0.0176 0.8988 0.9315

17 Germany 0.9128 0.0152 0.8908 0.9268

18 Austria 0.9070 0.0186 0.8866 0.9246

19 Sweden 0.9067 0.0209 0.8819 0.9269

20 Spain 0.9035 0.0150 0.8903 0.9171

21 United Kingdom 0.9035 0.0180 0.8812 0.9202

22 Portugal 0.8987 0.0229 0.8686 0.9202

23 Luxembourg 0.8807 0.0145 0.8630 0.8944

24 Italy 0.8755 0.0173 0.8561 0.8918

Median 0.9341 – – –

Mean 0.9318 – – –


educational systems among the European Union countries. Withthis aim, we use Data Envelopment Analysis (DEA) in a bootstrapapproach12: the two indexes about resources and background (IARand IFB) represent the two inputs, while the proficiency values inmathematics, reading and science are the three output of theeducational system13.

Table 2 and corresponding Fig. 2 present the 24 overallestimates of the efficiency scores (or the performance of the

12 We have chosen the DEA method because it is a multi-outputs and

nonparametric technique that does not need arbitrary hypothesis about the

mathematical form of the relationship between inputs and outputs. But, the classic

DEA is a data-driven approach and the results could deeply depend on the outliers

and extreme values with a prominent bias toward the upper bound. To avoid this

problem, we use the Simar and Wilson DEA-bootstrap version with 2000 Monte

Carlo replications following the homogeneous algorithm of Simar and Wilson

(1998, 2000a, 2000b). In some cases, the bootstrap estimates could be inconsistent

(Beran & Ducharme, 1991; Efron & Tibshirani, 1993), and this is a typical situation

for the naıve bootstrap (Ferrier & Hirschberg, 1997; see the criticism of Simar &

Wilson, 1999). Therefore, Simar and Wilson (1998, 2000b) suggest a homogeneous

and a heterogeneous procedure. The first approach is based on a homogeneity

assumption for the structure of inefficiency, whereas the second approach allows

for possible heterogeneity in the structure of inefficiency. In this paper, we follow

the homogeneous case of the Simar–Wilson method since the homogeneity

conjecture is here credible and the computations do not meet the typical problems

of the heterogeneous bootstrap case. For this matter, we defer to the cited literature.13 The traditional view of the Farrell-efficiency concept corresponds to the

relationship between inputs and outputs usually with reference to micro units, but

the extension to a macro context where territorial areas are the units does not

represent a formal difficulty. In this paper, the units are the 24 countries and the

production process is virtual because we consider the two indexes IAR and IFB as

inputs and the three students’ PV for mathematics, reading and science as outputs.

No specific consideration is made about the adopted technology (considered as

space-invariant) and about returns to scale, assumed here as variable; different

options or other restrictions have a higher level of arbitrariness. Moreover, we have

chosen the output orientation because it is more suitable than input orientation. It

implies the goal of a greater output, i.e. higher students’ proficiency for given inputs

(that is, educational resources at home and family background), under the realistic

assumption that the units, to say the countries, seen as the ensemble of private and

public efforts and policies, are able to exercise a sufficient impact on inputs and

outputs, so the inputs are not conceived as environmental factors but de facto as

explanatory variables.

educational system), the bias of the classical DEA values and theconfidence interval at 95 per cent. A smaller score indicates agreater incapacity of the educational system to obtain higher levelsof students’ proficiency for given educational resources available athome and family background; obviously, the reasons could derivefrom lower investment and lower quality in school facilities,teachers’ training, etc.

It is interesting to note that Italy is in the last positionwith 0.8755, following Luxembourg (0.8807), Portugal (0.8987),Spain and United Kingdom (0.9035): roughly speaking, we cansay that these countries have good inputs and not so goodoutputs.14 At the top, we have Czech Republic with 0.9742,Estonia (0.9736), Netherlands (0.9649) and Finland (0.9640): onthe contrary, these countries have good outputs and not so goodinputs15. Finland get 4th position in the performance rank since,despite the first position for all three proficiencies, it has lessgood positions for the IAR and IFB indexes. Bulgaria andRomania get 10th and 15th positions respectively, since thesecountries present low levels of inputs but also low levels ofoutputs. Other countries, for example Greece and SlovakRepublic, show very bad inputs but intermediate outputs andso the performance score has higher positions (8th and 5threspectively).16

We study in detail the performance by student’s gender, schoolmanagement, school size and community size; correspondingtables and figures are presented in Appendix (Tables A1–A4 andFigs. A1–A4).

