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Empirical Assessment and Comparison of Educational Efficiency between Major Countries across the World.

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  • Hanjiang Normal University

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Education is a fundamental factor to enhance a country's comprehensive national strength and international competitiveness. Recently, several governments have been attracting investments in educational sectors in contemplation of meliorating a country's overall strength. This study empirically assesses and compares the educational efficiency of 29 major countries across the world using panel data for 2010-2016 by employing data envelopment analysis (DEA) and the super-slacks-based measure (super-SBM) model at the static level combined with the Malmquist index (MI) to investigate educational efficiency at the dynamic level. The results indicate , inter alia, huge average education efficiency differences existed among the studied countries, the highest being Japan (3.2845) and lowest Norway (0.4137), there are differences in the bias of technological progress among the studied countries during the sample period and technological progress directly affects the sustainability of educational efficiency, the growth rate of total factor productivity (TFP) index has been reduced in 2010-2013 but increased in 2014-2016 and technological progress has been the dominant factor influencing the rise of the education TFP index. Based on the results, this study identifies the merits and drawbacks of education efficiency across the sample countries and presents relevant recommendations to promote investment in the education sector and human capital.
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Research Center of Open Economy
Working Paper
WP/22/001
Hubei University
Wuhan / China
Empirical Assessment and Comparison of Educational Efficiency between
Major Countries across the World
Lipeng Chen 1,2,#, Yang Yu 3,*,#, Amsalu K. Addis 1,2 and Xiao Guo 3
1 Research Center of Open Economy, Hubei University, Wuhan 430062, China; lpchen07@163.com (L.C.);
amy.kid370@gmail.com (A.K.A.)
2 School of Business, Hubei University, Youyi Avenue, Wuchang District No. 368, Wuhan 430062, China;
3 School of Education, Hubei University, Wuhan 430062, China; 18506152013@163.com
* Correspondence: yuyang20140037@126.com; Tel.: +86-13018093236
# These authors contributed equally to this work
Forthcoming: Sustainability
March 2022
2 of 18
Research Center of Open Economy WP/22/001
Empirical Assessment and Comparison of Educational
Efficiency between Major Countries across the World
Lipeng Chen 1,2,#, Yang Yu 3,*,#, Amsalu K. Addis 1,2 and Xiao Guo 3
1 Research Center of Open Economy, Hubei University, Wuhan 430062, China; lpchen07@163.com (L.C.);
amy.kid370@gmail.com (A.K.A.)
2 School of Business, Hubei University, Youyi Avenue, Wuchang District No. 368, Wuhan 430062, China;
3 School of Education, Hubei University, Wuhan 430062, China; 18506152013@163.com
* Correspondence: yuyang20140037@126.com; Tel.: +86-13018093236
# These authors contributed equally to this work
Abstract: Education is a fundamental factor to enhance a country’s comprehensive national
strength and international competitiveness. Recently, several governments have been attracting
investments in educational sectors in contemplation of meliorating a country’s overall strength.
This study empirically assesses and compares the educational efficiency of 29 major countries
across the world using panel data for 20102016 by employing data envelopment analysis (DEA)
and the super-slacks-based measure (super-SBM) model at the static level combined with the
Malmquist index (MI) to investigate educational efficiency at the dynamic level. The results indi-
cate, inter alia, huge average education efficiency differences existed among the studied countries,
the highest being Japan (3.2845) and lowest Norway (0.4137), there are differences in the bias of
technological progress among the studied countries during the sample period and technological
progress directly affects the sustainability of educational efficiency, the growth rate of total factor
productivity (TFP) index has been reduced in 20102013 but increased in 20142016 and techno-
logical progress has been the dominant factor influencing the rise of the education TFP index.
Based on the results, this study identifies the merits and drawbacks of education efficiency across
the sample countries and presents relevant recommendations to promote investment in the educa-
tion sector and human capital.
Keywords: Educational efficiency; Super-SBM model; Malmquist index; Total factor productivity
(TFP) index; Data envelopment analysis (DEA)
1. Introduction
Since the turn of the 21st century, international competition has become increasingly
fierce, and the key to their competition is the burgeoning of science and technology,
which is also a comprehensive national strength. The competition of science and tech-
nology across the world depends on the number of talented human capital, and the
training of talents is based on an efficient education system. Arguably, for all intents and
purposes education is one of the primary factors of development. No country across the
globe can achieve sustainable economic development and improve national strength
without substantial investment in human capital [14]. Hence, education is commonly
assumed to be the fundamental factor to enhance a country’s comprehensive national
strength and nourish international competitiveness, but to date, the evidence for this
assumption has been surprisingly weak. In addition, in recent years, many governments
have been increasing funding and incentivizing domestic and foreign investments in
educational sectors in a bid to improve a country’s comprehensive strength by improving
the level of education. However, does high investment input convey high output?
With the increasing investment in educational sectors, many countries are facing the
mismatch between education demand and education resource supply to varying degrees
[5,6]. Should countries necessitate investing more in education to promote economic
3 of 18
growth and sustainable development? How to boost the quality of educational invest-
ment and the level of educational efficiency in order to realize the significance of educa-
tion for sustainable development has become a hot issue [1,79]. Undoubtedly, clarifying
these problems has very important theoretical and practical significance for the future
direction of educational development in various countries. Therefore, this paper attempts
to present the nonparametric data envelopment analysis (DEA) method from the per-
spective of international comparison and examine educational development sustainabil-
ity by employing the data obtained from the World Bank education statistics-all indica-
tors database, the United Nations Educational, Scientific and Cultural Organization
(UNESCO) education database, and the OECD education and patents statistical database.
This paper analyzes and compares 29 major countries with different development levels,
and studies their current situation of educational efficiency.
“Educational efficiency” is a compound concept, which first appeared in the book
titled, Equality of Educational Opportunity by Coleman [10]. Since it was put forward,
countless scholars have conducted in-depth and extensive discussion and research on the
connotation and extension of the concept [4,11]. The international comparison of educa-
tional efficiency has always been a less concerning issue in educational academia; thus
little work has been done on this matter. Most scholars’ research on educational effi-
ciency mainly includes two aspects, such as research methods and research objects. (i)
From the perspective of research methods, several scholars mainly focused on quantita-
tive analysis and mostly combined it with the use of the production function model.
Nowadays, the most widely used analysis methods include stochastic frontier analysis
(SFA) of parametric methods, Solow residual analysis (SRA), and data envelopment
analysis (DEA) of nonparametric methods. For instance, Titus and Eagan [12] measured
the production efficiency of American higher education by using the SFA method and
put forward countermeasures and suggestions for the application of the SFA model in
higher education. Additionally, Rządziński and Sworowska [13] evaluated the efficiency
