Directory UMM :Data Elmu:jurnal:I:International Journal of Educational Management:Vol12.Issue2.1998:
Using DEA to evaluate the ef ficiency of secondary
schools: the case of Cyprus
Andreas C. Soteriou
De partme nt o f Busine ss Administratio n, Unive rsity o f Cyprus, Nic o sia, Cyprus
Elena Karahanna
De partme nt o f Busine ss Administratio n, Unive rsity o f Cyprus, Nic o sia, Cyprus
Constantinos Papanastasiou
De partme nt o f Educ atio n, Unive rsity o f Cyprus, Nic o sia, Cyprus
M anolis S. Diakourakis
De partme nt o f Busine ss Administratio n, Unive rsity o f Cyprus, Nic o sia, Cyprus
This study utilizes the
methodology of data envelopment analysis (DEA) to assess
the efficiency of secondary
schools in Cyprus. Apart from
evaluating the relative efficiency of schools, the study
provides recommendations
for improvement to inefficient
schools and discusses managerial implications. Furthermore, empirical fi ndings
based on an approach to
estimate efficiency environmental effects suggest that
no efficiency differences exist
between schools operating in
rural areas compared to
those operating in urban
areas.
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [ 1998] 6 5 –7 3
© MCB Unive rsity Pre ss
[ ISSN 0951-354X]
Introduction
Assessin g th e per for m a n ce of a n edu ca tion a l
system is a n im por ta n t bu t difficu lt to a ccom plish ta sk . E du ca tion a l ser vices fea tu r e a ll
th e distin ctive ch a r a cter istics of ser vices visà -vis m a n u fa ctu r in g, su ch a s per ish a bility,
h eter ogen eity a n d sim u lta n eity (F itzsim m on s a n d F itzsim m on s, 1994; Sa sser et a l.,
1978). Despite th e difficu lties in volved, sch ool
per for m a n ce a ssessm en t ca n , a m on g oth er s,
be u sed to set per for m a n ce ta r gets, to m a k e
r esou r ce a lloca tion decision s, a n d to im pr ove
over a ll sch ool per for m a n ce.
Sch ool u n its bea r fu r th er sim ila r ities to
ser vice or ga n iza tion a l u n its in th e sen se th a t
th ey u tilize m u ltiple in pu ts to pr odu ce m u ltiple ou tpu ts (Ca m er on , 1978). A n u m ber of
com m on pr oblem s em er ge wh en a ttem ptin g
to a ssess ser vice or ga n iza tion a n d sch ool
per for m a n ce. F ir st, n o u ltim a te cr iter ion of
effectiven ess exists, sin ce a u n it (ser vice
or ga n iza tion or sch ool) m ay typica lly pu r su e
m u ltiple, a n d often con tr a dictor y goa ls. Releva n t cr iter ia m ay a lso ch a n ge over th e lifecycle of th e u n it. Differ en t u n its m ay a ssign
pa r ticu la r im por ta n ce to differ en t or ga n iza tion a l a spects a t differ en t tim es. Mor eover,
cr iter ia a t on e or ga n iza tion a l level m ay n ot
be th e sa m e a s th ose a t a n oth er or ga n iza tion a l level, wh ile r ela tion sh ips a m on g va r iou s effectiven ess dim en sion s m ay be difficu lt
to discover.
Differ en t cr iter ia h ave tr a dition a lly been
defin ed for a ssessin g sch ool per for m a n ce.
Typica lly, sch ool effectiven ess h a s been m ea su r ed in ter m s of th e per for m a n ce of stu den ts
in exa m in a tion s (see Gr ay, 1981), for a discu ssion on sch ool ou tcom es). Oth er con textu a l
fa ctor s su ch a s th e stu den ts’ socioecon om ica l
ba ck gr ou n d a n d oth er en vir on m en ta l va r ia bles a r e a lso con sider ed. In th is pa per we
follow a (popu la r in th e liter a tu r e) pr odu ction
or “va lu e-a dded” a ppr oa ch in wh ich th e
sch ool u tilizes som e in pu ts (i.e. n u m ber of
in str u ctor s, exper ien ce of in str u ctor s, socioecon om ic ba ck gr ou n d of stu den ts, etc.) to pr odu ce som e ou tpu ts (i.e. exa m in a tion scor es).
On e of th e m eth odologies u sed in pr eviou s
stu dies of sch ool per for m a n ce eva lu a tion
ba sed on in pu t-ou tpu t a n a lysis h a s been or din a r y lea st squ a r es (OLS) r e gr ession a n a lysis.
Su ch stu dies h ave, h owever, two m a jor disa dva n ta ges (Ray, 1991). F ir st, pr edicted va lu es
r esu ltin g fr om a r e gr ession m odel pr ovide
th e aver a ge or expected level of ou tcom e
given cer ta in in pu ts, in stea d of th e m a xim u m
a ch ieva ble ou tcom e. Secon d, th e in pu t/ ou tpu t pr odu ction fu n ction specified by su ch
m odels m ay be pr oblem a tic. Most r e gr ession
m odels u se a sin gle ou tpu t pr odu ction fu n ction , wh ich m ay be u n r ea listic wh en a ssessin g sch ool per for m a n ce[1].
In th is pa per we focu s on th e a ssessm en t of
th e efficien cy of secon da r y sch ools in Cypr u s.
In a r ecen t stu dy by th e In ter n a tion a l Associa tion for th e E va lu a tion of E du ca tion a l
Ach ievem en t, th e sch ools of Cypr u s r a n k ed
low com pa r ed to 41 oth er cou n tr ies wh ich
a lso pa r ticipa ted in th e stu dy. However, exa m in in g on ly th e sch ools’ ou tpu t does n ot pr ovide a com plete pictu r e r e ga r din g per for m a n ce. It is im por ta n t to k n ow wh eth er
sch ools a r e a ctu a lly u tilizin g th eir r esou r ces
in th e m ost efficien t w ay to pr odu ce th e
obser ved r a n k in gs. In a ddition , it is a lso
im por ta n t to pr ovide gu idelin es on h ow
sch ools ca n im pr ove fu r th er.
Her e, we u tilize th e n on -pa r a m etr ic m eth odology of da ta envelopm en t a n a lysis (DE A)
(Ch a r n es et a l., 1978). DE A, a state-of-th e-a r t
n on -pa r a m etr ic m eth odology, ca n be u sed to
a ssess per for m a n ce of h om ogen eou s u n its
u tilizin g m u ltiple in pu ts to pr odu ce m u ltiple
ou tpu ts. DE A en joys a n u m ber of a dva n ta ges
over oth er tr a dition a l pa r a m etr ic m eth ods,
a n d h a s been u sed exten sively to a ssess sch ool
per for m a n ce (Nor m a n a n d Stock er, 1991;
Sa m m on s et a l., 1993; Th a n a ssou lis a n d
Du n sta n , 1994). Apa r t fr om eva lu a tin g th e
[ 65 ]
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
r ela tive efficien cy of secon da r y sch ools, th is
stu dy pr ovides r ecom m en da tion s for im pr ovem en t to in efficien t sch ools a n d discu sses
m a n a ger ia l im plica tion s.
Th e pa per is or ga n ized a s follow s. We n ext
pr ovide a descr iption of th e da ta envelopm en t
a n a lysis m eth odology. A br ief liter a tu r e
r eview on th e DE A a pplica tion s in edu ca tion a l settin gs follow s. N ext, we descr ibe a n
em pir ica l stu dy wh ich u tilizes DE A to a ssess
th e efficien cy of secon da r y sch ools in th e
cou n tr y of Cypr u s. Addition a l in sigh ts to th e
pr oblem of sch ool eva lu a tion a r e pr esen ted by
ben ch m a r k in g th e effect of th e exter n a l en vir on m en t th r ou gh th e com pa r ison of u r ba n
a n d r u r a l sch ool efficien cy. Ma n a ger ia l im plica tion s, lim ita tion s a n d fu tu r e r esea r ch a r e
a lso discu ssed. Con clu din g r em a r k s follow.
u r K = weigh t given to ou tpu t r,
0
v iK
0
R
I
= weigh t given to in pu t i,
= n u m ber of ou tpu ts,
= n u m ber of in pu ts.
As lon g a s th e u n it u n der con sider a tion
r em a in s a sin gle DMU, we cou ld r eta in th e
pr ecedin g defin ition . However, a n attem pt of
defin in g efficien cy for a gr ou p of DMUs
sim u lta n eou sly is n ot possible u sin g ju st
defin ition (1), sin ce a com m on set of weigh ts
is difficu lt to be set a m on g a ll DMUs of a ser vice or ga n iza tion or system .
E a ch DMU ca n be a llowed to ch oose its ow n
set of weigh ts ba sed on its ow n va lu e system
(Ch a r n es et a l., 1978) in a n a ttem pt to a ppea r
a s efficien t a s possible. Th e follow in g m odel
is for m ed ba sed on defin ition (1):
(M 1)
Data envelopment analysis
Th e m eth odology of da ta envelopm en t a n a lysis, in itia lly in tr odu ced by Ch a r n es et a l.
(1978), is a m a th em a tica l pr ogr a m m in g tech n iqu e u sed to eva lu a te th e r ela tive efficien cy
of h om ogen eou s u n its. Th is efficien cy eva lu a tion der ives fr om a n a lysin g em pir ica l obser va tion s obta in ed fr om decision -m a k in g u n its
(DMUs), a ter m coin ed by Ch a r n es et a l. (1978)
to defin e pr odu ctive u n its wh ich a r e ch a r a cter ized by com m on m u ltiple ou tpu ts a n d
com m on design a ted in pu ts.
Rela tive h om ogen eity of or ga n iza tion a l
u n its su ch a s sch ools, ba n k br a n ch es or h ospita ls, pr ovides in sta n ces for im plem en ta tion
of th e DE A m eth odology. In a m or e gen er a l
m a n n er, DE A is m ost u sefu l in ca ses wh er e
a ccou n tin g a n d fi n a n cia l r a tios a r e of little
va lu e, m u ltiple ou tpu ts a r e pr odu ced th r ou gh
th e tr a n sfor m a tion of m u ltiple in pu ts, a n d
th e in pu t-ou tpu t tr a n sfor m a tion r ela tion sh ips a r e n ot k n ow n (Ch a r n es et a l., 1978).
In a br oa d sen se, efficien cy of a sin gle DMU
k 0 oper a tin g in a h om ogen eou s set of N
DMUs, u tilizin g m u ltiple in pu ts I to pr odu ce
m u ltiple ou tpu ts R , ca n be defi n ed a s follow s :
(1)
Ma xim ize
(2)
su bject to:
(3)
u r K , v iK ≥ 0 for a ll r = 1, …, R , a n d i = 1, …, I,
0
0
(4)
Th r ou gh M 1, ea ch DMU K 0 a n a lysed w ill
specify th e pa r ticu la r in pu t a n d ou tpu t
weigh ts (u a n d v r espectively), wh ich m a xim ize its ow n r a tio of weigh ted ou tpu t to
weigh ted in pu t, su bject to th e con str a in t th a t
n o oth er u n it u tilizin g th e sa m e weigh ts
cou ld exceed a n efficien cy r a tin g of 1. A DMU
w ith efficien cy r a tin g of 1 w ill be given th e
ch a r a cter iza tion of efficien t r ela tive to oth er
DMUs. Vice ver sa , a n efficien cy r a tin g of less
th a n 1 w ill lea d u s to ch a r a cter izin g th is specific u n it a s in efficien t in r ela tion to oth er s.