About student’s gender, we note that 7 among the first 10positions are occupied by male; on the contrary, the lastpositions are occupied by female. It is interesting to notice thatthe male for Italy is third from the last (0.8790), while Poland isfirst for male but 20th for female. Mostly, the male position isbetter than the female one with some exceptions, for exampleBulgaria (37 male vs. 30 female), Lithuania (21 vs. 15) andSlovenia (28 vs. 23).

Concerning the public or private management, in generalterms, we note that private is better than public; in fact, in thefirst 10 positions we find 7 countries with private management,even if two public are very near to the relative private (Finlandand Estonia). The first position is for private in Greece (0.9840)but its public is 12th, while Luxembourg is in the last positionswith private and public. We note a great distance betweenprivate and public for United Kingdom and Slovenia. Italy,Austria, Slovak Republic and Czech Republic have betterpositions for public.17

About the school size, Czech Republic and Estonia get,respectively, 1st and 2nd positions in large schools (0.9917 and0.9850), but they obtain worse positions in medium andespecially in small schools. The last positions are in the smallsize with Austria (0.8262), Italy (0.8239) and Germany (0.8227).As general rule, students’ performance is higher in large schoolsthan in medium and, so, medium schools are better than smallschools. We note that Germany, Netherlands and Sloveniapresent a great distance among large, medium and smallschools. Italy has low ranks in all the three categories since it

14 Italy is 13th in the IAR ranking and 15th in the IFB ranking, but 21st, 19th and

20th for proficiency in mathematics, reading and science respectively. Luxembourg

gets 6th and 4th positions in inputs but it is 16th in mathematics and reading and

19th in science.15 Czech Republic gets 12th and 17th positions in inputs but it is 6th in

mathematics and 7th in science even if it is 14th in reading.16 The ordered scores and the confidence intervals suggest some interpretative

cautions since sometimes they are wide and overlapping (that is in Romania, Poland

and Greece). But, Italy remains undoubtedly in the last position.17 Data about France and Bulgaria are missing while Romania has only public

management.

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Fig. 2. Efficiency scores and confidence intervals: overall estimates.


get 49th position in large, 64th in medium and 68th in smallschools.18

As to community size, we notice the 1st position of CzechRepublic in city (13th in town and 25th in village) and the 2ndposition of Estonia. The last positions are for Italy (town),Luxembourg (village) and Italy again (village); however, also thescore for the Italian cities is in a bad 60th position. On the whole,the better performance is in cities, then in towns and villages. Onthe contrary, some countries such as Belgium, Romania and UnitedKingdom show better positions in village.

4.2. Heterogeneity and clustering among the EU countries

The efficiency analysis shows some unexpected and interestingresults, for example the first positions of Czech Republic andEstonia or the last positions of some Euro-Mediterraneancountries; in these cases, the combination of different rankingsin inputs and outputs has an important role. So, we have appliedthe cluster analysis on inputs and outputs for a better interpreta-tion of the efficiency scores.19

The first analysis considers the IAR and IFB indexes on theoverall values for the 24 countries.20 With a hierarchical clusteranalysis three groups have been identified (Table 3):

18 We note that information about schools and community size in France is

missing.19 It is known that cluster analysis deals with forming groups of similar objects.

Here, we are interested in forming groups of similar countries, to say with a small

distance respect to the used variables. A popular distance measure based on

continuous variables is the Euclidean metric, and since all the five variables (the two

IAR and IFB indexes and the three skills values) are build in a continuous space, we

prefer to use this metric. At first, we have chosen a hierarchical agglomeration

technique to explore the aggregations of the 24 countries; the aggregation

algorithm is the unweighted pair-group average. In this method, the distance

between two clusters is calculated as the average distance between all the pairs of

objects. This method is recommended when the objects form natural distinct

clumps; however, it performs equally well with elongated chain clusters. Sneath

and Sokal (1973) introduce the abbreviation UPGMA to refer to this method as

unweighted pair-group technique using arithmetic averages.20 The results for student’s gender, private or public management, school size and

community size are similar and they are not worthy of special note.

- group 1 includes four countries (Bulgaria, Greece, Romania andSlovak Republic);

- group 2 includes eight countries (Czech Republic, Estonia,Hungary, Italy, Lithuania, Poland, Portugal and Spain);

- group 3 includes twelve countries (Austria, Belgium, Denmark,Finland, France, Germany, Ireland, Luxemburg, Netherland,Slovenia, Sweden and United Kingdom).