of 27 higher vocational colleges in Poland based on SFA and DEA methods. They believe
that the size and scale of teaching may influence the efficiency of school educational ac-
tivities, and recommended that the DEA-VRS model should be applied for the efficiency
evaluation of higher education institutions. Similarly, Izadi, Johnes, Oskrochi, and Crouch-
ley [14] used stochastic frontier analysis to estimate the cost efficiency of British universi-
ties and Johnes [15] illustrates the application of the DEA method in the field of higher
education technical and scale efficiency in England. Besides, Sibiano and Agasisti [16,17]
used the DEA analysis method to examine educational efficiency brought by educational
input and output in different regions of Italian junior middle school and put forward
solutions accordingly. (ii) From the perspective of research objects, scholars have also
studied educational efficiency, for instance, Dincă, Dincă, Andronic, and Pasztori [18] em-
ployed the mathematical approach of DEA to compare the educational efficiency of 28
EU countries and concluded that the educational efficiency of the old member states was
generally higher than that of the new member states. Likewise, Xu and Liu [4] also used
the DEA method to explore and compare the relationship between education efficiency
and national development in major international countries from two aspects of educa-
tion, input and output. Additionally, Johes and Yu [19] evaluated the inputoutput effi-
ciency of scientific research of higher education institutions in China and concluded that
comprehensive universities consistently outperform specialist institutions and the level
of efficiency depends on subjective measures of research output. Moreover, Guccio,
Martorana, and Monaco [20] evaluated the impact of Italian university reform on educa-
tional efficiency by employing bootstrapped DEA algorithms and indicated that univer-
sities have become more efficient progressively. Başkaya and Klumpp [21] also compared
the different educational efficiency of public universities and private universities in
Germany by calculating the efficiency of input and output of education. In a like manner,
Yalçin and Tavsancil [22] studied the efficiency of educational inputoutput of some
schools in Turkey and conclude that quality differences among schools are prominent
4 of 18
due to limited off-campus study. Al-Bagoury [23] analyzed the efficiency of educational
inputoutput of higher education institutions in 15 African countries and their environ-
mental influences. However, these studies have been limited on the inputoutput effi-
ciency of education and lack extensive education quality assessments that are compara-
ble.
Furthermore, we can understand that, first, the existing literature mostly used
quantitative analysis for the research of educational efficiency, mainly based on the tra-
ditional DEA static model, and lacks in-depth investigation of the efficiency of the dy-
namic DEA model. Second, most of the previous literature that studied educational effi-
ciency focused on the research of higher education institutions’ efficiency, and the per-
spective of analysis on the overall educational efficiency is fewer. Third, the existing lit-
erature focused on the domestic or regional level and there is little literature on the in-
ternational comparison and assessment of educational efficiency. Fourth, while examin-
ing the educational efficiency index, only a few studies took the sustainable development
of education into consideration. Therefore, this paper attempts to assess, analyze, and
compare the overall education efficiency and sustainability of major countries across the
world through the super-slacks-based measure (super-SBM) model combined with the
Malmquist total factor productivity (TFP) index, based on the national-level panel data of
29 countries from 2010 to 2016, aiming to clarify the overall educational efficiency level,
compare and analyze the education development status of various countries, suggest a
reasonable allocation of educational resources, and contribute to the academic research.
2. Materials and Methods
The contribution of this study mainly focuses on measuring, analyzing, and com-
paring the efficiency of education and technology among international countries in the
given sample period using the DEA model. The evaluation of education and technology
efficiency can foreground the effective utilization of budget and resources. In addition to
human capital growth, efficient education in a given country has a prominent effect on
economic development [18,24]. Therefore, it is reasonable to evaluate the efficiency of
education and technology.
Due to the integrity and availability of data, the sample period of this paper is se-
lected from 2010 to 2016. After excluding countries with less education input and output
data, this study selected 29 sample countries across the world and classified them into
two, developing economy and developed economy, based on the UN economic classifi-
cation (See Table 1). The selection criteria of these sample countries are, inter alia, these
countries are recognized as the world’s largest economies, high education expenditure,
and little work has been done on the comparative perspective. The total education ex-
penditure, per capita education expenditure, and the proportion of education expendi-
ture in GDP of these countries are distributed at all levels, with obvious differences.
Furthermore, from the perspective of geographical location, these 29 countries are dis-
tributed in all regions of the world’s five continents and have good geographical repre-
sentation. From the perspective of the education economy, the economic volume of the
sample countries accounted for 79.72% of the world’s total economic volume in 2021
(calculated according to the World Bank’s GDP data in 2020). Therefore, it is conducive
to providing a good sample in data quality.
There are some limitations of the study. In the traditional measurement of produc-
tivity, there are often capital input and labor input. Due to the inability to obtain the
human capital input of various countries in education such as the efficiency of teaching
staff and graduation rate of students, and some countries' index statistics quality is not
thoroughly consistent; thus, this paper primarily uses the data of capital input in the in-
putoutput index system of educational efficiency, which could be the main defect of this
paper and could be an indication for future research.
Table 1. Sample countries and classifications.
5 of 18
Continents
Countries
Developed
Developing
OECD
Non-OECD
Africa
South Africa
America
Argentina
Brazil
Canada
Chile
Costa Rica
Mexico
United States
Asia
China
Japan
Israel
Australia
Australia
Eurasia
Russia
Europe
Austria
Czech Republic
Finland
France
Germany
Hungary
Ireland
Italy
Norway
Poland
Portugal
Slovak Republic
Spain
Sweden
Switzerland
United Kingdom
2.1. Super-SBM Model
The DEA method is a nonparametric method used to evaluate the relative effec-
tiveness of the same type of multi-input and multi-output decision-making units (DMU)
[25,26]. The basic models include CharnesCooperRhodes (CCR), which works under
the assumption of constant returns to scale, and BankerCharnesCooper (BCC), which
works under the assumption of variable returns to scale [27]. These models improve the
invalid DMU by adjusting the proportion of all inputs or outputs, which is called the ra-
dial DEA model. However, for ineffective DEA, the gap between the current state and the
strong effective target value, except for the part with equal proportion improvement,
does not consider the “Slacks” impact of elements, so its efficiency evaluation may be
biased. The non-radial SBM model proposed by Tone [28] effectively solves this problem,
but there will be multiple effective elements in the calculation process, and the efficiency
value of multiple DMU is 1. Therefore, Tone [29] introduced the super-efficiency SBM
model. It complemented the shortcoming that the SBM model cannot distinguish effec-
tive DMU by removing the effective units from the production possibility set and meas-
uring the distance to the production front. This cannot only sort the ineffective units but
also distinguish effective units. The model is shown in Equation (1), where x and y rep-
resent the input and output variables, m and s are the numbers of input and output in-
dicators, and
,
ir
ss