(M 1) r epr esen ts a fr a ction a l lin ea r pr ogr a m m in g (LP ) m odel. Th is ca n be ea sily
tr a n sfor m ed in to a sim ple lin ea r pr ogr a m , a s
follow s:
(M 2)
wh er e,
EK
0
yrK
0
Ma xim ize
(5)
= efficien cy of u n it K 0,
= a m ou n t of ou tpu t r = 1, …, R pr odu ced
su bject to:
by DMU K 0,
x iK
0
= a m ou n t of in pu t i = 1, …, I con su m ed
by DMU K 0,
[ 66 ]
(6)
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
(7)
(8)
wh er e,
E K = efficien cy of u n it K 0,
0
y rK
x iK
0
0
= a m ou n t of ou tpu t r pr odu ced by
DMU K 0,
= a m ou n t of in pu t i con su m ed by
DMU K 0,
u r K = weigh t given to ou tpu t r ,
0
v iK
0
= weigh t given to in pu t i,
Th e tr a n sfor m a tion is obta in ed by settin g th e
den om in a tor of (2) to a n a r bitr a r ily selected
con sta n t. A sim ila r m a n ipu la tion of equ a tion
(2) ca n r esu lt in a n in pu t m in im iza tion or ien ted lin ea r pr ogr a m m in g m odel[2].
Th e du a l for m u la tion of (M2) ca n pr ovide
a ddition a l in sigh ts a n d is com pu ta tion a lly
less expen sive:
(M 3)
Min im ize
(9)
Th e size of th e n ecessa r y decr ea se is in dica ted by th e va lu e of H K .
0
F r om th e scope of com pu ta tion a l effor t, th e
fa ct th a t (M 3) h a s on ly (I + R ) con str a in ts
com pa r ed to (N + R + I + 1) con str a in ts of
m odel (M 2) a n d N is typica lly m u ch la r ger
th a n I + R , deem s (M 3) ea sier to solve in
com pa r ison to (M 2). An a ddition a l a dva n ta ge
of (M 3) is th e pr ovision of ta r get va lu es for
in efficien t u n its by com pa r in g th em a ga in st a
com posite u n it con str u cted by th e a ctu a l
per for m a n ce of th e r est of th e u n its (Bou ssofia n e et a l., 1991). Th ese ta r gets ca n pr ovide
gu idelin es for im pr ovem en t to in efficien t
u n its. At optim a lity, th e follow in g in pu t/
ou tpu t va lu es occu r :
for a ll i = 1, 2, …, n
(14)
for a ll r = 1, 2, …, m
(15)
wh er e * in dica tes optim a lity. Th ese a r e in pu tor ien ted ta r gets sin ce th e a ttem pt h er e is to
m in im ize in pu ts. Ou tpu t-or ien ted ta r gets ca n
a lso be der ived by dividin g both
su bject to:
for a ll i = 1, 2, …, I,
(10)
for a ll r = 1, 2, …, R ,
(11)
(12)
(13)
wh er e s r+ a n d s i– r epr esen t th e sla ck va r ia bles
cor r espon din g to th e ou tpu ts a n d in pu ts
r espectively.
Ba sed on m odel (M 3) we ca n ch a r a cter ize
DMU K 0 efficien t a s lon g a s th e va lu e of H K is
0
equ a l to 1. If H K exceeds th e lower lim it of 1,
0
th e DMU u n der a ssessm en t is ch a r a cter ized
in efficien t in com pa r ison to oth er DMUs.
Th a t is, th er e exists a weigh ted com bin a tion
of a ctu a l per for m a n ce of oth er u n its, su ch
th a t n o ou tpu t of u n it K 0 exceeds th a t of th e
weigh ted ou tpu t of th e weigh ted com bin a tion . At th e sa m e tim e, we cou ld r edu ce a ll
in pu ts of K 0 by th e pr opor tion H K w ith ou t
0
a n y in pu t fa llin g below th a t of th e
cor r espon din g weigh ted com bin a tion of oth er
u n its. If DMU K 0 is deem ed in efficien t, m a n a gem en t cou ld decr ea se a ll th e in pu ts of K 0 in
th e sa m e pr opor tion , in or der to a ch ieve th e
desir ed weigh ted com bin a tion per for m a n ce.
Model (M 3) w a s in tr odu ced by Ch a r n es et a l.
(1978) ba sed on th e a ssu m ption of con sta n t
r etu r n s to sca le. However, wh ile th is a ssu m ption cou ld often be le gitim a te, it m ay n ot be
va lid in ca ses wh er e th e sca le of oper a tion s
cou ld in flu en ce a DMU’s efficien cy r a tin g,
su ch a s, for exa m ple, wh en a ssessin g sch ool
per for m a n ce. Mor eover, in for m a tion con cer n in g th e a m ou n t of in efficien cies ow in g to
th e sca le of oper a tion s wou ld pr ove to be ver y
u sefu l for m a n a ger ia l decision s. Appen dix 1
pr esen ts a m odel descr ibed by Ba n k er et a l.
(1984) to cover th e issu e of in efficien cies du e
to sca le of oper a tion s, th r ou gh a n exten sion
of m odel (M 3).
Applications of DEA in education
Applica tion s of DE A to m ea su r e th e efficien cy
of edu ca tion a l pr odu ction h ave exten sively
been r epor ted in liter a tu r e, begin n in g w ith
th e in tr odu ctor y pa per of DE A (Ch a r n es et a l.,
1978), wh ich in tr odu ced th e DE A m eth odology
by dem on str a tin g it in a sch ool settin g. Th e
a im of th is section is n ot to pr esen t a th or ou gh
liter a tu r e r eview of DE A a pplica tion s in edu ca tion , bu t r a th er to pr esen t som e of th e m or e
r eleva n t stu dies to th is wor k .
Ch a r n es et a l. (1981) a lso u sed da ta fr om th e
edu ca tion sector. Th e a u th or s con cen tr a ted in
th e com pa r ison of th e pr ogr a m m e follow
[ 67 ]
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
[ 68 ]
th r ou gh (P F T) a n d n on follow th r ou gh (N F T)
sch em es for pr im a r y sch ool ch ildr en in th e
USA. P a r ticipa n ts in P F T wer e ch ildr en wh o
ca m e fr om less a dva n ta ged ba ck gr ou n ds,
wh ile th e exper im en t a lso in clu ded a con tr ol
gr ou p of N F T ch ildr en for ea ch distr ict th a t
pa r ticipa ted in th e P F T. DE A w a s u sed in
or der to a ssess th e efficien cies of policies
w ith in wh ich m a n a ger s oper a te wh ile elim in a tin g th e in efficien cies or igin a tin g fr om th e
m a n a ger s th em selves.
An a lter n a tive u se of DE A is pr esen ted by
Bessen t a n d Bessen t (1983). Mor e specifica lly,
DE A is u sed for r esou r ce a lloca tion of va r iou s
pr ogr a m s in th e en vir on m en t of a com m u n ity
colle ge. Th e m a in con tr ibu tion of th e stu dy
w a s th e r ecogn ition th a t, in spite of som e
lim ita tion s, DE A cou ld pr ove h elpfu l in
r esou r ce a lloca tion . DE A ca n n ot, h owever,
pr ovide a n a n swer to th e qu estion of a lloca tin g tota l or ga n iza tion a l r esou r ces in or der to
obta in m a xim u m ou tpu t fr om th e u n its.
Bou ssofia n e et a l. (1991) u tilize th e con text
of com pa r in g sch ools for th e pu r pose of
dem on str a tin g pr a ctica l issu es en cou n ter ed
in selectin g a n d qu a lifyin g in pu ts a n d ou tpu ts. Sch ools wer e ch osen a s a n illu str a tion
m a in ly du e to th e im por ta n ce of en vir on m en ta l fa ctor s in th eir oper a tion . An im por ta n t
obser va tion of th e a u th or s is th e effect of th e
selection of in pu ts a n d ou tpu ts in th e discr im in a tor y power of DE A, wh ich m or e
specifica lly is r ela ted to th e n u m ber of
selected in pu ts a n d ou tpu ts. As a m in im u m
n u m ber of u n its th a t w ill be given th e ta g of
efficien t, a u th or s set th e pr odu ct of th e n u m ber of in pu ts a n d ou tpu ts.
In a sim ila r m a n n er, Gola n y a n d Ta m ir
(1995), u tilize h ypoth etica l da ta ta k en fr om a n
eva lu a tion of som e elem en ta r y sch ools in a
sch ool distr ict. Aim of th e illu str a tion is th e
distin ction between differ en t a spects eva lu a ted by efficien cy, effectiven ess a n d equ a lity,
in a ddition to specifyin g poten tia l tr a de-off
a m on g th em . In a n oth er r ecen t stu dy, Th a n a ssou lis (1996) dem on str a ted h ow to u se DE A to
set ta r gets for differ en tia lly effective sch ools.
J oh n es a n d J oh n es (1993) r efer to a n a pplica tion of th e m eth odology in u n iver sities. In
th e pa r ticu la r stu dy, DE A is u sed for a ssessin g th e r esea r ch per for m a n ce of UK depa r tm en ts of econ om ics du r in g 1984-88. DE A w a s
especia lly va lu a ble sin ce n o u n iver sa lly
a ccepted im por ta n ce weigh ts exist r e ga r din g
th e r eleva n t in pu ts a n d ou tpu ts. Th e pr oblem
w a s a ddr essed th r ou gh th e a llow a n ce of DE A
for ea ch u n it to deter m in e its ow n set of in pu t
a n d ou tpu t weigh ts su ch th a t it m a xim izes its
efficien cy. However, ea ch u n it is n ot com pletely fr ee to defin e its set, sin ce it is su bject
to th e con str a in t th a t n o oth er u n it cou ld
a ccom plish a n efficien cy r a tin g th a t exceeds
u n ity, ba sed on th e sa m e set of weigh ted
in pu ts a n d ou tpu ts.
Ray (1991) u tilized th e DE A m eth odology in
com bin a tion to r e gr ession a n a lysis in or der
to a ssess r ela tive efficien cy in pu blic sch ool
distr icts in Con n ecticu t, USA. Th r ou gh h is
a n a lysis h e poin ted ou t th e effect of socioecon om ic va r ia bles in pr odu ctivity va r ia tion s. A r ela tive pa per, in th e sen se th a t it
r efer s to com bin ed u se of DE A w ith r e gr ession a n a lysis, is pr esen ted by Sexton a n d
Sleeper (1994), a im in g a t fa cin g th e la ck of
h om ogen eity between DMUs in volved.
Assessing the ef fectiveness of
schools in Cyprus
M odel description
Stu dies of edu ca tion a l pr odu ction fu n ction
defin e two m a jor w ays of descr ibin g th e in fl u en ces of sch oolin g on stu den t a ch ievem en t.