Consequently a non-hierarchical cluster analysis has beenapplied using the k-means method choosing a classification intothree groups of countries. The clusters obtained are perfectlycoincident with those identified from the previous hierarchicaltechnique.21

The second cluster analysis has been applied on the competen-cies values in mathematics, reading and science always on theoverall values for the 24 countries. With a hierarchical method,countries are grouped according to four clusters (see Table 3again):

- group 1 includes two countries (Bulgaria and Romania);- group 2 includes seven countries (Greece, Italy, Lithuania,

Luxemburg, Portugal, Slovak Republic and Spain);- group 3, the largest one, it is formed by fourteen countries

(Austria, Belgium, Czech Republic, Denmark, Estonia, France,Germany, Hungary, Ireland, Netherlands, Poland, Slovenia,Sweden and United Kingdom);

- group 4 includes Finland only.

21 Cluster 3 has the highest average values of the two IAR and IFB indexes,

followed by cluster 2. The distances between clusters shows that the groups more

distant from each other are the first and the third while the most similar are the

second and the third one. Concerning the distances between each country and the

respective cluster centre, for cluster 3 we note that the countries further from the

centre are Sweden and France, while less distant are Netherlands and United

Kingdom. For cluster 2 the furthest country is Poland, while Estonia is the least

distant country. Finally, for cluster 1, the furthest country is Greece and the least is

Bulgaria.

Table 3Clusters analysis: overall results.

Inputs Outputs

Clusters Countries Centroids Clusters Countries Centroids

Cluster 1 Bulgaria IAR 5.88 Cluster 1 Bulgaria MATH 414.12

Low values Greece IFB 4.83 Low values Romania READ 398.93

Romania SCIEN 426.23

Slovak Republic Cluster 2 Greece MATH 476.51

Cluster 2 Czech Republic IAR 6.78 Medium-low values Italy READ 468.17

Medium values Estonia IFB 5.31 Lithuania SCIEN 482.03

Hungary Luxembourg

Italy Portugal

Lithuania Slovak Republic

Poland Spain

Portugal Austria

Spain Cluster 3 Belgium MATH 504.38

Cluster 3 Austria IAR 7.07 Medium-high values Czech Republic READ 497.33

High values Belgium IFB 6.52 Denmark SCIEN 510.29

Denmark Estonia

Finland France

France Germany

Germany Hungary

Ireland Ireland

Luxembourg Netherlands

Netherlands Poland

Slovenia Slovenia

Sweden Sweden

United Kingdom United Kingdom

Cluster 4 Finland MATH 548.36

High values READ 546.87

SCIEN 563.32


This result is confirmed by a non-hierarchical clustering (k-means).22

From these analyses it emerges a high level of heterogeneity forthe European Union countries. Wide differences are present bothwith reference to the IAR and IFB indexes and with reference to thethree competencies. In particular, Bulgaria and Romania show theworst scenario, while Italy Spain, Portugal and Lithuania are in anintermediate position. The best results are in many NorthernEuropean Union countries (i.e. Finland, Denmark, Ireland andSweden).

Luxembourg belongs to the group with the highest values ofboth indexes, but it belongs to the group with medium-low valuesin competencies; this explains the second position from the end inthe ranking of the efficiency scores. Czech Republic and Estonia arein the group with medium values for inputs, but they belong to thegroup with medium-high values of competencies obtaining thehighest efficiency scores.

Among the countries in intermediate position in the ranking ofefficiency scores, we note that Romania and Bulgaria, 10th and15th respectively, belong to the clusters with low values both forinputs and for outputs. Instead, France, Germany, Austria, Swedenand United Kingdom belong to the groups with high inputs andmedium-high outputs obtaining an efficiency score lower thanRomania and Bulgaria.

22 As regards the average scores for each cluster, the highest values of the three

competencies are in cluster 4. This cluster includes only Finland that represent a

‘‘peak of excellence’’. Clusters 3 and 2 follow. Cluster 1, composed by Romania and

Bulgaria, has the lowest average values for all the competencies. Obviously the

distance is greater between cluster 1 and cluster 4 which are, as mentioned above,

those with the lowest and highest average values respectively. Instead, the clusters

with minimum distance are the no.2 and no.3. About distances between each

country and the respective cluster centre, for cluster 2 we note that the furthest

country from the centre is Greece, while the least is Spain. For cluster 3, Netherland

is the furthest country while Germany is the least distant.