represents the relaxation variables of input and output respectively,
whereas represents the weight vector.
6 of 18
 

 
 
     

   


   
     
 
 
(1)
2.2. The Malmquist Index Model
Using the super-SBM model, we can effectively evaluate the cross-sectional data of
educational efficiency in all countries in the world. However, educational development
itself is a dynamic process, including the progress of educational technology and the
improvement of educational skills. Therefore, this paper uses the Malmquist index to
analyze the dynamic changes in educational efficiency. The Malmquist index can be di-
vided into two parts, catch-up effect and frontier-shift effect [30,31]. The catch-up effect
reflects the rate of change effect of DMU relative technical efficiency over time, and the
frontier shift reflects the movement of production frontier referenced by the combination
of input and output DMUs in the two adjacent periods. Scholars [32] described the
Malmquist productivity change index reflecting productivity change measured from t to
t + 1 can be expressed by the geometric average of total factor productivity change index
(tfpch), as shown in Equation (2),
(2)
In the analysis of education efficiency, the Malmquist total factor productivity
change index can be further decomposed into technical efficiency change index (effch)
and technical progress index (techch) [32]. The effch index is the ratio of technical effi-
ciency in phase t+1 and phase t as shown in Equation (3); besides, the techch index is the
relative distance between the production frontier in phase t + 1 and phase t, which is the
moving distance of the production front, as indicated in Equation (4),
 
 
1
0 1 1
0
,
,

ttt
ttt
D x y
effch D x y
(3)
 
 
 
 
1/2
0 1 1 0
11
0 1 1 0
,,
,,




 



tt
t t t t
tt
t t t t
D x y D x y
tfpch
techch effch D x y D x y
(4)
Furthermore, the technical efficiency change index (effch) can be decomposed into
pure technical efficiency change index (pech) and scale efficiency change index (sech).
The pech index is the change of technical efficiency calculated under the condition of
variable returns to scale, as shown in Equation (5). The sech index is calculated as the
effch under the condition of constant return to scale divided by the pech under the con-
dition of variable return to scale, as presented in Equation (6),
 