E ith er ta k e in to a ccou n t th e cu m u la tive in flu en ce of fa m ily ba ck gr ou n d, peer s, sch ool
in pu t a n d in n a te a bilities on stu den t a ch ievem en t a t cer ta in tim e poin ts or m ea su r e th ese
fa ctor s du r in g th e per iod stu den t is a tten din g
sch ool.
Ou r stu dy u ses th e secon d a lter n a tive, a lso
k n ow n a s th e va lu e a d d ed m odel. Th is m odel
is con ven ien t in th e sen se th a t it r edu ces da ta
r equ ir em en ts, sin ce sch ool-level a ggr e ga ted
da ta ca n be u sed. Mor eover, edu ca tion a l
a ch ievem en t is a pr odu ct of both in pu ts con tr olla ble by th e sch ool bu t a lso of oth er fa ctor s su ch a s fa m ily ba ck gr ou n d, in n a te a bilities, peer s a n d for m er ou tcom es.
F igu r e 1 pr esen ts th e th eor etica l fr a m ewor k u n der lyin g th e developed m odels.
Th r ee gen er ic deter m in a n ts dr ive sch ool
per for m a n ce (Th a n a ssou lis, 1996). F ir st,
sch ool-specific fa ctor s su ch a s th e size of th e
sch ool, a n d th e n u m ber a n d qu a lity of th e
tea ch er s; secon d, fa ctor s wh ich a r e fa m ily a n d
exter n a l envir on m en t specific, su ch a s for
exa m ple, th e stu den ts’ socioecon om ic ba ck gr ou n d or th e location of th e sch ool; a n d
fin a lly, th e a bilities of th e stu den t h im / h er self.
Th r ee m odels, a s pr esen ted in Ta ble I wer e
con str u cted, ba sed on th e a bove fr a m ewor k
a n d on da ta ava ila bility. Th e sm a ll n u m ber of
Figure 1
Ge ne ric drive rs o f sc ho o l pe rfo rmanc e
Sc ho o l Re late d
Fac to rs
Stude nt
Charac te ristic s
Family and Exte rnal
Enviro nme nt Influe nc e s
Stude nt’ s
Pe rfo rmanc e
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
sch ools ava ila ble lim ited th e n u m ber of in pu t
a n d ou tpu t va r ia bles, in or der to pr eser ve th e
DE A m odel’s discr im in a tor y power. Th e m odels pr esen ted in Ta ble I pr oceed fr om a sim ple
(Model 1) to a m or e com plica ted in pu t set
(Model 3). All m odels in clu de a sin gle, com m on ou tpu t, con sistin g of th e scor e fr om
sta n da r dized exa m in a tion s su ch a s th e
TIMSS, to be discu ssed in th e n ext section .
Th e fir st m odel u ses in pu ts wh ich ca n be
obta in ed fr om tea ch er s’ a n d stu den ts’ qu estion n a ir es. Mor e specifica lly, it in clu des th e
a ge a n d edu ca tion a l level of tea ch er s, in a ddition to th e pa r en ts’ edu cation a n d th e socioecon om ic statu s of th e fa m ily. Model 2 a lso
in clu des sch ool da ta . Th a t is, th e size of th e
sch ool, defin ed a s th e stu den ts’ popu lation
w a s in clu ded. An a ddition a l in pu t is con sider ed by Model 3 to captu r e th e socioecon om ic
ba ck gr ou n d of stu den ts. Th e n u m ber of book s
a t stu den t’s h om e w a s u sed a s a pr oxy for th a t.
A descr iption of a ll th e va r ia bles in clu ded in
a ll th e m odels is sh ow n in Appen dix 2.
Data
Th e Th ir d In ter n a tion a l Ma th em a tics a n d
Scien ce Stu dy (TIMSS) w a s con du cted du r in g
th e m on th s of May-J u n e 1995. TIMSS is con du cted by th e In ter n a tion a l Associa tion for
th e E va lu a tion of E du ca tion a l Ach ievem en t
(IE A), in a tota l of 45 cou n tr ies, cover in g m or e
th a n h a lf a m illion stu den ts a t five gr a des
levels in m or e th a n 15,000 sch ools. Th e m a in
goa l of TIMSS is to pr ovide in ter n a tion a l
ben ch m a r k s r e ga r din g sch ool per for m a n ce.
Da ta wer e collected u sin g sta n da r dized
qu estion n a ir es, a dju sted to r efl ect cu ltu r a l
differ en ces, com pleted by sch ool pr in cipa ls,
tea ch er s a n d stu den ts.
TIMSS pr ovides th e va r iou s pa r ticipa tin g
cou n tr ies a veh icle w ith wh ich to in vestiga te
a va r iety of issu es, in clu din g wh a t con cepts
stu den ts u n der sta n d, h ow well th ey ca n a pply
th eir k n ow ledge in pr oblem -solvin g situ a tion s, a n d wh eth er th ey ca n com m u n ica te
th eir u n der sta n din gs. In for m a tion r e ga r din g
Table I
Variable s use d in the DEA e ffic ie nc y me asure me nt
Inputs
Age of teacher
Education level of teacher
Parents’ education
Socioeconomic status
School size
Number of books at student’s home
Output
International mathematics score
M odel 1
M odel 2
M odel 3
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
th ese issu es is ver y im por ta n t. Sk ills in m a th em a tics a n d scien ce a r e becom in g cr itica l to
econ om ic pr ogr ess du e to th e tr a n sfor m a tion
of m oder n societies in to m or e tech n ologica lly
ba sed, wh er e h igh er levels of tech n ica l com peten ce a n d flexible th in k in g a r e r equ ir ed[3].
TIMSS u tilized in for m a tion fr om stu den ts,
tea ch er s a n d sch ool pr in cipa ls a s follow s:
• Pr in cipa l qu estion n a ire. Th is in str u m en t
w a s a dm in ister ed to th e sch ool’s pr in cipa l.
It obta in ed gen er a l in for m a tion a bou t th e
sch ool, i.e. sch ool size, n u m ber of tea ch er s
tea ch in g a t sch ool for five or m or e yea r s,
in for m a tion on th e sch ool’s com m u n ity a n d
on th e n u m ber of depa r tm en t h ea ds.
• T ea ch er of m a th em a tics a n d scien ce qu estion n a ire. Da ta collected th r ou gh th is
in str u m en t, wh ich w a s a dm in ister ed to
tea ch er s, in clu de th e tea ch er ’s edu ca tion a l
ba ck gr ou n d, co-oper a tion w ith oth er tea ch er s for lesson en h a n cem en t, a n d tea ch in g
m eth odologies.
• S tu d en t in for m a tion . In for m a tion on su ch
va r ia bles a s th e socioecon om ic sta tu s of
stu den t’s fa m ily, pa r en ts’ edu ca tion a n d
n u m ber of book s a t h om e w a s ga th er ed via
a qu estion n a ir e. F u r th er m or e, m a th tests
wh ich cover ed six con ten t a r ea s (fr a ction s
a n d n u m ber s (34 per cen t), m ea su r em en t
(12 per cen t), pr opor tion a lity (7 per cen t),
da ta r epr esen ta tion , a n a lysis, a n d pr oba bility (14 per cen t), geom etr y (15 per cen t), a n d
a lgebr a (18 per cen t)) wer e a lso a dm in ister ed to seven th a n d eigh th gr a de stu den ts.
Ou r stu dy w a s ba sed on th e Ma th em a tics
TIMSS da ta a s collected in Cypr u s w ith th e
colla bor a tion of th e Min istr y of E du ca tion
a n d Cu ltu r e, th e Peda gogica l In stitu te, a n d
th e Un iver sity of Cypr u s. Da ta wer e ga th er ed
fr om 55 h igh sch ools, wh ich r eflects th e tota l
of lower secon da r y sch ools (gym n a siu m s) in
Cypr u s. In ter m s of stu den ts popu la tion , 5,852
ou t of a tota l of 19,694 stu den ts pa r ticipa ted in
th e stu dy, fr om both th e seven th a n d eigh th
gr a des of h igh sch ool (a ges 13-14 yea r s old).
Da ta a r e a ggr e ga ted to th e sch ool level. F u r th er m or e, n o da ta wer e u sed in th is stu dy
fr om th e pr in cipa ls’ qu estion n a ir e beca u se of
th e ver y low r espon se r a te obser ved, r e ga r din g fu lly com pleted qu estion n a ir es (less th a n
10 per cen t). Sch ool size w a s obta in ed fr om
secon da r y sou r ces th r ou gh th e Min istr y of
E du ca tion a n d Cu ltu r e.
For th e pu r poses of th is stu dy, a distin ction
w a s m a de between sch ools loca ted in u r ba n
a r ea s (33 sch ools) a n d th ose loca ted in r u r a l
a r ea s (22 sch ools). Th u s, two sepa r a te gr ou ps
wer e for m ed, a n d a ssessed sepa r a tely. Th is
distin ction pr ovides two desir a ble ou tcom es.
F ir st, th e cover a ge of DE A’s h om ogen eity of
u n its r equ ir em en t is m a in ta in ed. Secon d, th e
[ 69 ]
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
two gr ou ps w ill be u sed to dem on str a te possible en vir on m en ta l effects on th e efficien cies
of sch ools th r ou gh a ben ch m a r k in g a ppr oa ch
wh ich w ill be discu ssed la ter. Ta ble II pr esen ts descr iptive sta tistics on th e da ta collected fr om th e two gr ou ps.
th e TIMSS test cou ld be im pr oved, given its
in pu ts. Th e in pu t m in im iza tion m odel pr ovides in for m a tion on h ow m u ch a n in efficien t sch ool cou ld fu r th er r edu ce som e of its
in pu ts wh ile m a in ta in th e cu r r en t level of
per for m a n ce. Ta ble III pr ovides descr iptive
sta tistics on th e r esu ltin g efficien cy distr ibu tion s of in pu t m in im iza tion m odels.
It is n otewor th y th a t even th ou gh som e
in efficien cies a r e eviden t, th e over a ll efficien cies obser ved a r e h igh . Assu m in g, for exa m ple, CRS a n d u sin g Model 2, we h ave a m ea n
efficien cy va lu e of 96.56 for u r ba n a r ea
sch ools a n d 94.82 for r u r a l a r ea sch ools. A
possible expla n a tion of th is m ay in volve th e
tigh t con tr ol exh ibited by th e Min istr y of
E du ca tion w ith r espect to tea ch in g cu r r icu la ,
sch ool a ctivities a n d over a ll per for m a n ce.