5. Conclusion

In this paper it emerges an interesting differentiation amongthe European Union countries about the efficiency scores of theeducational systems. In particular, we have run a DEA-bootstrapanalysis where the educational resources available at home andthe family background of students are inputs in a virtual processwith proficiency values in mathematics, reading and science asoutputs. The analysis is carried out in a macro context because theresults could be useful for national policy. In fact, it is appropriateto compare students’ abilities contextualizing the PISA valuesunder the students’ conditions about the educational resourcesavailable at home and the family background. The DEA score variesfrom 0 to 1 in relation to the capability of the educational system toobtain a higher level in students’ proficiency for given resources athome and family background. Thus, the greater ability of thisprocess to transform inputs to outputs, i.e. greater efficiency,shows a better educational system, benchmark for those nationswhere efficiency is lower.

Italy has the lowest efficiency score while the best performanceis in Czech Republic. It is interesting to note the bad positioning ofSpain (20th), United Kingdom (21st), Portugal (22nd) andLuxembourg (23rd), while Estonia, Netherlands, Finland andSlovak Republic get into the top of ranking (2nd, 3rd, 4th and5th respectively). In general terms, the Euro-Mediterraneancountries show worse positions than the Northern ones; thisresult is confirmed subdividing the data by some specificcharacteristics (student’s gender, private or public management,school size and community size).

About student’s gender, the male position is generally betterthan the female one and, with regard to the school management,private is better than public. The efficiency is higher in largeschools than in medium schools and, similarly, medium schoolsare better than small schools. Finally, about the community size,the best efficiency is in cities, then in towns and villages. In


particular, we note again Czech Republic and Estonia in the firstpositions, on the contrary Italy and Luxembourg get into the lastpositions.

These differences among the European Union countriesdemand to identify an interpretative framework to searchpossible common paths and so to realize the reasons of thisheterogeneity. Cluster analysis on the IAR and IFB indexes hasdetected three groups of countries with low, medium and highvalues. Cluster analysis on the three competencies scoresdetermines four groups with low, medium-low, medium-highand high values. The cluster with highest values includes justFinland, which is a peak of excellence. These results appearstatistically robust since the groups obtained with the hierarchi-cal analysis coincide with the groups obtained through the non-hierarchical analysis. Therefore, cluster analysis about the IARand IFB indexes and the competency values generates differentgroupings and, then, it is useful to explain the intermediatepositions come out from the efficiency ranking. In fact, we note bothcountries with low values of inputs (IAR and IFB indexes) and lowvalues of outputs (the three competencies), i.e. Romania andBulgaria, and countries with high values of inputs and high values ofoutputs. However, among these latter, five countries have worsepositions in the efficiency ranking respect to Romania and Bulgaria:France, Germany, Austria, Sweden and United Kingdom.

Italy is always around the last positions in the performanceranking of the educational systems. The reasons could derive fromthe critical state of the national economic and social system, forexample lower investment and lower quality in school facilities,teachers’ training or, generally speaking, an unfavorable economic

Appendix

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Fig. A1. Efficiency scores and confide

and social context. Mostly, the more industrialized and developedcountries should have better educational resources available athome and better family background and also higher students’proficiency in mathematics, reading and science. Nevertheless, thisdoes not always happen in the European Union countries: theperformance of the educational system certainly depends on thequantity but above all on the quality of the economic and socialdevelopment of a country and, therefore, how the economicresources are used. For example, in Italy the middle and highschools often have poor facilities, especially in the Southern areas,and it is well-known that Italian schools give scarce attention toforeign languages and scientific subjects, while most economicresources are absorbed by unproductive expenditures (i.e.teachers’ salaries).

This paper has used PISA data, but another analysis can be doneon IEA data (TIMSS and PIRLS) to verify if the findings aboutdisparities of the educational systems among some EU countriesare confirmed at different educational grades and different skillsareas. Although study goals, target population, participatingcountries and sampling design do not coincide with PISA survey,there are significant overlapping areas and, therefore, thecomparison is interesting. The use of IEA surveys could be usefulto confirm the efficiency ranking and, in case, to seek more detailedexplanations about the countries positioning. Moreover, furtherresearch could choose few specific countries with high dataavailability (Italy is a good example) to focus on some contextvariables and, thus, to connect explicitly the efficiency scores to, i.e.teachers’ skills, educational facilities in schools or socio-economicindicators.

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1,00

Fig. A3. Efficiency scores and confidence intervals: school size.