 
1
0 1 1
0
,/
,/

ttt
ttt
D x y VRS
pech D x y VRS
(5)
7 of 18
effch
sech pech
(6)
3. Variable Selection and Data Source
An inputoutput model shows the relationship of those factors going in (input) so
that efficient education can yield sustainable national development (output). The values
of these educational inputoutput variables are taken into analysis in the study. In terms
of education input, in addition to the traditional variables of total public expenditure on
education, this paper also adds variables including total public expenditure per capita on
education and the proportion of public expenditure on education in GDP, which can
more comprehensively reflect the input of educational resources and proper utilization in
a country. In terms of education output, in addition to the variables such as graduation
rate, basic education, and higher education achievement that are used in several studies,
this paper also employed the Program for International Student Assessment (PISA)
scores, the triadic patent families, and other variables, which can not only reflect the ed-
ucational efficiency in quantity but also reflect the educational efficiency in quality to
reduce the deviation caused by the selection of indicators (discussed below).
3.1. Variable Selection
The ideal evaluation of educational efficiency quantifies the educational activities
and related factors by constructing and selecting the index system of factors related to
educational activities and puts forward corresponding decisions. In recent years, scholars
in the field of education have usually measured educational efficiency and improved the
efficiency of educational resource allocation by constructing educational input and out-
put indicators based on the internationally developed education indicators of the United
Nations Educational, Scientific and Cultural Organization (UNESCO), the World Bank
and the Organization for Economic Cooperation and Development (OECD), etc. Moreo-
ver, this study also selects the indicators from the perspectives of input and output based
on the principles of availability, rationality, and pertinence. The specific indicators are
illustrated in Table 2 below.
1. Input variables. (i), the total expenditure on education. It refers to the general expenditure
(flow, capital, and transfer) of the government (district, regional, and central authority). It in-
cludes expenditures transferred from international funds to the government. The total gov-
ernment expenditure of a certain education level such as primary school, secondary school,
higher education, or the sum of all education levels calculated in national currency reflects the
total level of education expenditure of various countries. (ii), the total public expenditure on
education per capita. It refers to the total expenditure of the government on student education
from primary school to the completion/graduation of higher education. Due to different
economic levels and population scales of various countries, the total public expenditure on
education per capita reflects the level of education investment from an individual aspect. (iii),
the proportion of total public expenditure on education in GDP. It reflects the different poli-
cies and attention of various countries to the education industry. Through the different pro-
portions of public expenditure on education in GDP, it reflects the differences of input levels
among countries in terms of financial resources/budgetary.
2. Output variables. (i), the graduation rate of basic education. This refers to the percentage of
students who have completed nine-year compulsory education in the relevant age group,
which can reflect the level of basic education in a country; (ii), the achievements of higher
education. It refers to the percentage of people who have received college or undergraduate
education in the total population, which reflects the level of higher education in a country;
(iii), the Program for International Student Assessment (PISA) scores. PISA is a research pro-
ject on the evaluation of 15-year-old students’ reading, mathematics, and science abilities
carried out by the OECD [33]. Similarly, PISA assesses how far students near the end of
compulsory education have acquired some of the knowledge and skills that are essential for
full participation in society. Generally, the domains of reading and mathematical and scien-
tific literacy are not merely covered in terms of mastery of the school curriculum, but in terms
8 of 18
of important knowledge and skills needed in adult life [33]. Major countries in the world have
participated in the evaluation. PISA can reflect the deficiency of the participant countries’
education efficiency according to the international comparison of students’ performance in
PISA; therefore, this paper uses PISA score data to evaluate the quality and efficiency of a
country’s education; (iv), the triadic patent families. A triadic patent family is defined as a set
of patents registered in various countries (i.e., patent offices) filed at three of these major pa-
tent offices: the European Patent Office (EPO), the Japan Patent Office (JPO), and the United
States Patent and Trademark Office (USPTO). Innovation is one of the criteria to measure
sustainable development. These patent families can well evaluate various countries’ innova-
tion strength and thus reflect the ability of education to sustain development.
Table 2. Input and output index system of education efficiency.
Variable Descriptions
Variable Units
Education investment index
Total public expenditure on
Education
Million dollars
Total public expenditure on
education per capita
Dollar
Proportion of public ex-
penditure on Education
Percentage of GDP
Education output indicators
Graduation rate of basic ed-
ucation
Percentage of relevant age
groups receiving full-time
education
Achievements in Higher Ed-
ucation
Percentage of population
with higher education
PISA score
Test scores of 15-year-old
students in reading, mathe-
matics, and science
Triadic patent families
Quantity
3.2. Data Source
The data of this paper mainly come from the World Bank’s education statistics-all
indicators database, the UNESCO education database, and the OECD education and pa-
tents statistical database. In accordance with the integrity and availability of data, the
sample of this paper is selected from 2010 to 2016. After excluding countries with less
education input and output, the main countries selected are Argentina, Australia, Aus-
tria, Brazil, Canada, Chile, China, Costa Rica, Czech Republic, Finland, France, Germany,
Hungary, Ireland, Israel, Italy, Japan, Mexico, Norway, Poland, Portugal, Russia, Slo-
vakia, South Africa, Spain, Sweden, Switzerland, the United Kingdom (UK), and the
United States (US).
4. Analysis and Result of Educational Efficiency
4.1. Analysis of Educational Efficiency
To begin, this study adopts DEAP2.1 software to measure and statically analyze the
total factor productivity (TFP) of education of the 29 countries by employing the national
panel data. The results show that there are many countries with an efficiency value of 1,
which is when the DMU is located on the frontier. In order to further effectively analyze
the efficiency level of the DMU this paper further employs DEA solver pro5.0 software