Results and discussion
All th r ee m odels wer e r u n u n der both con sta n t r etu r n s to sca le (CRS) a n d va r ia ble
r etu r n s to sca le (VRS), sepa r a tely for th e
u r ba n a n d r u r a l gr ou p. F u r th er m or e, both
in pu t m in im iza tion a n d ou tpu t m a xim iza tion
DE A m odels wer e r u n for ea ch sch ool in ea ch
gr ou p, in or der to iden tify in efficien t a n d
best-pr a ctice sch ools. Th e ou tpu t m a xim iza tion m odel pr ovides in for m a tion on h ow
m u ch th e aver a ge stu den t per for m a n ce on
Table II
De sc riptive statistic s o f data c o lle c te d fo r urban and rural are a sc ho o ls
M aximum
M inimum
M ean
M edian
Std Dev
Urban area schools
Inputs
Age of teacher
Education level of teacher
Parents’ education
Socioeconomic status
School size
Number of books at student’s home
5
8
7.852
12.073
625
3.977
3
5
3.484
9.020
160
2.846
3.857
6.018
5.330
10.572
390.939
3.393
4
6
5.128
10.582
408
3.408
0.571
0.523
1.255
0.730
119.720
0.271
Output
International mathematics score
527.598
439.184
482.727
482.233
26.852
Rural area schools
Inputs
Age of teacher
Education level of teacher
Parents’ education
Socioeconomic status
School size
Number of books at student’s home
4.5
6.5
4.853
10.732
504
3.413
3
5
2.5
8.674
134
2.839
3.55
5.789
3.518
9.665
308.773
3.158
3.5
6
3.4
9.753
345
3.179
0.486
0.445
0.690
0.605
146.0053
0.184
Output
International mathematics score
484.511
418.969
455.740
454.123
18.327
Note:
See Appendix 2 for variable definition
Table III
De sc riptive statistic s o n e ffic ie nc y distributio ns o btaine d by the thre e mo de ls
M odel 1
CRS
VRS
Urban
Rural
Urban
Rural
M ean
M inimum
M aximum
Percentage share of
efficient schools
[ 70 ]
M odel 2
CRS
VRS
Urban
Rural
Urban
Rural
M odel 3
CRS
VRS
Urban
Rural
Urban
Rural
95.95
86.82
100
94.34
83.68
100
97.00
88.96
100
96.71
86.67
100
96.56
87.31
100
94.82
83.68
100
97.94
92.33
100
96.71
86.67
100
97.10
90.30
100
96.78
88.13
100
98.11
91.75
100
98.50
90.04
100
27.3
27.3
33.3
59.1
33.3
31.8
36.4
59.1
36.4
45.5
39.4
68.2
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
Ta ble IV pr esen ts in pu t m in im iza tion sa m ple
r esu lts a n d su ggested im pr ovem en t gu idelin es for on e of th e in efficien t sch ools, sch ool
X, th a t cou ld br in g it in lin e w ith its peer
gr ou p. Accor din g to th e ta ble, a n oth er sch ool
(or com bin a tion of oth er sch ools) exists, in
wh ich th e tea ch er s a r e on aver a ge you n ger,
th e pa r en ts’ edu ca tion , th e socioecon om ic
sta tu s a n d th e tea ch er s’ edu ca tion is lower,
bu t th e aver a ge scor e on th e TIMSS exa m w a s
equ a lly good. Th e m odel poin ts tow a r ds a r ea s
wh ich m ay n eed im pr ovem en t, su ch a s, for
exa m ple, th e qu a lity of th e tea ch er s a s it
r ela tes to th eir a ge a n d edu ca tion , a n d th e
r esu ltin g im plica tion s for on -goin g tea ch er
tr a in in g.
Clea r ly, n ot a ll th e r ecom m en da tion s of th e
m odel a r e fea sible. Im pr ovin g th e stu den ts’
socioecon om ic sta tu s is n ot a sh or t-ter m
effor t, n eith er is a fea sible effor t by th e
pr in cipa l of th e sch ool a lon e. Oth er r ecom m en da tion s, su ch a s th e qu a lity of th e tea ch er s ca n be im plem en ted w ith th e colla bor a tion of th e a u th or ities. Su ch a possible str a te gy cou ld in volve th e r ota tion of tea ch er s
a m on g differ en t sch ools[4]. Th e fea sibility of
th e m odels’ r ecom m en da tion s m u st be exa m in ed on a sch ool ba sis in colla bor a tion w ith
th e pr in cipa l of th e sch ool a n d th e pr oper
a u th or ities. Th e ou tpu t m a xim iza tion ver sion of th e m odel ca n a lso pr ovide th e exa m
scor e level wh ich cold be a ch ieved by th e
sch ool, given its cu r r en t in pu ts.
We a lso obser ve in Ta ble IV th a t th e ta r get
sch ool con str u cted by th e m odel – wh ich is a
lin ea r com bin a tion of existin g sch ools – is
sm a ller in size com pa r ed to sch ool X. Th is
ca n , to som e exten t, expla in wh y th e vir tu a l
sch ool per for m s better sin ce sm a ller sch ools
m ay per for m “better ”. On th e oth er h a n d,
su ch size differ en ce m ay deem th e com pa r ison u n fa ir. E xa m in a tion of th e peer sch ools of
sch ool X ca n h elp iden tify “well-beh aved”
sch ools a n d pr ovide th e m ea n s for a m or e fa ir
com pa r ison . For exa m ple, Ta ble V pr esen ts
a ctu a l da ta fr om sch ool Y, on e of th e peer
Table IV
Ac tual and targe t value s fo r all variable s as
indic ate d by DEA fo r sc ho o l X
School X
Actual value
Target value
Socioeconomic status
Teachers’ age
Teachers’ education
Parents’ education
Students’ population
International
mathematics score
10.00
4.50
6.00
4.10
344.00
8.60
3.00
5.00
3.20
69.00
450.10
450.10
Table V
Co mpariso n o f an ine ffic ie nt sc ho o l with a
sc ho o l similar in size
Socioeconomic status
Teachers’ age
Teachers’ education
Parents’ education
Students’ population
International
mathematics score
School X
(actual)
Peer for X
(actual)
10.00
4.50
6.00
4.10
344.00
8.90
4.00
5.00
3.90
337.00
450.10
463.10
sch ools of sch ool X. Th e two sch ools a r e sim ila r in size.
We obser ve th a t th e aver a ge edu ca tion of
tea ch er s, for exa m ple, a t th e peer of sch ool X
is lower th a n th a t obser ved a t X. F u r th er
investiga tion in to h ow ca n sch ool X ca pita lize
on th e a dva n ta ge of its tea ch er s to in cr ea se
th e TIMSS exa m in a tion scor e sh ou ld be
in itia ted.
Benchmarking the ef fects of the
environment
On e of th e pr im a r y goa ls of th e stu dy is to
ben ch m a r k th e possible en vir on m en ta l effect
on th e efficien cies of sch ools. Ba sed on th e
distin ction of ou r da ta set in to two h om ogen eou s su bgr ou ps – u r ba n a n d r u r a l a r ea
sch ools – we w ill u tilize a n a ppr oa ch pr oposed by Ch a r n es et a l. (1981) wh ich isola tes
a n d eva lu a tes sch ool pr ogr a m m e efficien cy.
Her e, we follow th e a ppr oa ch in a sim ila r
m a n n er to isola te a n d a ssess th e en vir on m en ta l im pa ct on sch ool efficien cy.
Th e a ppr oa ch (a lso descr ibed in Zen ios et
a l., 1995), pr oceeds in th r ee steps:
S tep 1. Ru n th e DE A m odel on two gr ou ps
oper a tin g in two differ en t en vir on m en ts.
S tep 2. P r oject in efficien t u n its on th eir
cor r espon din g efficien t fr on tier. Com bin e
pr ojected a n d efficien t u n its fr om both
gr ou ps a n d r u n th e DE A a ga in on th e pooled
da ta set.
S tep 3. E xa m in e wh eth er th e r esu ltin g efficien cy distr ibu tion s in ea ch gr ou p a r e differ en t. Th is ca n be don e by u sin g Ma n n -Wh itn ey
n on -pa r a m etr ic tests, sin ce th e r esu ltin g
distr ibu tion s a r e n ot lik ely to follow n or m a lity.
Th e u r ba n a n d r u r a l a r ea sch ools wer e
pooled togeth er a n d th e a bove pr ocedu r e w a s
followed. Th e r esu ltin g efficien cies su ggest
th a t th er e is n o sta tistica lly sign ifica n t efficien cy differ en ces between u r ba n a n d r u r a l
a r ea sch ools (p < 0.001).
[ 71 ]
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
Th e TIMSS scor es sh ow n in Ta ble II su ggest
th a t u r ba n sch ools in deed ou tper for m ed r u r a l
sch ools (p < 0.05). Th e a bove r esu lt, h owever,
su ggests th a t differ en ces in in efficien cy of
sch ools ca n n ot be attr ibu ted to envir on m en ta l
in flu en ces. Th u s, a n y cor r ective a ction s
sh ou ld be a im ed at ch a n gin g th e in ter n a l
r a th er th a n th e exter n a l envir on m en t.
Limitations and future research
Th e m odels developed in th e stu dy we
descr ibed a bove wer e lim ited by da ta ava ila bility, a n d th u s m yopic in n a tu r e. On ly a
sin gle ou tpu t w a s con sider ed, ba sed on a
sin gle exa m on a sin gle su bject, given to
eigh th gr a der s. Th e ou tpu t set sh ou ld be
expa n ded to r efl ect m or e desir a ble sch ool
ou tcom es. Th u s, ou tpu ts wh ich in clu de oth er
su bjects sh ou ld a lso be in cor por a ted in th e
set, r epr esen ta tive of th e wh ole body of stu den ts. Mu sic a n d a th letics ou tpu ts sh ou ld
a lso be con sider ed. Th e in pu t set sh ou ld a lso
in clu de fu r th er in for m a tion on th e tea ch er s’
tr a in in g a n d qu a lity, th e sch ools’ r esou r ces,
a n d th e socioecon om ic en vir on m en t.
F u r th er m or e, th is w a s a cr oss-section a l
stu dy con du cted a t a sin gle poin t in tim e.
Stu dies of a dyn a m ic n a tu r e sh ou ld a lso con sider ch a n ges over tim e. As da ta ava ila bility
th r ou gh stu dies su ch a s TIMSS in cr ea ses,
su ch dyn a m ic stu dies w ill a lso be m a de
possible.
F in a lly, of extr em e in ter est w ill be stu dies
wh ich w ill focu s on in ter n a tion a l com pa r ison s. Th e focu s of TIMSS for exa m ple w a s to
pr ovide th e m ea n s to com m u n ica te k n ow ledge a cr oss cou n tr ies. Sch ool per for m a n ce
ca n gr ea tly ben efi t fr om in ter n a tion a l stu dies
wh ich w ill exa m in e both th e in pu t a n d th e
ou tpu t side of th e sch ool effectiven ess pictu r e. It wou ld be of gr ea t in ter est to exa m in e
h ow th e efficien cy of sch ools ch a n ge a s th ey
a r e com pa r ed a ga in st sch ools oper a tin g in
differ en t edu ca tion a l system s.
Conclusion
In th is pa per we develop DE A m odels to
a ssess th e efficien cy of secon da r y sch ools in
Cypr u s. We dem on str a te h ow in efficien t
u n its ca n ben efi t fr om su ch a n a lysis a n d be
dir ected tow a r ds a r ea s wh ich m ay r equ ir e
im pr ovem en t.
On e of th e m a jor fi n din gs w a s th a t in th e
ca se of Cypr u s, r oom for sch ool efficien cy
im pr ovem en t exists, even th ou gh n ot gr ea t.