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Fig. A4. Efficiency scores and confidence intervals: community size.

Table A1Efficiency scores, bias and confidence intervals: student’s gender.

Efficiency rank Gender Countries Efficiency Bias Inf. bound Sup. bound

1 Male Poland 0.9795 0.0205 0.9503 0.9985

2 Male Czech Republic 0.9769 0.0078 0.9666 0.9837

3 Male Estonia 0.9750 0.0154 0.9592 0.9892

4 Male Greece 0.9719 0.0281 0.9420 0.9983

5 Female Estonia 0.9714 0.0286 0.9514 0.9984

6 Male Finland 0.9695 0.0305 0.9516 0.9987

7 Male Slovak Republic 0.9674 0.0326 0.9404 0.9985

8 Female Finland 0.9668 0.0332 0.9429 0.9985

9 Female Slovak Republic 0.9647 0.0353 0.9377 0.9987

10 Male Netherlands 0.9623 0.0111 0.9485 0.9724

11 Male Hungary 0.9603 0.0141 0.9461 0.9730

12 Female Czech Republic 0.9601 0.0134 0.9440 0.9722

13 Female Netherlands 0.9575 0.0089 0.9473 0.9652

14 Female Belgium 0.9540 0.0084 0.9430 0.9607

15 Female Lithuania 0.9534 0.0222 0.9284 0.9740

16 Male Romania 0.9524 0.0321 0.9111 0.9830

17 Male Belgium 0.9516 0.0075 0.9410 0.9583

18 Female Greece 0.9512 0.0488 0.9110 0.9983

19 Female Hungary 0.9507 0.0189 0.9345 0.9680

20 Female Poland 0.9460 0.0540 0.8996 0.9983

21 Male Lithuania 0.9443 0.0157 0.9242 0.9587

22 Female Romania 0.9436 0.0564 0.8987 0.9982

23 Female Slovenia 0.9301 0.0159 0.9121 0.9445

24 Female Ireland 0.9278 0.0207 0.9040 0.9474

25 Male Ireland 0.9249 0.0168 0.9101 0.9407

26 Male Denmark 0.9243 0.0106 0.9095 0.9345

27 Male Germany 0.9235 0.0119 0.9106 0.9343

28 Male Slovenia 0.9229 0.0105 0.9119 0.9322

29 Male Austria 0.9213 0.0147 0.9051 0.9351

30 Female Bulgaria 0.9192 0.0194 0.8967 0.9371

31 Female France 0.9166 0.0129 0.9045 0.9283

32 Female Denmark 0.9150 0.0121 0.9003 0.9256

33 Male France 0.9132 0.0166 0.8975 0.9280

34 Male United Kingdom 0.9120 0.0138 0.8952 0.9242

35 Male Portugal 0.9117 0.0116 0.8975 0.9220

36 Female Sweden 0.9086 0.0219 0.8820 0.9292


Table A2Efficiency scores, bias and confidence intervals: school management.