and adopts the super-SBM model based on input orientation. The detailed results are
shown in Table 3 below.
Table 3. Measurement results of education efficiency in major countries in the world from 2010 to
2016.
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DMU
2010
2011
2012
2013
2014
2015
2016
Mean
Rank
Argentina
1.1052
1.0396
1.0189
1.0330
1.0446
0.7237
0.8617
0.9752
12
Australia
0.5550
0.6673
0.7662
0.6182
0.6604
0.6990
0.7492
0.6736
18
Austria
0.4917
0.4698
0.4773
0.4923
0.4918
0.5242
0.4482
0.4850
25
Brazil
0.4985
0.4748
0.4722
0.4938
0.5092
0.5469
0.5232
0.5026
24
Canada
0.4317
0.4335
0.4267
0.4568
0.4576
0.4733
0.4473
0.4467
27
Chile
1.2213
1.1907
1.0216
1.0468
1.1332
1.0633
1.0209
1.0997
8
China
1.9954
1.7367
1.5578
1.5512
1.4898
1.4219
1.2858
1.5769
2
Costa Rica
1.3606
1.2964
1.2850
1.2886
1.3865
1.1227
1.0526
1.2561
4
Czech Republic
1.0213
0.7174
0.7470
1.0162
1.0398
0.7464
0.7229
0.8587
15
Finland
0.5737
0.5639
0.5518
0.5668
0.5760
0.6090
0.5569
0.5712
22
France
0.4978
0.4975
0.4792
0.4973
0.4819
0.4854
0.4259
0.4807
26
Germany
0.5839
0.5752
0.6005
0.6269
0.5972
0.6229
0.5696
0.5966
21
Hungary
0.9430
0.9768
1.0973
1.1074
1.0708
1.1186
1.0415
1.0508
10
Ireland
0.6754
0.6744
0.4665
0.6180
0.7799
1.1056
1.0398
0.7657
16
Israel
1.1741
1.1152
1.1705
1.1454
1.1735
1.1610
1.0594
1.1427
6
Italy
0.5502
1.0027
1.0016
0.8609
1.0126
0.8245
0.7669
0.8599
14
Japan
3.2452
3.0264
2.7579
2.3946
3.1131
3.8673
4.5872
3.2845
1
Mexico
0.6448
0.9376
1.0300
1.0218
0.6630
1.0528
1.2171
0.9382
13
Norway
0.3956
0.4007
0.3707
0.4016
0.4226
0.4787
0.4263
0.4137
29
Poland
1.0026
1.0317
1.1100
1.1073
1.1043
1.1575
1.1441
1.0939
9
Portugal
0.5513
0.5472
0.6152
0.6032
0.6621
0.7479
0.6160
0.6204
19
Russia
1.0775
1.0811
1.0971
1.1184
1.0799
1.1196
1.1906
1.1092
7
Slovak Republic
1.3475
1.3873
1.3018
1.3451
1.3208
1.3623
1.6321
1.3853
3
South Africa
1.1116
1.1114
1.1516
1.2625
1.2626
1.3766
1.3323
1.2298
5
Spain
0.4961
0.5011
0.6586
0.7542
0.7710
0.8480
0.6880
0.6739
17
Sweden
0.4508
0.4338
0.4004
0.4138
0.4183
0.4527
0.4189
0.4270
28
Switzerland
1.0148
1.0125
1.0167
1.0588
1.0415
1.0392
1.0210
1.0292
11
United Kingdom
0.5247
0.5311
0.5563
0.6020
0.5708
0.5337
0.5309
0.5499
23
United States
0.6038
0.6163
0.6230
0.6736
0.6082
0.5733
0.4922
0.5986
20
Mean
0.9015
0.8983
0.8907
0.9026
0.9291
0.9606
0.9610
0.9205
In terms of years, the average educational efficiencies of the investigated countries
from 2010 to 2016 were 0.9015, 0.8983, 0.8907, 0.9026, 0.9291, 0.9606, and 0.9610, respec-
tively. It can be observed that the efficiency values over the years were less than 1. The
overall educational efficiency was in the DEA ineffective state, indicating that the utili-
zation rate of educational investment factors in the studied countries was not high
enough and the allocation of educational resources was not reasonable. Except for 2011
and 2012, the educational efficiency in the mentioned countries had been gradually im-
proved, and in 2016, which was very close to the production frontier, indicates that the
utilization rate of educational input factors and the allocation of educational resources
were exceptionally effective.
In terms of countries, the countries with the highest educational efficiency are Japan,
China, Slovakia, Costa Rica, South Africa, Israel, Russia, Chile, Poland, Hungary, and
Switzerland. The average educational efficiency of these countries during the study pe-
riod was greater than 1, indicating that these countries had been basically achieved DEA
efficiency. Nevertheless, Argentina, Mexico, Italy, the Czech Republic, Ireland, Spain,
Australia, Portugal, the US, Germany, Finland, the UK, Brazil, Austria, France, Canada,
Sweden, and Norway had been an average educational efficiency of less than 1, which
was in a DEA ineffective state. It can be seen that education efficiency in some developing
economic countries has been either equal or better than some developed countries, which
demonstrates that they have made considerable strides in realizing education for devel-
10 of 18
opment, rapidly building a quality and efficient education system for their society. To
support the result of this study, Xu and Liu [4] found that the countries with considerable
efficiency progress in education and technology were primarily concentrated in East
Asia, specifically Japan and China. Not to mention that the quality and efficiency of
higher education are necessary to achieve massive human capital. Besides, efficient ed-
ucation conveys sustainable endogenous economic development and boosts technology
progress [3].
There are two main reasons for the high educational efficiency in these developing
economic countries. First is the educational policy reform advantage. For instance,
countries like China and South Africa are in the early stage of economic development and
their educational development was mainly focused on elementary education. In recent
years, with the improvement of economic development and the transformation of edu-
cational policies, the facilities of higher education in these countries have been developed
rapidly [34,35]. Accordingly, compared with other countries, it has a certain scale ad-
vantage, resulting in higher marginal efficiency. Second, there are certain late develop-
ment advantages. Education in developing economic countries started relatively late [8].
By learning from the experience of advanced economic countries the layout of educa-
tional input and output became relatively efficient and established effective government
regulations, which is conducive to the effective allocation of educational resources
[34,35].
Compared with developing economic countries, most of the western countries that
are investigated in this study have basically completed the popularization of compulsory
education and higher education earlier. However, this study result demonstrates that
most of these countries have had lower education efficiency due to, inter alia, the alloca-
tion of educational resources perhaps not optimized in time, which leads to the waste of
educational input resources and the reduction of expenditure efficiency, followed by the
inevitable decline of educational efficiency. Therefore, with the increase of the budget
and investment in education sectors, the overall scale of educational efficiency could be
increased but there are also obvious competitive effects and spatial spillover characteris-
tics that need to be taken into consideration, including policy formulation, operation ef-
ficiency, technological strategies, and policy sustainability.
Incidentally, according to the results of educational efficiency value, this paper
classified the studied countries into three levels, such as countries with p 1 value as high
educational efficiency, countries with 1 > p ≥ 0.5 value as medium educational efficiency,
and countries with p < 0.5 value as low educational efficiency. The number of countries
included in each education efficiency interval is shown in Table 4 below. It can be seen
that the education efficiency of most of the studied countries has been mainly medium
and high education efficiency. Similarly, the trend of transformation from low-efficiency
countries to medium-high efficiency countries has been lingering, indicating that the
overall efficiency improvement rate has been slow.