Despite th e low r a n k in gs sch ools in Cypr u s
obta in ed du r in g th e TIMSS, m ost of th e
sch ools fin d th em selves ver y close to th e
efficien t fr on tier. Th ese r esu lts em ph a size th e
existin g h om ogen eity between sch ools a s fa r
[ 72 ]
a s efficien cy is con cer n ed, a n d u n der lin e th e
im por ta n ce of fu tu r e in ter n a tion a l efficien cy
stu dies. As in ter n a tion a l da ta ava ila bility
th r ou gh stu dies su ch a s TIMSS in cr ea ses,
su ch stu dies w ill a lso be m a de possible.
F u r th er m or e, we fou n d n o efficien cy differ en ces wh ich ca n be a ttr ibu ted solely to th e
en vir on m en t, despite th e lower scor es
obser ved in r u r a l a r ea s. Th is is a n im por ta n t
fin din g for sch ools in Cypr u s, sin ce th e
effor ts tow a r ds im pr ovem en t ca n n ow focu s
on th e sch ool level a lon e.
Notes
1 E ven th ou gh n ot a s popu la r, sim u lta n eou s
equ a tion m odels to estim a te m u ltiple ou tpu t
pr odu ction tech n ologies, a n d th u s over com e
th is pr oblem , h ave been pr oposed by Levin
(1970) a n d Mich elson (1970).
2 Th is ca n be a ch ieved by settin g th e n u m er a tor
of (2) to a con sta n t a n d m in im izin g th e
den om in a tor
(Min im ize
3 F u r th er in for m a tion on th e TIMSS stu dy is
pr ovided in th e follow in g In ter n et a ddr ess
h ttp:/ / w w w csteep.bc.edu / tim ss
4 Alth ou gh tea ch er r ota tion a m on g differ en t
sch ools is cu r r en tly obser ved, efficien cy fin din gs su ch a s th e on es obta in ed h er e a r e n ot
con sider ed wh en m a k in g decision s on th ese
r ota tion s.
References and further reading
Ba n k er, R.D., Ch a r n es, A. a n d Cooper, W.W. (1984),
“Models for estim a tion of tech n ica l a n d sca le
in efficien cies in da ta en velopm en t a n a lysis”,
M a n a gem en t S cien ce, Vol. 30, pp. 1078-92.
Bessen t, A. a n d Bessen t, W. (1983), “E va lu a tion of
edu ca tion a l pr ogr a m pr oposa ls by m ea n s of
da ta en velopm en t a n a lysis”, Ed u ca tion a l
A d m in istra tion Qu a r terly, Vol. 19 N o. 2,
pp. 82-107.
Bou ssofi a n e, A., Dyson , R.G. a n d Th a n a ssou lis, E .
(1991), “Applied da ta en velopm en t a n a lysis”,
Eu ropea n J ou r n a l of Opera tion a l R esea rch ,
Vol. 52, pp. 1-15.
Ca m er on , K. (1978), “Mea su r in g or ga n iza tion a l
effectiven ess in in stitu tion s of h igh er edu ca tion ”, A d m in istra tiv e S cien ce Qu a r terly,
Vol. 23, pp. 604-32.
Ch a r n es, A., Cooper, W.W. a n d Rh odes, E . (1978),
“Mea su r in g th e efficien cy of decision m a k in g
u n its”, Eu ropea n J ou r n a l of Opera tion a l
R esea rch , Vol. 2, pp. 429-44.
Ch a r n es, A., Cooper, W.W. a n d Rh odes, E . (1981),
“E va lu a tin g pr ogr a m a n d m a n a ger ia l efficien cy: a n a pplica tion of da ta en velopm en t
a n a lysis to pr ogr a m follow th r ou gh ”, M a n a gem en t S cien ce, Vol. 27, pp. 668-97.
F itzsim m on s, J .A. a n d F itzsim m on s, M.J . (1994),
S er vice M a n a gem en t for Com petitiv e A dva n ta ge, McGr aw -Hill, N ew Yor k , N Y.
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
Gola n y, B. a n d Ta m ir, E . (1995), “E va lu a tin g efficien cy-effectiven ess-equ a lity tr a de-offs: a da ta
en velopm en t a n a lysis a ppr oa ch ”, M a n a gem en t S cien ce, Vol. 41 N o. 7, pp. 1172-84.
Gr ay, J . (1981), “Sch ool effectiven ess r esea r ch : k ey
issu es”, Ed u ca tion a l R esea rch , Vol. 24 N o. 1,
pp. 49-54.
J oh n es, G. a n d J oh n es, J . (1993), “Mea su r in g th e
r esea r ch per for m a n ce of UK econ om ics
depa r tm en ts: a n a pplica tion of da ta en velopm en t a n a lysis”, Ox ford Econ om ic Pa pers,
Vol. 45, pp. 332-47.
Levin , H.M. (1970), “A n ew m odel of sch ool effectiven ess”, in US Depa r tm en t of Hea lth , E du ca tion a n d Welfa r e, Do T ea ch ers M a k e a Differ en ce?, US Gover n m en t P r in tin g Office, Wa sh in gton , DC.
Mich elson , S. (1970), “Th e a ssocia tion of tea ch er
r esou r ces w ith ch ildr en ch a r a cter istics”, in
US Depa r tm en t of Hea lth , E du ca tion a n d
Welfa r e, Do T ea ch ers M a k e a Differen ce?, US
Gover n m en t P r in tin g Office, Wa sh in gton , DC.
N or m a n , M. a n d Stock er, B. (1991), Da ta En v elopm en t A n a lysis: th e A ssessm en t of Per for m a n ce,
Wiley, Ch ich ester.
Ray, S.C. (1991), “Resou r ce-u se efficien cy in pu blic
sch ools: a stu dy of Con n ecticu t da ta ”, M a n a gem en t S cien ce, Vol. 37 N o. 12, pp. 1620-8.
Sa m m on s, P., N u tta ll, D. a n d Cu tta n ce, D. (1993),
“Differ en tia l sch ool effectiven ess: r esu lts
fr om a r ea n a lysis of th e In n er Lon don Au th or ity’s ju n ior sch ool pr oject da ta ”, B r itish Ed u ca tion a l R esea rch J ou r n a l, Vol. 19, pp. 381-405.
Sa sser, W.E ., Olsen , R.P. a n d Wyckoff, D.D. (1978),
M a n a gem en t of S er vice Opera tion s, Allyn &
Ba con , Boston .
Sexton , T.R. a n d Sleeper, S. (1994), “Im pr ovin g
pu pil tr a n spor ta tion in N or th Ca r olin a ”,
In ter fa ces, Vol. 24 N o. 1, pp. 87-103.
Th a n a ssou lis, E . (1996), “Alter in g th e bia s in
differ en tia l sch ool effectiven ess u sin g da ta
en velopm en t a n a lysis”, J ou r n a l of th e Opera tion a l R esea rch S ociety, Vol. 47, pp. 882-94.
Th a n a ssou lis, E . a n d Du n sta n , P. (1994), “Gu idin g
sch ools to im pr oved per for m a n ce u sin g da ta
en velopm en t a n a lysis: a n illu str a tion w ith
da ta fr om a loca l edu ca tion a l a u th or ity”,
J ou r n a l of th e Opera tion a l R esea rch S ociety,
Vol. 45, pp. 1247-62.
Zen ios, C., Zen ios, A.S., Aga th ocleou s, K. a n d
Soter iou , A.C. (1995), B en ch m a rk s of th e Efficien cy of B a n k B ra n ch es, Repor t 95-10, Depa r tm en t of P u blic a n d Bu sin ess Adm in istr a tion ,
Un iver sity of Cypr u s, N icosia , Cypr u s.
su bject to:
for a ll i = 1, 2, …, I,
(17)
for a ll r = 1, 2, …, R ,
(18)
(19)
(20)
(21)
Com pa r in g (M 4) to (M 3), we n otice th a t th eir
on ly differ en ce is estim a ted in th e in clu sion
of con str a in t (18). Th is con vexity con str a in t
r equ ir es th a t m u ltiplier s λj sh ou ld a dd u p to
1, th u s en su r in g th e com pa r ison of DMUs
a ga in st a com posite u n it of sim ila r size.
Appendix 2
Variables used
Inputs
Age of teacher
Parents’
education
Categories inc lude sec ondary
educ ation, university or postgraduate
studies, etc .
Socioeconomic
status
Data are obtained from questioning
the student about the existenc e of a
variety of things at his home, suc h as
tape rec order, c omputer, speed boat,
satellite antenna
School size
Measured by student population
Number of
books at
student’s
home
Existenc e of five c ategories:
1. 0-10 books
2. 11-25
3. 26-100
4. 101-200
5. More than 200 books
The student is asked to estimate
the number of books at his home,
exc luding sc hool books, newspapers
and magazines
Variable returns to scale model
Min im ize
(16)
Below 25 years
25-29
30-39
40-49
50-59
60 and above
Education level Categories inc lude options suc h as
of teacher
BSc / BA, MA, PhD etc .
Appendix 1
(M 4)
1.
2.
3.
4.
5.
6.
Output
International
mathematics
score
Average sc ore ac hieved at the sc hool
level in the mathematic s sec tion of
the TIMSS study
[ 73 ]
schools: the case of Cyprus
Andreas C. Soteriou
De partme nt o f Busine ss Administratio n, Unive rsity o f Cyprus, Nic o sia, Cyprus
Elena Karahanna
De partme nt o f Busine ss Administratio n, Unive rsity o f Cyprus, Nic o sia, Cyprus
Constantinos Papanastasiou
De partme nt o f Educ atio n, Unive rsity o f Cyprus, Nic o sia, Cyprus
M anolis S. Diakourakis
De partme nt o f Busine ss Administratio n, Unive rsity o f Cyprus, Nic o sia, Cyprus
This study utilizes the
methodology of data envelopment analysis (DEA) to assess
the efficiency of secondary
schools in Cyprus. Apart from
evaluating the relative efficiency of schools, the study
provides recommendations
for improvement to inefficient
schools and discusses managerial implications. Furthermore, empirical fi ndings
based on an approach to
estimate efficiency environmental effects suggest that
no efficiency differences exist
between schools operating in
rural areas compared to
those operating in urban
areas.
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [ 1998] 6 5 –7 3
© MCB Unive rsity Pre ss
[ ISSN 0951-354X]
Introduction
Assessin g th e per for m a n ce of a n edu ca tion a l
system is a n im por ta n t bu t difficu lt to a ccom plish ta sk . E du ca tion a l ser vices fea tu r e a ll
th e distin ctive ch a r a cter istics of ser vices visà -vis m a n u fa ctu r in g, su ch a s per ish a bility,
h eter ogen eity a n d sim u lta n eity (F itzsim m on s a n d F itzsim m on s, 1994; Sa sser et a l.,
1978). Despite th e difficu lties in volved, sch ool
per for m a n ce a ssessm en t ca n , a m on g oth er s,
be u sed to set per for m a n ce ta r gets, to m a k e
r esou r ce a lloca tion decision s, a n d to im pr ove
over a ll sch ool per for m a n ce.