Efficiency rank Management Countries Efficiency Bias Inf. bound Sup. bound

1 Private Greece 0.9840 0.0160 0.9686 0.9967

2 Public Finland 0.9731 0.0136 0.9583 0.9846

3 Private Finland 0.9697 0.0152 0.9544 0.9825

4 Private United Kingdom 0.9584 0.0226 0.9340 0.9792

5 Private Estonia 0.9534 0.0226 0.9349 0.9731

6 Public Estonia 0.9490 0.0263 0.9232 0.9724

7 Public Slovak Republic 0.9462 0.0538 0.9052 0.9969

8 Private Poland 0.9432 0.0232 0.9218 0.9636

9 Private Lithuania 0.9407 0.0593 0.9078 0.9970

10 Private Ireland 0.9396 0.0107 0.9271 0.9485

11 Public Hungary 0.9321 0.0234 0.9092 0.9528

12 Public Greece 0.9297 0.0703 0.8781 0.9964

13 Public Ireland 0.9281 0.0167 0.9114 0.9424

14 Private Slovenia 0.9278 0.0452 0.8856 0.9716

15 Private Slovak Republic 0.9277 0.0230 0.9034 0.9482

16 Private Hungary 0.9244 0.0152 0.9096 0.9368

17 Public Poland 0.9193 0.0807 0.8735 0.9962

18 Public Czech Republic 0.9188 0.0227 0.8979 0.9383

19 Public Lithuania 0.9152 0.0337 0.8837 0.9460

20 Public Romania 0.9150 0.0850 0.8589 0.9971

21 Private Sweden 0.9142 0.0132 0.8958 0.9260

22 Public Sweden 0.8993 0.0102 0.8873 0.9081

23 Private Germany 0.8956 0.0202 0.8753 0.9135

24 Private Portugal 0.8926 0.0176 0.8746 0.9075

25 Public Netherlands 0.8822 0.0174 0.8641 0.8969

26 Private Czech Republic 0.8806 0.0233 0.8626 0.9007

27 Private Netherlands 0.8804 0.0202 0.8624 0.8977

28 Public Portugal 0.8689 0.0367 0.8322 0.9032

29 Private Belgium 0.8675 0.0255 0.8483 0.8905

30 Public Austria 0.8622 0.0165 0.8460 0.8761

31 Public Spain 0.8592 0.0252 0.8387 0.8817

32 Public Italy 0.8548 0.0169 0.8371 0.8691

33 Public United Kingdom 0.8527 0.0139 0.8372 0.8647

34 Private Spain 0.8522 0.0183 0.8365 0.8678

35 Public Denmark 0.8457 0.0159 0.8275 0.8596

36 Private Denmark 0.8438 0.0228 0.8234 0.8644

37 Public Belgium 0.8411 0.0196 0.8258 0.8585

38 Public Germany 0.8404 0.0197 0.8228 0.8577

39 Private Austria 0.8395 0.0207 0.8225 0.8577

40 Public Slovenia 0.8355 0.0289 0.8166 0.8621

41 Private Italy 0.8334 0.0090 0.8233 0.8405

42 Public Luxembourg 0.8298 0.0138 0.8141 0.8417

43 Private Luxembourg 0.8291 0.0096 0.8184 0.8364

Table A1 (Continued )

Efficiency rank Gender Countries Efficiency Bias Inf. bound Sup. bound

37 Male Bulgaria 0.9068 0.0212 0.8805 0.9266

38 Male Spain 0.9046 0.0151 0.8923 0.9181

39 Male Sweden 0.9015 0.0137 0.8877 0.9141

40 Female Germany 0.9013 0.0161 0.8788 0.9163

41 Female Spain 0.8945 0.0131 0.8819 0.9063

42 Female United Kingdom 0.8931 0.0175 0.8725 0.9091

43 Female Austria 0.8920 0.0191 0.8714 0.9101

44 Female Portugal 0.8911 0.0243 0.8632 0.9141

45 Male Luxembourg 0.8864 0.0124 0.8728 0.8981

46 Male Italy 0.8790 0.0089 0.8703 0.8866

47 Female Luxembourg 0.8762 0.0118 0.8593 0.8869

48 Female Italy 0.8734 0.0194 0.8532 0.8913

Table A3Efficiency scores, bias and confidence intervals: school size.