Table 4. The number of countries in each education efficiency interval.
2010
2011
2012
2013
2014
2015
2016
Mean
Number of countries with high
educational efficiency
12
12
14
14
13
13
13
13
Number of countries with mid-
dle educational efficiency
11
11
8
10
12
12
10
11
Number of countries with low
educational efficiency
6
6
7
5
4
4
6
5
Furthermore, according to the average efficiency over the years this paper ranked
the educational efficiency of the studied countries, and the results are demonstrated in
Figure 1 below. During the study period, hierarchically, countries from Japan to Swit-
11 of 18
zerland are ranked high in educational efficiency. Similarly, countries from Argentina to
Brazil are ranked middle education efficiency countries, whereas countries from Austria
to Norway are low education efficiency countries. Apparently, it is not difficult to see
that there are huge differences between high and low education efficiency countries, and
the average difference of the highest education efficiency was 2.8708. This indicates that
there were huge differences in the level of education efficiency among the 29 countries,
and reveals that the development of education level in the world has been absolutely
unbalanced (See Figure 1).
Figure 1. Education efficiency values and average values of education efficiency in the investigated
countries over the sample period.
4.2. Assessment Result of Educational Efficiency in the World’s Major Economies
With the acceleration of globalization, some economic countries, especially world
economic powers, have an increasing impact on the overall education efficiency of the
world. On account of this fact, this section precisely compares the education efficiency of
nine world economies, such as the US, China, Japan, Germany, the UK, France, Italy,
Brazil, and Canada aiming to clarify their education efficiency level and the driving fac-
tors (see Figure 2).
As can be seen from the above figure, Japan’s educational efficiency leads and China
follows. This denotes that Japan’s educational efficiency was at the forefront of technol-
ogy and the main driving country in educational efficiency. Comparatively, although the
educational efficiency value of China has been declining during the research period, the
overall efficiency value was greater than 1, indicating that China was also one of the
driving countries in educational efficiency, but its impact has been gradually decreasing
due to various reasons [36]. According to the analyzed result, the educational efficiencies
of the US, Germany, the UK, France, Canada, and Brazil were less than 1. This implies
that the educational efficiency of these countries had been in a DEA ineffective state
during the research period. However, it is worth noting that the low level of educational
efficiency does not mean that the educational strength was low because the DEA method
measures relative efficiency. The low-efficiency value only indicates that these countries
have considerable deficiencies in the utilization level of educational resources and rela-
tively low substantial investment in human capital [37]. It is assumed that the US, the UK,
Germany, and France are still countries with traditionally high educational strength.
However, Brazil is quite different from these countries. It is not considered as one of the
traditional educational power countries, but its educational efficiency value was also low.
12 of 18
This demonstrates that there is a significant gap in this country and concurrently implies
a direction for future research. Differently, Italy’s education efficiency fluctuated signif-
icantly during the study period, and the DEA value was effective in 2011, 2012, and 2014,
but on the overall level, its DEA value was still ineffective.
Figure 2. Assessment results of education efficiency of the world’s major economies from 2010 to
2016.
4.3. Decomposition Results of Malmquist Total Factor Productivity (TFP) Index
In order to further clarify the sustainable development of educational efficiency in
major countries across the world and analyze the factors affecting educational efficiency,
the Malmquist TFP index based on the DEA method provides a convenient tool for ana-
lyzing the changes in educational efficiency of all elements of education in various
countries. Based on this method, this section analyzes the changes and decomposition
results of the TFP of education in major countries in the world from 2010 to 2016, as
presented in Table 5.
Table 5. Changes and decomposition of the Malmquist index of overall education efficiency in
major countries in the world from 2010 to 2016.
Year
effch
techch
pech
sech
tfpch
20102011
1.014
0.980
1.002
1.012
0.994
20112012
0.982
1.003
0.998
0.984
0.985
20122013
1.002
0.986
0.984
1.019
0.988
20132014
1.002
1.015
1.003
0.999
1.017
20142015
1.000
1.020
1.003
0.997
1.020
20152016
0.986
1.034
0.982
1.005
1.020
Mean
0.998
1.006
0.995
1.003
1.004
From the perspective of time series, the overall education TFP index of major coun-
tries in the world shows a downward trend first and then an upward trend. The trend of
technological progress change index (techch) is basically consistent with the trend of
education total factor productivity change index (tfpch), indicating that technological
progress directly affects the sustainability of educational efficiency. Similarly, the scale
efficiency change index (sech) can promote education TFP, whereas the technical effi-
ciency change index (effch), especially the pure technical efficiency change index (pfch),
can subdue the tfpch of education. Generally, the growth rate of education TFP has been
reduced in 20102011, 20112012, and 20122013, of which in 20112012 was the highest
13 of 18
decline, which was 1.5%. The growth rate of the education TFP index in 20132014, 2014
2015, and 20152016 was increased, of which the growth rate in 20142015 and 20152016
was comparatively the highest (2.0%.). As for the factors causing the change of the edu-
cation TFP index, there are differences among the sample period. To illustrate, from 2010
to 2011 and 20122013, the decline of the tfpch index was mainly due to the decline of the
techch index, whereas from 2011 to 2012, the tfpch index was mainly due to the decline of
the effch index. At the same time, the increases of the tfpch index in 20132014, 2014
2015, and 20152016 were mainly due to the rise of the techch index.
From an overall perspective, the average annual tfpch index of education in the
studied countries was greater than 1, with an average annual growth of 0.4%, indicating
that the overall level of education efficiency in the world has been on the rise, but the rise
was relatively slow, which is consistent with the conclusion that the education efficiency
of investigated countries has been gradually improving from the previous static analysis.
By further decomposing the tfpch index, it is found that the mean value of the techch was
1.006, indicating that technological progress has been the main factor leading to the
growth of TFP of education, and technical efficiency inhibited the growth of TFP of ed-
ucation. Moreover, technical efficiency can be decomposed into the product of pure
technical efficiency and scale efficiency. The pech index was less than 1 and the sech in-