Sch ool u n its bea r fu r th er sim ila r ities to
ser vice or ga n iza tion a l u n its in th e sen se th a t
th ey u tilize m u ltiple in pu ts to pr odu ce m u ltiple ou tpu ts (Ca m er on , 1978). A n u m ber of
com m on pr oblem s em er ge wh en a ttem ptin g
to a ssess ser vice or ga n iza tion a n d sch ool
per for m a n ce. F ir st, n o u ltim a te cr iter ion of
effectiven ess exists, sin ce a u n it (ser vice
or ga n iza tion or sch ool) m ay typica lly pu r su e
m u ltiple, a n d often con tr a dictor y goa ls. Releva n t cr iter ia m ay a lso ch a n ge over th e lifecycle of th e u n it. Differ en t u n its m ay a ssign
pa r ticu la r im por ta n ce to differ en t or ga n iza tion a l a spects a t differ en t tim es. Mor eover,
cr iter ia a t on e or ga n iza tion a l level m ay n ot
be th e sa m e a s th ose a t a n oth er or ga n iza tion a l level, wh ile r ela tion sh ips a m on g va r iou s effectiven ess dim en sion s m ay be difficu lt
to discover.
Differ en t cr iter ia h ave tr a dition a lly been
defin ed for a ssessin g sch ool per for m a n ce.
Typica lly, sch ool effectiven ess h a s been m ea su r ed in ter m s of th e per for m a n ce of stu den ts
in exa m in a tion s (see Gr ay, 1981), for a discu ssion on sch ool ou tcom es). Oth er con textu a l
fa ctor s su ch a s th e stu den ts’ socioecon om ica l
ba ck gr ou n d a n d oth er en vir on m en ta l va r ia bles a r e a lso con sider ed. In th is pa per we
follow a (popu la r in th e liter a tu r e) pr odu ction
or “va lu e-a dded” a ppr oa ch in wh ich th e
sch ool u tilizes som e in pu ts (i.e. n u m ber of
in str u ctor s, exper ien ce of in str u ctor s, socioecon om ic ba ck gr ou n d of stu den ts, etc.) to pr odu ce som e ou tpu ts (i.e. exa m in a tion scor es).
On e of th e m eth odologies u sed in pr eviou s
stu dies of sch ool per for m a n ce eva lu a tion
ba sed on in pu t-ou tpu t a n a lysis h a s been or din a r y lea st squ a r es (OLS) r e gr ession a n a lysis.
Su ch stu dies h ave, h owever, two m a jor disa dva n ta ges (Ray, 1991). F ir st, pr edicted va lu es
r esu ltin g fr om a r e gr ession m odel pr ovide
th e aver a ge or expected level of ou tcom e
given cer ta in in pu ts, in stea d of th e m a xim u m
a ch ieva ble ou tcom e. Secon d, th e in pu t/ ou tpu t pr odu ction fu n ction specified by su ch
m odels m ay be pr oblem a tic. Most r e gr ession
m odels u se a sin gle ou tpu t pr odu ction fu n ction , wh ich m ay be u n r ea listic wh en a ssessin g sch ool per for m a n ce[1].
In th is pa per we focu s on th e a ssessm en t of
th e efficien cy of secon da r y sch ools in Cypr u s.
In a r ecen t stu dy by th e In ter n a tion a l Associa tion for th e E va lu a tion of E du ca tion a l
Ach ievem en t, th e sch ools of Cypr u s r a n k ed
low com pa r ed to 41 oth er cou n tr ies wh ich
a lso pa r ticipa ted in th e stu dy. However, exa m in in g on ly th e sch ools’ ou tpu t does n ot pr ovide a com plete pictu r e r e ga r din g per for m a n ce. It is im por ta n t to k n ow wh eth er
sch ools a r e a ctu a lly u tilizin g th eir r esou r ces
in th e m ost efficien t w ay to pr odu ce th e
obser ved r a n k in gs. In a ddition , it is a lso
im por ta n t to pr ovide gu idelin es on h ow
sch ools ca n im pr ove fu r th er.
Her e, we u tilize th e n on -pa r a m etr ic m eth odology of da ta envelopm en t a n a lysis (DE A)
(Ch a r n es et a l., 1978). DE A, a state-of-th e-a r t
n on -pa r a m etr ic m eth odology, ca n be u sed to
a ssess per for m a n ce of h om ogen eou s u n its
u tilizin g m u ltiple in pu ts to pr odu ce m u ltiple
ou tpu ts. DE A en joys a n u m ber of a dva n ta ges
over oth er tr a dition a l pa r a m etr ic m eth ods,
a n d h a s been u sed exten sively to a ssess sch ool
per for m a n ce (Nor m a n a n d Stock er, 1991;
Sa m m on s et a l., 1993; Th a n a ssou lis a n d
Du n sta n , 1994). Apa r t fr om eva lu a tin g th e
[ 65 ]
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
r ela tive efficien cy of secon da r y sch ools, th is
stu dy pr ovides r ecom m en da tion s for im pr ovem en t to in efficien t sch ools a n d discu sses
m a n a ger ia l im plica tion s.
Th e pa per is or ga n ized a s follow s. We n ext
pr ovide a descr iption of th e da ta envelopm en t
a n a lysis m eth odology. A br ief liter a tu r e
r eview on th e DE A a pplica tion s in edu ca tion a l settin gs follow s. N ext, we descr ibe a n
em pir ica l stu dy wh ich u tilizes DE A to a ssess
th e efficien cy of secon da r y sch ools in th e
cou n tr y of Cypr u s. Addition a l in sigh ts to th e
pr oblem of sch ool eva lu a tion a r e pr esen ted by
ben ch m a r k in g th e effect of th e exter n a l en vir on m en t th r ou gh th e com pa r ison of u r ba n
a n d r u r a l sch ool efficien cy. Ma n a ger ia l im plica tion s, lim ita tion s a n d fu tu r e r esea r ch a r e
a lso discu ssed. Con clu din g r em a r k s follow.
u r K = weigh t given to ou tpu t r,
0
v iK
0
R
I
= weigh t given to in pu t i,
= n u m ber of ou tpu ts,
= n u m ber of in pu ts.
As lon g a s th e u n it u n der con sider a tion
r em a in s a sin gle DMU, we cou ld r eta in th e
pr ecedin g defin ition . However, a n attem pt of
defin in g efficien cy for a gr ou p of DMUs
sim u lta n eou sly is n ot possible u sin g ju st
defin ition (1), sin ce a com m on set of weigh ts
is difficu lt to be set a m on g a ll DMUs of a ser vice or ga n iza tion or system .
E a ch DMU ca n be a llowed to ch oose its ow n
set of weigh ts ba sed on its ow n va lu e system
(Ch a r n es et a l., 1978) in a n a ttem pt to a ppea r
a s efficien t a s possible. Th e follow in g m odel
is for m ed ba sed on defin ition (1):
(M 1)
Data envelopment analysis
Th e m eth odology of da ta envelopm en t a n a lysis, in itia lly in tr odu ced by Ch a r n es et a l.
(1978), is a m a th em a tica l pr ogr a m m in g tech n iqu e u sed to eva lu a te th e r ela tive efficien cy
of h om ogen eou s u n its. Th is efficien cy eva lu a tion der ives fr om a n a lysin g em pir ica l obser va tion s obta in ed fr om decision -m a k in g u n its
(DMUs), a ter m coin ed by Ch a r n es et a l. (1978)
to defin e pr odu ctive u n its wh ich a r e ch a r a cter ized by com m on m u ltiple ou tpu ts a n d
com m on design a ted in pu ts.
Rela tive h om ogen eity of or ga n iza tion a l
u n its su ch a s sch ools, ba n k br a n ch es or h ospita ls, pr ovides in sta n ces for im plem en ta tion
of th e DE A m eth odology. In a m or e gen er a l
m a n n er, DE A is m ost u sefu l in ca ses wh er e
a ccou n tin g a n d fi n a n cia l r a tios a r e of little
va lu e, m u ltiple ou tpu ts a r e pr odu ced th r ou gh
th e tr a n sfor m a tion of m u ltiple in pu ts, a n d
th e in pu t-ou tpu t tr a n sfor m a tion r ela tion sh ips a r e n ot k n ow n (Ch a r n es et a l., 1978).
In a br oa d sen se, efficien cy of a sin gle DMU
k 0 oper a tin g in a h om ogen eou s set of N
DMUs, u tilizin g m u ltiple in pu ts I to pr odu ce
m u ltiple ou tpu ts R , ca n be defi n ed a s follow s :
(1)
Ma xim ize
(2)
su bject to:
(3)
u r K , v iK ≥ 0 for a ll r = 1, …, R , a n d i = 1, …, I,
0
0
(4)
Th r ou gh M 1, ea ch DMU K 0 a n a lysed w ill
specify th e pa r ticu la r in pu t a n d ou tpu t
weigh ts (u a n d v r espectively), wh ich m a xim ize its ow n r a tio of weigh ted ou tpu t to
weigh ted in pu t, su bject to th e con str a in t th a t
n o oth er u n it u tilizin g th e sa m e weigh ts
cou ld exceed a n efficien cy r a tin g of 1. A DMU
w ith efficien cy r a tin g of 1 w ill be given th e
ch a r a cter iza tion of efficien t r ela tive to oth er
DMUs. Vice ver sa , a n efficien cy r a tin g of less
th a n 1 w ill lea d u s to ch a r a cter izin g th is specific u n it a s in efficien t in r ela tion to oth er s.
(M 1) r epr esen ts a fr a ction a l lin ea r pr ogr a m m in g (LP ) m odel. Th is ca n be ea sily
tr a n sfor m ed in to a sim ple lin ea r pr ogr a m , a s
follow s:
(M 2)
wh er e,
EK
0
yrK
0
Ma xim ize
(5)
= efficien cy of u n it K 0,
= a m ou n t of ou tpu t r = 1, …, R pr odu ced
su bject to:
by DMU K 0,
x iK
0
= a m ou n t of in pu t i = 1, …, I con su m ed
by DMU K 0,
[ 66 ]
(6)
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
(7)
(8)
wh er e,
E K = efficien cy of u n it K 0,
0
y rK
x iK
0
0
= a m ou n t of ou tpu t r pr odu ced by
DMU K 0,
= a m ou n t of in pu t i con su m ed by
DMU K 0,
u r K = weigh t given to ou tpu t r ,
0
v iK
0
= weigh t given to in pu t i,
Th e tr a n sfor m a tion is obta in ed by settin g th e
den om in a tor of (2) to a n a r bitr a r ily selected
con sta n t. A sim ila r m a n ipu la tion of equ a tion
(2) ca n r esu lt in a n in pu t m in im iza tion or ien ted lin ea r pr ogr a m m in g m odel[2].
Th e du a l for m u la tion of (M2) ca n pr ovide
a ddition a l in sigh ts a n d is com pu ta tion a lly
less expen sive:
(M 3)
Min im ize
(9)
Th e size of th e n ecessa r y decr ea se is in dica ted by th e va lu e of H K .