Efficiency rank School Countries Efficiency Bias Inf. bound Sup. bound

1 Large Czech Republic 0.9917 0.0076 0.9837 0.9977

2 Large Estonia 0.9850 0.0150 0.9746 0.9981

3 Medium Slovak Republic 0.9832 0.0168 0.9637 0.9983

4 Large Netherlands 0.9807 0.0193 0.9674 0.9981

5 Medium Greece 0.9795 0.0164 0.9615 0.9938

6 Medium Finland 0.9792 0.0208 0.9616 0.9981

7 Small Greece 0.9786 0.0214 0.9560 0.9977



Efficiency rank School Countries Efficiency Bias Inf. bound Sup. bound

8 Large Slovak Republic 0.9768 0.0170 0.9579 0.9921

9 Medium Estonia 0.9768 0.0173 0.9610 0.9921

10 Large Germany 0.9720 0.0143 0.9571 0.9847

11 Large Finland 0.9717 0.0283 0.9531 0.9980

12 Large Poland 0.9710 0.0290 0.9427 0.9974

13 Large Slovenia 0.9676 0.0125 0.9531 0.9782

14 Small Finland 0.9675 0.0197 0.9496 0.9860

15 Large Greece 0.9675 0.0152 0.9530 0.9801

16 Medium Czech Republic 0.9663 0.0074 0.9580 0.9724

17 Large Belgium 0.9644 0.0120 0.9525 0.9740

18 Medium Poland 0.9644 0.0356 0.9237 0.9977

19 Small Estonia 0.9621 0.0379 0.9421 0.9978

20 Small Slovak Republic 0.9620 0.0187 0.9419 0.9792

21 Large Lithuania 0.9609 0.0085 0.9510 0.9675

22 Small Poland 0.9556 0.0444 0.9131 0.9979

23 Small Lithuania 0.9520 0.0265 0.9307 0.9761

24 Medium Romania 0.9520 0.0480 0.8965 0.9979

25 Large Ireland 0.9512 0.0143 0.9357 0.9642

26 Large Hungary 0.9455 0.0156 0.9340 0.9590

27 Large Austria 0.9430 0.0152 0.9297 0.9563

28 Medium Lithuania 0.9427 0.0215 0.9226 0.9615

29 Medium Netherlands 0.9402 0.0114 0.9296 0.9495

30 Medium Ireland 0.9400 0.0172 0.9275 0.9551

31 Medium Belgium 0.9377 0.0096 0.9284 0.9456

32 Small Bulgaria 0.9307 0.0693 0.8624 0.9977

33 Small Romania 0.9294 0.0706 0.8633 0.9981

34 Large Sweden 0.9267 0.0117 0.9086 0.9375

35 Small Ireland 0.9245 0.0147 0.9126 0.9372

36 Large Denmark 0.9177 0.0116 0.9035 0.9275

37 Large Portugal 0.9166 0.0163 0.9010 0.9310

38 Medium Hungary 0.9111 0.0179 0.8962 0.9271

39 Medium Luxembourg 0.9093 0.0106 0.8973 0.9184

40 Large Spain 0.9080 0.0091 0.9000 0.9152

41 Large United Kingdom 0.9072 0.0156 0.8912 0.9217

42 Medium Slovenia 0.9070 0.0099 0.8980 0.9146

43 Small Czech Republic 0.9068 0.0135 0.8931 0.9183

44 Medium Denmark 0.9060 0.0116 0.8928 0.9158

45 Small Hungary 0.9058 0.0157 0.8902 0.9197

46 Small Denmark 0.9031 0.0128 0.8884 0.9145

47 Medium United Kingdom 0.8991 0.0138 0.8839 0.9111

48 Large Romania 0.8974 0.0219 0.8783 0.9173

49 Large Italy 0.8972 0.0147 0.8854 0.9099

50 Small Spain 0.8950 0.0106 0.8857 0.9036

51 Medium Spain 0.8943 0.0095 0.8854 0.9021

52 Small United Kingdom 0.8932 0.0141 0.8792 0.9052

53 Small Sweden 0.8931 0.0153 0.8765 0.9066

54 Medium Sweden 0.8903 0.0169 0.8730 0.9063

55 Medium Portugal 0.8775 0.0160 0.8573 0.8918

56 Small Netherlands 0.8753 0.0106 0.8653 0.8840

57 Medium Germany 0.8709 0.0108 0.8616 0.8795

58 Medium Austria 0.8683 0.0124 0.8577 0.8788

59 Small Belgium 0.8666 0.0105 0.8577 0.8751

60 Large Bulgaria 0.8660 0.0211 0.8490 0.8853

61 Large Luxembourg 0.8641 0.0100 0.8549 0.8722

62 Small Portugal 0.8598 0.0226 0.8314 0.8804

63 Small Luxembourg 0.8597 0.0134 0.8459 0.8719

64 Medium Italy 0.8543 0.0106 0.8445 0.8631

65 Small Slovenia 0.8469 0.0085 0.8403 0.8535

66 Medium Bulgaria 0.8449 0.0189 0.8240 0.8621

67 Small Austria 0.8262 0.0151 0.8118 0.8395

68 Small Italy 0.8239 0.0116 0.8147 0.8333

69 Small Germany 0.8227 0.0099 0.8140 0.8306

Table A4Efficiency scores, bias and confidence intervals: community size.