dex was greater than 1, which further denotes that pech index inhibits the growth of ed-
ucational TFP, but scale efficiency plays a certain role in promoting educational TFP.
Specifically, during the study period, the improvement of educational technology level
and scale efficiency in the analyzed countries improved the frontier of educational pro-
ductions, and the production function curve moved upward. Apparently, the allocation
and management level of educational resources restricts the development of educational
efficiency [3840]. Therefore, while paying considerable attention to the improvement of
educational technology, educational authorities must scientifically adjust the allocation
of educational resources, increase investment in human capital, and ensure the en-
hancement of educational efficiency and effectiveness as well as the improvement of
management skills.
Table 6. Changes and decomposition of the Malmquist index of education efficiency in major
countries in the world from 2010 to 2016.
Country
effch
techch
pech
sech
tfpch
Argentina
0.991
0.993
0.996
0.995
0.984
Australia
1.010
1.022
1.000
1.010
1.032
Austria
0.969
1.034
0.938
1.033
1.002
Brazil
1.040
0.990
1.019
1.021
1.029
Canada
0.987
1.007
0.984
1.003
0.993
Chile
1.000
0.960
1.000
1.000
0.960
China
1.000
0.941
1.000
1.000
0.941
Costa Rica
1.000
0.946
1.000
1.000
0.946
Czech Republic
0.980
0.994
1.000
0.980
0.974
Finland
0.980
1.012
1.000
0.980
0.992
France
0.982
1.008
0.979
1.003
0.990
Germany
0.995
1.019
0.998
0.997
1.015
Hungary
1.005
0.988
1.000
1.005
0.993
Ireland
1.021
1.020
1.000
1.021
1.041
Israel
1.000
0.989
1.000
1.000
0.989
Italy
1.013
1.007
1.000
1.013
1.020
Japan
1.000
1.025
1.000
1.000
1.025
Mexico
1.029
1.010
1.021
1.008
1.039
Norway
0.978
1.018
0.981
0.997
0.996
14 of 18
Poland
1.000
1.028
1.000
1.000
1.028
Portugal
1.002
1.008
0.993
1.009
1.010
Russia
1.000
1.017
1.000
1.000
1.017
Slovak Republic
1.000
1.004
1.000
1.000
1.004
South Africa
1.000
1.025
1.000
1.000
1.025
Spain
1.021
1.019
1.019
1.002
1.040
Sweden
0.965
1.016
0.943
1.023
0.980
Switzerland
1.000
1.016
1.000
1.000
1.016
United Kingdom
0.989
1.033
0.992
0.996
1.022
United States
0.981
1.041
1.000
0.981
1.021
Mean
0.998
1.006
0.995
1.003
1.004
Furthermore, as the Malmquist index in table 6 indicates, there were 17 countries
whose average tfpch index was greater than 1 during the study period, namely Australia,
Austria, Brazil, Germany, Ireland, Italy, Japan, Mexico, Poland, Portugal, Russia, Slo-
vakia, South Africa, Spain, Switzerland, the UK, and the US. It shows that the overall TFP
of education in these countries has been increasing. Comparatively speaking, among the
29 countries, Ireland ranked first with a 1.041 average value of TFP. Simultaneously, it
can be seen that the average values of effch index, techch index, pech index, sech index,
and tfpch index of Ireland was greater than 1, which indicates that the overall efficiency
of education inputoutput in Ireland was exceptional. The main reasons for the growth of
TFP of education in Ireland could be the improvement of technological progress and
technological efficiency among others. Technological efficiency can be decomposed into
the product of pure technological efficiency and scale efficiency, while its pech index was
1, which has not been changed, and the sech index was 1.021. Therefore, we can conclude
that the improvement of technological efficiency mainly comes from the improvement of
scale efficiency.
Contrarily, those countries whose average value of the tfpch index was less than 1,
discloses that the TFP of education in these countries showed a downward trend and
needed to be improved. Among them, the most obvious decline was in China and Costa
Rica, where the average TFP of education decreased by 5.9% and 5.4% respectively. From
the results of the tfpch index decomposition, techch index showed a downward trend
and decreased by 5.9%, whereas effch index, sech index, and pech index did not change,
implying that the decline of the techch index was the main reason for the decline of
China’s TFP of education. The situation in Costa Rica was somewhat similar to that of
China.
To summarize, this study discovered that technological progress is the primary
factor leading to the growth and development of TFP of education in a given country [4].
Similarly, scale efficiency also plays a certain role in promoting the TFP of education,
whereas technical efficiency, especially pure technical efficiency, plays a restraining role
[41]. Therefore, for any country in the world, the key to improving educational efficiency
is to advance the level of educational technology. How to improve the level of educa-
tional technology is directly related to whether the total factor productivity of education
can be further improved. At the same time, we also need to pay significant attention to
technical efficiency and scientifically adjust the allocation of educational resources, im-
prove the level of educational resource management and the scale of technology-related
as well as innovative approach educations.
5. Conclusions
Nowadays, there is much scrutiny on the quality and efficiency of education due to
the rising issue of public concern for increasing public expenditure on education in the
15 of 18
face of the low moral standard of graduates, inadequate public services, increasingly low
self-esteem, highly unsatisfactory scholastic performance, and escalation of national
unemployment rate questioning the relevance of education at all levels. Consequently,
this paper empirically assesses and compares the educational efficiency across developed
and developing economic countries in an effort to discover the problems existing in the
utilization of educational resources, the causes of low efficiency in education, and the
significance of investment in the education sector.
This paper constructed the education inputoutput index by using the national-level
panel data of 29 major countries across the world, and assesses and analyzes the educa-
tion efficiency of these countries by using the super-SBM model and the Malmquist in-
dex. Hence, the analysis and assessment of this paper can be summarized as follows.
(1) From the static analysis results, the overall education efficiency of the studied countries was
in the DEA ineffective state. Except for 2011 and 2012, the education efficiency was gradually
improving during the study period. Similarly, the educational efficiency of analyzed coun-
tries was mainly medium and high educational efficiency during the study period. In terms of
years, the trend of transformation from low-efficiency countries to medium-high efficiency
countries was slow. In addition, while ranking the educational efficiency of various countries
based on the study result of the average efficiency over the years, this study observed that in
addition to some developed countries, the educational efficiency of a number of developing
countries was also at the forefront of technology. This study also discovered that there are
huge differences in the level of educational efficiency among the investigated countries, and
the development of the world educational level was quite unbalanced.
(2) From the dynamic analysis results at the time series level, the overall education TPF index of