0
F r om th e scope of com pu ta tion a l effor t, th e
fa ct th a t (M 3) h a s on ly (I + R ) con str a in ts
com pa r ed to (N + R + I + 1) con str a in ts of
m odel (M 2) a n d N is typica lly m u ch la r ger
th a n I + R , deem s (M 3) ea sier to solve in
com pa r ison to (M 2). An a ddition a l a dva n ta ge
of (M 3) is th e pr ovision of ta r get va lu es for
in efficien t u n its by com pa r in g th em a ga in st a
com posite u n it con str u cted by th e a ctu a l
per for m a n ce of th e r est of th e u n its (Bou ssofia n e et a l., 1991). Th ese ta r gets ca n pr ovide
gu idelin es for im pr ovem en t to in efficien t
u n its. At optim a lity, th e follow in g in pu t/
ou tpu t va lu es occu r :
for a ll i = 1, 2, …, n
(14)
for a ll r = 1, 2, …, m
(15)
wh er e * in dica tes optim a lity. Th ese a r e in pu tor ien ted ta r gets sin ce th e a ttem pt h er e is to
m in im ize in pu ts. Ou tpu t-or ien ted ta r gets ca n
a lso be der ived by dividin g both
su bject to:
for a ll i = 1, 2, …, I,
(10)
for a ll r = 1, 2, …, R ,
(11)
(12)
(13)
wh er e s r+ a n d s i– r epr esen t th e sla ck va r ia bles
cor r espon din g to th e ou tpu ts a n d in pu ts
r espectively.
Ba sed on m odel (M 3) we ca n ch a r a cter ize
DMU K 0 efficien t a s lon g a s th e va lu e of H K is
0
equ a l to 1. If H K exceeds th e lower lim it of 1,
0
th e DMU u n der a ssessm en t is ch a r a cter ized
in efficien t in com pa r ison to oth er DMUs.
Th a t is, th er e exists a weigh ted com bin a tion
of a ctu a l per for m a n ce of oth er u n its, su ch
th a t n o ou tpu t of u n it K 0 exceeds th a t of th e
weigh ted ou tpu t of th e weigh ted com bin a tion . At th e sa m e tim e, we cou ld r edu ce a ll
in pu ts of K 0 by th e pr opor tion H K w ith ou t
0
a n y in pu t fa llin g below th a t of th e
cor r espon din g weigh ted com bin a tion of oth er
u n its. If DMU K 0 is deem ed in efficien t, m a n a gem en t cou ld decr ea se a ll th e in pu ts of K 0 in
th e sa m e pr opor tion , in or der to a ch ieve th e
desir ed weigh ted com bin a tion per for m a n ce.
Model (M 3) w a s in tr odu ced by Ch a r n es et a l.
(1978) ba sed on th e a ssu m ption of con sta n t
r etu r n s to sca le. However, wh ile th is a ssu m ption cou ld often be le gitim a te, it m ay n ot be
va lid in ca ses wh er e th e sca le of oper a tion s
cou ld in flu en ce a DMU’s efficien cy r a tin g,
su ch a s, for exa m ple, wh en a ssessin g sch ool
per for m a n ce. Mor eover, in for m a tion con cer n in g th e a m ou n t of in efficien cies ow in g to
th e sca le of oper a tion s wou ld pr ove to be ver y
u sefu l for m a n a ger ia l decision s. Appen dix 1
pr esen ts a m odel descr ibed by Ba n k er et a l.
(1984) to cover th e issu e of in efficien cies du e
to sca le of oper a tion s, th r ou gh a n exten sion
of m odel (M 3).
Applications of DEA in education
Applica tion s of DE A to m ea su r e th e efficien cy
of edu ca tion a l pr odu ction h ave exten sively
been r epor ted in liter a tu r e, begin n in g w ith
th e in tr odu ctor y pa per of DE A (Ch a r n es et a l.,
1978), wh ich in tr odu ced th e DE A m eth odology
by dem on str a tin g it in a sch ool settin g. Th e
a im of th is section is n ot to pr esen t a th or ou gh
liter a tu r e r eview of DE A a pplica tion s in edu ca tion , bu t r a th er to pr esen t som e of th e m or e
r eleva n t stu dies to th is wor k .
Ch a r n es et a l. (1981) a lso u sed da ta fr om th e
edu ca tion sector. Th e a u th or s con cen tr a ted in
th e com pa r ison of th e pr ogr a m m e follow
[ 67 ]
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
[ 68 ]
th r ou gh (P F T) a n d n on follow th r ou gh (N F T)
sch em es for pr im a r y sch ool ch ildr en in th e
USA. P a r ticipa n ts in P F T wer e ch ildr en wh o
ca m e fr om less a dva n ta ged ba ck gr ou n ds,
wh ile th e exper im en t a lso in clu ded a con tr ol
gr ou p of N F T ch ildr en for ea ch distr ict th a t
pa r ticipa ted in th e P F T. DE A w a s u sed in
or der to a ssess th e efficien cies of policies
w ith in wh ich m a n a ger s oper a te wh ile elim in a tin g th e in efficien cies or igin a tin g fr om th e
m a n a ger s th em selves.
An a lter n a tive u se of DE A is pr esen ted by
Bessen t a n d Bessen t (1983). Mor e specifica lly,
DE A is u sed for r esou r ce a lloca tion of va r iou s
pr ogr a m s in th e en vir on m en t of a com m u n ity
colle ge. Th e m a in con tr ibu tion of th e stu dy
w a s th e r ecogn ition th a t, in spite of som e
lim ita tion s, DE A cou ld pr ove h elpfu l in
r esou r ce a lloca tion . DE A ca n n ot, h owever,
pr ovide a n a n swer to th e qu estion of a lloca tin g tota l or ga n iza tion a l r esou r ces in or der to
obta in m a xim u m ou tpu t fr om th e u n its.
Bou ssofia n e et a l. (1991) u tilize th e con text
of com pa r in g sch ools for th e pu r pose of
dem on str a tin g pr a ctica l issu es en cou n ter ed
in selectin g a n d qu a lifyin g in pu ts a n d ou tpu ts. Sch ools wer e ch osen a s a n illu str a tion
m a in ly du e to th e im por ta n ce of en vir on m en ta l fa ctor s in th eir oper a tion . An im por ta n t
obser va tion of th e a u th or s is th e effect of th e
selection of in pu ts a n d ou tpu ts in th e discr im in a tor y power of DE A, wh ich m or e
specifica lly is r ela ted to th e n u m ber of
selected in pu ts a n d ou tpu ts. As a m in im u m
n u m ber of u n its th a t w ill be given th e ta g of
efficien t, a u th or s set th e pr odu ct of th e n u m ber of in pu ts a n d ou tpu ts.
In a sim ila r m a n n er, Gola n y a n d Ta m ir
(1995), u tilize h ypoth etica l da ta ta k en fr om a n
eva lu a tion of som e elem en ta r y sch ools in a
sch ool distr ict. Aim of th e illu str a tion is th e
distin ction between differ en t a spects eva lu a ted by efficien cy, effectiven ess a n d equ a lity,
in a ddition to specifyin g poten tia l tr a de-off
a m on g th em . In a n oth er r ecen t stu dy, Th a n a ssou lis (1996) dem on str a ted h ow to u se DE A to
set ta r gets for differ en tia lly effective sch ools.
J oh n es a n d J oh n es (1993) r efer to a n a pplica tion of th e m eth odology in u n iver sities. In
th e pa r ticu la r stu dy, DE A is u sed for a ssessin g th e r esea r ch per for m a n ce of UK depa r tm en ts of econ om ics du r in g 1984-88. DE A w a s
especia lly va lu a ble sin ce n o u n iver sa lly
a ccepted im por ta n ce weigh ts exist r e ga r din g
th e r eleva n t in pu ts a n d ou tpu ts. Th e pr oblem
w a s a ddr essed th r ou gh th e a llow a n ce of DE A
for ea ch u n it to deter m in e its ow n set of in pu t
a n d ou tpu t weigh ts su ch th a t it m a xim izes its
efficien cy. However, ea ch u n it is n ot com pletely fr ee to defin e its set, sin ce it is su bject
to th e con str a in t th a t n o oth er u n it cou ld
a ccom plish a n efficien cy r a tin g th a t exceeds
u n ity, ba sed on th e sa m e set of weigh ted
in pu ts a n d ou tpu ts.
Ray (1991) u tilized th e DE A m eth odology in
com bin a tion to r e gr ession a n a lysis in or der
to a ssess r ela tive efficien cy in pu blic sch ool
distr icts in Con n ecticu t, USA. Th r ou gh h is
a n a lysis h e poin ted ou t th e effect of socioecon om ic va r ia bles in pr odu ctivity va r ia tion s. A r ela tive pa per, in th e sen se th a t it
r efer s to com bin ed u se of DE A w ith r e gr ession a n a lysis, is pr esen ted by Sexton a n d
Sleeper (1994), a im in g a t fa cin g th e la ck of
h om ogen eity between DMUs in volved.
Assessing the ef fectiveness of
schools in Cyprus
M odel description
Stu dies of edu ca tion a l pr odu ction fu n ction
defin e two m a jor w ays of descr ibin g th e in fl u en ces of sch oolin g on stu den t a ch ievem en t.
E ith er ta k e in to a ccou n t th e cu m u la tive in flu en ce of fa m ily ba ck gr ou n d, peer s, sch ool
in pu t a n d in n a te a bilities on stu den t a ch ievem en t a t cer ta in tim e poin ts or m ea su r e th ese
fa ctor s du r in g th e per iod stu den t is a tten din g
sch ool.
Ou r stu dy u ses th e secon d a lter n a tive, a lso
k n ow n a s th e va lu e a d d ed m odel. Th is m odel
is con ven ien t in th e sen se th a t it r edu ces da ta
r equ ir em en ts, sin ce sch ool-level a ggr e ga ted
da ta ca n be u sed. Mor eover, edu ca tion a l
a ch ievem en t is a pr odu ct of both in pu ts con tr olla ble by th e sch ool bu t a lso of oth er fa ctor s su ch a s fa m ily ba ck gr ou n d, in n a te a bilities, peer s a n d for m er ou tcom es.
F igu r e 1 pr esen ts th e th eor etica l fr a m ewor k u n der lyin g th e developed m odels.
Th r ee gen er ic deter m in a n ts dr ive sch ool
per for m a n ce (Th a n a ssou lis, 1996). F ir st,
sch ool-specific fa ctor s su ch a s th e size of th e
sch ool, a n d th e n u m ber a n d qu a lity of th e
tea ch er s; secon d, fa ctor s wh ich a r e fa m ily a n d
exter n a l envir on m en t specific, su ch a s for
exa m ple, th e stu den ts’ socioecon om ic ba ck gr ou n d or th e location of th e sch ool; a n d
fin a lly, th e a bilities of th e stu den t h im / h er self.
Th r ee m odels, a s pr esen ted in Ta ble I wer e
con str u cted, ba sed on th e a bove fr a m ewor k
a n d on da ta ava ila bility. Th e sm a ll n u m ber of
Figure 1
Ge ne ric drive rs o f sc ho o l pe rfo rmanc e
Sc ho o l Re late d
Fac to rs
Stude nt
Charac te ristic s
Family and Exte rnal
Enviro nme nt Influe nc e s
Stude nt’ s
Pe rfo rmanc e
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
sch ools ava ila ble lim ited th e n u m ber of in pu t
a n d ou tpu t va r ia bles, in or der to pr eser ve th e
DE A m odel’s discr im in a tor y power. Th e m odels pr esen ted in Ta ble I pr oceed fr om a sim ple
(Model 1) to a m or e com plica ted in pu t set
(Model 3). All m odels in clu de a sin gle, com m on ou tpu t, con sistin g of th e scor e fr om
sta n da r dized exa m in a tion s su ch a s th e
TIMSS, to be discu ssed in th e n ext section .