Efficiency rank Community Countries Efficiency Bias Inf. bound Sup. bound

1 City Czech Republic 0.9893 0.0107 0.9825 0.9986

2 City Estonia 0.9870 0.0130 0.9784 0.9983

3 City Slovak Republic 0.9854 0.0146 0.9742 0.9982

4 City Greece 0.9853 0.0146 0.9669 0.9985

5 Town Slovak Republic 0.9835 0.0164 0.9671 0.9980

6 Town Estonia 0.9814 0.0143 0.9681 0.9938

7 Village Greece 0.9800 0.0195 0.9576 0.9981



Efficiency rank Community Countries Efficiency Bias Inf. bound Sup. bound

8 Village Finland 0.9796 0.0204 0.9593 0.9984

9 Town Finland 0.9781 0.0219 0.9588 0.9986

10 Town Lithuania 0.9780 0.0127 0.9647 0.9890

11 Village Estonia 0.9749 0.0251 0.9602 0.9984

12 City Finland 0.9731 0.0269 0.9523 0.9982

13 Town Czech Republic 0.9708 0.0090 0.9618 0.9784

14 Town Netherlands 0.9706 0.0062 0.9629 0.9760

15 City Poland 0.9705 0.0295 0.9436 0.9984

16 Village Belgium 0.9703 0.0053 0.9633 0.9748

17 Village Slovak Republic 0.9690 0.0310 0.9450 0.9983

18 City Netherlands 0.9689 0.0080 0.9591 0.9758

19 Town Poland 0.9658 0.0286 0.9321 0.9927

20 Town Belgium 0.9615 0.0054 0.9547 0.9661

21 City Lithuania 0.9572 0.0099 0.9483 0.9655

22 Town Greece 0.9554 0.0173 0.9348 0.9715

23 Town Hungary 0.9540 0.0146 0.9420 0.9672

24 Village Lithuania 0.9527 0.0162 0.9340 0.9671

25 Village Czech Republic 0.9523 0.0089 0.9434 0.9599

26 Village Poland 0.9496 0.0504 0.9134 0.9985

27 Village Romania 0.9440 0.0560 0.8907 0.9984

28 City Denmark 0.9428 0.0072 0.9328 0.9495

29 City Hungary 0.9411 0.0143 0.9277 0.9535

30 Village Ireland 0.9390 0.0144 0.9231 0.9519

31 Village Hungary 0.9385 0.0123 0.9259 0.9491

32 City Ireland 0.9383 0.0153 0.9219 0.9521

33 City Slovenia 0.9374 0.0108 0.9246 0.9466

34 Village Netherlands 0.9366 0.0079 0.9289 0.9427

35 Town Romania 0.9345 0.0242 0.9072 0.9574

36 Town Ireland 0.9331 0.0145 0.9151 0.9463

37 City Austria 0.9325 0.0093 0.9224 0.9406

38 Town Denmark 0.9319 0.0058 0.9233 0.9373

39 Town Germany 0.9300 0.0100 0.9166 0.9389

40 Town Austria 0.9236 0.0090 0.9127 0.9319

41 Village United Kingdom 0.9217 0.0138 0.9022 0.9347

42 Village Slovenia 0.9215 0.0077 0.9149 0.9280

43 Village Denmark 0.9214 0.0064 0.9125 0.9274

44 Town Slovenia 0.9211 0.0092 0.9113 0.9290

45 City Sweden 0.9189 0.0125 0.9041 0.9299

46 City Luxembourg 0.9153 0.0059 0.9072 0.9207

47 City Germany 0.9137 0.0082 0.9048 0.9206

48 City Belgium 0.9116 0.0078 0.9054 0.9179

49 Village Sweden 0.9110 0.0144 0.8926 0.9245

50 City Spain 0.9109 0.0086 0.9033 0.9183

51 City Portugal 0.9100 0.0167 0.8935 0.9255

52 Village Spain 0.9060 0.0099 0.8972 0.9147

53 Village Bulgaria 0.9056 0.0264 0.8722 0.9307

54 Town Portugal 0.9042 0.0136 0.8865 0.9162

55 Town Sweden 0.9034 0.0147 0.8865 0.9169

56 Village Germany 0.8990 0.0088 0.8857 0.9068

57 City Romania 0.8988 0.0149 0.8804 0.9126

58 Town Spain 0.8975 0.0090 0.8893 0.9051

59 City United Kingdom 0.8974 0.0121 0.8871 0.9083

60 City Italy 0.8965 0.0126 0.8851 0.9071

61 Town United Kingdom 0.8963 0.0153 0.8785 0.9106

62 Village Austria 0.8952 0.0131 0.8804 0.9071

63 Town Luxembourg 0.8949 0.0082 0.8849 0.9024

64 Village Portugal 0.8934 0.0249 0.8675 0.9168

65 Town Bulgaria 0.8926 0.0116 0.8794 0.9030

66 City Bulgaria 0.8860 0.0124 0.8750 0.8968

67 Town Italy 0.8778 0.0140 0.8648 0.8904

68 Village Luxembourg 0.8631 0.0071 0.8561 0.8689

69 Village Italy 0.8317 0.0141 0.8211 0.8442


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Educational systems efficiency in European Union countries

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