major countries in the world shows a downward trend first and then an upward trend. The
trend of techch was basically consistent with the trend of tfpch, and the pech and sech have
also had varying degrees of impact on the education TPF index. Similarly, the average annual
education of the investigated countries’ tfpch index was greater than 1 with an average an-
nual growth of 0.4%, which demonstrated that the overall level of education efficiency shows
an upward trend; however, the upward range has been relatively slow. The study discovers
that technological progress was the main factor to promote the growth of education total
factor productivity [42]. Moreover, during the study period, there were 17 countries with a
mean value of the tfpch index greater than 1, which signifies that the overall TFP of education
in these countries has been increasing. In particular, the mean value of Ireland’s TFP was
1.041, ranked first among 29 countries. Technical efficiency and technological progress were
the major reasons for the increment of Ireland’s TFP. Except for the above 17 countries, the
average tfpch index of other countries was less than 1, which discloses that the TFP of educa-
tion in these countries had a downward trend and required improvement. Among them,
China and Costa Rica have a large decline, with an average annual decline of 5.9% and 5.4%
respectively. The decline of the techch index could be the primary reason for the decline of
efficiency of education in these countries [4].
To conclude, with the increasing investment of educational resources in various
countries, the level of educational efficiency was improving, but the growth rate is rela-
tively slow. In addition to Japan, Slovakia, Israel, Hungary, Switzerland, and other de-
veloped countries, some old-developed countries, such as the UK and US, due to the
constraints brought by the high development of its education level, showed that the
overall educational efficiency was in a DEA ineffective state. Therefore, these countries
can improve it by learning from the educational development model of Japan and other
developed countries. Although some developing countries, such as China have basically
achieved DEA effectiveness by increasing budgetary in educational resources, educa-
tional efficiency, and TFP of education had been dramatically decreased during the study
period and improvement was greatly required.
This study observed that educational technological progress was the leading factor
influencing the improvement of educational TFP in the studied countries. Moreover, ac-
cording to the theory of efficiency and productivity, the high contribution rate of tech-
nological progress to TFP in the education sector generally occurs only when the country
enters the mature period of development [4345]. Consequently, these countries need to
16 of 18
constantly optimize their educational resource allocation structure, strengthen the inte-
gration of resource stock, and adopt the shared resource model to optimize the utilization
efficiency of existing resources. Simultaneously, in order to attain a sustainable educa-
tional efficiency and educational productivity, countries must strengthen the overall
management of the educational sector, establish a resource integration mechanism,
compose a set of top-down responsibility and special education resource integration
guarantee mechanisms, create a policy control for the flow of educational financial re-
sources, and maximize educational resource stocks.
Once the external and internal government strategies ensure that educational agen-
cies and institutes are vibrant, inputs are enabling, outputs are examined, legal frame-
works are in place, and the processes are expeditiously effective; thus, the following
outcomes can be expected including professionalism will be increased, the knowledge
gap will be bridged, national economic development will be sustained, and international
competitiveness will be enhanced. The degree of sustainable development is closely re-
lated to the comprehensive quality of education in society. The government of the coun-
try can promote the level of educational modernization by increasing the investment in
educational technology, investment in research and development (R&D), improving
competency-based learning, enhancing knowledge-intensive services, and actively
changing the talent training mode in coordination with the concept of “innovation” [46].
In addition, effectively improving the professional level of teachers, increasing educa-
tional output with technological progress, and integrating innovation with the education
system are also equally important [44,45]. Apparently, a country’s innovation strategies
must coordinate disparate policies toward scientific research, information technology
investments, technology commercialization, and education development. Thus, these
cumulative efforts could guide quality and efficiency in the education sectors in the
country.
Author Contributions: Conceptualization, Y.Y.; methodology L.C. and Y.Y.; software L.C.; valida-
tion, L.C., A.K.A., and Y.Y.; formal analysis, Y.Y., L.C., A.K.A., and X.G.; investigation, L.C. and
A.K.A.; resources, L.C., A.K.A., Y.Y., and X.G.; data curation L.C. and X.G.; writingoriginal draft
preparation, L.C. and Y.Y.; writingreview and editing, Y.Y. and A.K.A.; visualization, L.C. and
A.K.A.; supervision, Y.Y.; project administration, Y.Y.; funding acquisition, Y.Y. All authors have
read and agreed to the published version of the manuscript.
Funding: This research was funded by the Education Project for Youth of National Social Science
Fund of China, grant number CGA180247. We would like to show gratitude for their research
funding support.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Our study did not report any data.
Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the
design of the study; in the collection, analyses, or interpretation of data; in the writing of the man-
uscript, or in the decision to publish the results.
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The Farrell technical efficiency measure computes the maximum proportional reduction that can be operated on inputs without affecting the level of output. In a multi-input and multi-output context, the first mathematical programming based reformulation of this problem is known as CCR/BCC efficiency measures. There are two drawbacks to this measure. First, it does not give value to any inefficiency resulting from the possibility of reducing some inputs and/or increasing some outputs in addition to the maximum proportional reduction in inputs. Second, as a result of the above, it does not unequivocally identify Pareto-Koopmans efficient activities. This article presents a strong efficiency measure similar to CCR/BCC models which overcome these drawbacks. It accounts for all non-zero slacks in inputs and outputs once the proportional reduction path in the inputs has been exhausted. This allows for the correct classification of production units in an efficiency ranking and facilitates the measurement of inefficiency by inputs and outputs, thereby helping to improve business management decision-making. We extend our model to deal with zero and negative input or output values. A numerical example shows the applicability of our approach.