Th e fir st m odel u ses in pu ts wh ich ca n be
obta in ed fr om tea ch er s’ a n d stu den ts’ qu estion n a ir es. Mor e specifica lly, it in clu des th e
a ge a n d edu ca tion a l level of tea ch er s, in a ddition to th e pa r en ts’ edu cation a n d th e socioecon om ic statu s of th e fa m ily. Model 2 a lso
in clu des sch ool da ta . Th a t is, th e size of th e
sch ool, defin ed a s th e stu den ts’ popu lation
w a s in clu ded. An a ddition a l in pu t is con sider ed by Model 3 to captu r e th e socioecon om ic
ba ck gr ou n d of stu den ts. Th e n u m ber of book s
a t stu den t’s h om e w a s u sed a s a pr oxy for th a t.
A descr iption of a ll th e va r ia bles in clu ded in
a ll th e m odels is sh ow n in Appen dix 2.
Data
Th e Th ir d In ter n a tion a l Ma th em a tics a n d
Scien ce Stu dy (TIMSS) w a s con du cted du r in g
th e m on th s of May-J u n e 1995. TIMSS is con du cted by th e In ter n a tion a l Associa tion for
th e E va lu a tion of E du ca tion a l Ach ievem en t
(IE A), in a tota l of 45 cou n tr ies, cover in g m or e
th a n h a lf a m illion stu den ts a t five gr a des
levels in m or e th a n 15,000 sch ools. Th e m a in
goa l of TIMSS is to pr ovide in ter n a tion a l
ben ch m a r k s r e ga r din g sch ool per for m a n ce.
Da ta wer e collected u sin g sta n da r dized
qu estion n a ir es, a dju sted to r efl ect cu ltu r a l
differ en ces, com pleted by sch ool pr in cipa ls,
tea ch er s a n d stu den ts.
TIMSS pr ovides th e va r iou s pa r ticipa tin g
cou n tr ies a veh icle w ith wh ich to in vestiga te
a va r iety of issu es, in clu din g wh a t con cepts
stu den ts u n der sta n d, h ow well th ey ca n a pply
th eir k n ow ledge in pr oblem -solvin g situ a tion s, a n d wh eth er th ey ca n com m u n ica te
th eir u n der sta n din gs. In for m a tion r e ga r din g
Table I
Variable s use d in the DEA e ffic ie nc y me asure me nt
Inputs
Age of teacher
Education level of teacher
Parents’ education
Socioeconomic status
School size
Number of books at student’s home
Output
International mathematics score
M odel 1
M odel 2
M odel 3
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
th ese issu es is ver y im por ta n t. Sk ills in m a th em a tics a n d scien ce a r e becom in g cr itica l to
econ om ic pr ogr ess du e to th e tr a n sfor m a tion
of m oder n societies in to m or e tech n ologica lly
ba sed, wh er e h igh er levels of tech n ica l com peten ce a n d flexible th in k in g a r e r equ ir ed[3].
TIMSS u tilized in for m a tion fr om stu den ts,
tea ch er s a n d sch ool pr in cipa ls a s follow s:
• Pr in cipa l qu estion n a ire. Th is in str u m en t
w a s a dm in ister ed to th e sch ool’s pr in cipa l.
It obta in ed gen er a l in for m a tion a bou t th e
sch ool, i.e. sch ool size, n u m ber of tea ch er s
tea ch in g a t sch ool for five or m or e yea r s,
in for m a tion on th e sch ool’s com m u n ity a n d
on th e n u m ber of depa r tm en t h ea ds.
• T ea ch er of m a th em a tics a n d scien ce qu estion n a ire. Da ta collected th r ou gh th is
in str u m en t, wh ich w a s a dm in ister ed to
tea ch er s, in clu de th e tea ch er ’s edu ca tion a l
ba ck gr ou n d, co-oper a tion w ith oth er tea ch er s for lesson en h a n cem en t, a n d tea ch in g
m eth odologies.
• S tu d en t in for m a tion . In for m a tion on su ch
va r ia bles a s th e socioecon om ic sta tu s of
stu den t’s fa m ily, pa r en ts’ edu ca tion a n d
n u m ber of book s a t h om e w a s ga th er ed via
a qu estion n a ir e. F u r th er m or e, m a th tests
wh ich cover ed six con ten t a r ea s (fr a ction s
a n d n u m ber s (34 per cen t), m ea su r em en t
(12 per cen t), pr opor tion a lity (7 per cen t),
da ta r epr esen ta tion , a n a lysis, a n d pr oba bility (14 per cen t), geom etr y (15 per cen t), a n d
a lgebr a (18 per cen t)) wer e a lso a dm in ister ed to seven th a n d eigh th gr a de stu den ts.
Ou r stu dy w a s ba sed on th e Ma th em a tics
TIMSS da ta a s collected in Cypr u s w ith th e
colla bor a tion of th e Min istr y of E du ca tion
a n d Cu ltu r e, th e Peda gogica l In stitu te, a n d
th e Un iver sity of Cypr u s. Da ta wer e ga th er ed
fr om 55 h igh sch ools, wh ich r eflects th e tota l
of lower secon da r y sch ools (gym n a siu m s) in
Cypr u s. In ter m s of stu den ts popu la tion , 5,852
ou t of a tota l of 19,694 stu den ts pa r ticipa ted in
th e stu dy, fr om both th e seven th a n d eigh th
gr a des of h igh sch ool (a ges 13-14 yea r s old).
Da ta a r e a ggr e ga ted to th e sch ool level. F u r th er m or e, n o da ta wer e u sed in th is stu dy
fr om th e pr in cipa ls’ qu estion n a ir e beca u se of
th e ver y low r espon se r a te obser ved, r e ga r din g fu lly com pleted qu estion n a ir es (less th a n
10 per cen t). Sch ool size w a s obta in ed fr om
secon da r y sou r ces th r ou gh th e Min istr y of
E du ca tion a n d Cu ltu r e.
For th e pu r poses of th is stu dy, a distin ction
w a s m a de between sch ools loca ted in u r ba n
a r ea s (33 sch ools) a n d th ose loca ted in r u r a l
a r ea s (22 sch ools). Th u s, two sepa r a te gr ou ps
wer e for m ed, a n d a ssessed sepa r a tely. Th is
distin ction pr ovides two desir a ble ou tcom es.
F ir st, th e cover a ge of DE A’s h om ogen eity of
u n its r equ ir em en t is m a in ta in ed. Secon d, th e
[ 69 ]
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
two gr ou ps w ill be u sed to dem on str a te possible en vir on m en ta l effects on th e efficien cies
of sch ools th r ou gh a ben ch m a r k in g a ppr oa ch
wh ich w ill be discu ssed la ter. Ta ble II pr esen ts descr iptive sta tistics on th e da ta collected fr om th e two gr ou ps.
th e TIMSS test cou ld be im pr oved, given its
in pu ts. Th e in pu t m in im iza tion m odel pr ovides in for m a tion on h ow m u ch a n in efficien t sch ool cou ld fu r th er r edu ce som e of its
in pu ts wh ile m a in ta in th e cu r r en t level of
per for m a n ce. Ta ble III pr ovides descr iptive
sta tistics on th e r esu ltin g efficien cy distr ibu tion s of in pu t m in im iza tion m odels.
It is n otewor th y th a t even th ou gh som e
in efficien cies a r e eviden t, th e over a ll efficien cies obser ved a r e h igh . Assu m in g, for exa m ple, CRS a n d u sin g Model 2, we h ave a m ea n
efficien cy va lu e of 96.56 for u r ba n a r ea
sch ools a n d 94.82 for r u r a l a r ea sch ools. A
possible expla n a tion of th is m ay in volve th e
tigh t con tr ol exh ibited by th e Min istr y of
E du ca tion w ith r espect to tea ch in g cu r r icu la ,
sch ool a ctivities a n d over a ll per for m a n ce.
Results and discussion
All th r ee m odels wer e r u n u n der both con sta n t r etu r n s to sca le (CRS) a n d va r ia ble
r etu r n s to sca le (VRS), sepa r a tely for th e
u r ba n a n d r u r a l gr ou p. F u r th er m or e, both
in pu t m in im iza tion a n d ou tpu t m a xim iza tion
DE A m odels wer e r u n for ea ch sch ool in ea ch
gr ou p, in or der to iden tify in efficien t a n d
best-pr a ctice sch ools. Th e ou tpu t m a xim iza tion m odel pr ovides in for m a tion on h ow
m u ch th e aver a ge stu den t per for m a n ce on
Table II
De sc riptive statistic s o f data c o lle c te d fo r urban and rural are a sc ho o ls
M aximum
M inimum
M ean
M edian
Std Dev
Urban area schools
Inputs
Age of teacher
Education level of teacher
Parents’ education
Socioeconomic status
School size
Number of books at student’s home
5
8
7.852
12.073
625
3.977
3
5
3.484
9.020
160
2.846
3.857
6.018
5.330
10.572
390.939
3.393
4
6
5.128
10.582
408
3.408
0.571
0.523
1.255
0.730
119.720
0.271
Output
International mathematics score
527.598
439.184
482.727
482.233
26.852
Rural area schools
Inputs
Age of teacher
Education level of teacher
Parents’ education
Socioeconomic status
School size
Number of books at student’s home
4.5
6.5
4.853
10.732
504
3.413
3
5
2.5
8.674
134
2.839
3.55
5.789
3.518
9.665
308.773
3.158
3.5
6
3.4
9.753
345
3.179
0.486
0.445
0.690
0.605
146.0053
0.184
Output
International mathematics score
484.511
418.969
455.740
454.123
18.327
Note:
See Appendix 2 for variable definition
Table III
De sc riptive statistic s o n e ffic ie nc y distributio ns o btaine d by the thre e mo de ls
M odel 1
CRS
VRS
Urban
Rural
Urban
Rural
M ean
M inimum
M aximum
Percentage share of
efficient schools
[ 70 ]
M odel 2
CRS
VRS
Urban
Rural
Urban
Rural
M odel 3
CRS
VRS
Urban
Rural
Urban
Rural
95.95
86.82
100
94.34
83.68
100
97.00
88.96
100
96.71
86.67
100
96.56
87.31
100
94.82
83.68
100
97.94
92.33
100
96.71
86.67
100
97.10
90.30
100
96.78
88.13
100
98.11
91.75
100
98.50
90.04
100
27.3
27.3
33.3
59.1
33.3
31.8
36.4
59.1
36.4
45.5
39.4
68.2
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
Ta ble IV pr esen ts in pu t m in im iza tion sa m ple
r esu lts a n d su ggested im pr ovem en t gu idelin es for on e of th e in efficien t sch ools, sch ool
X, th a t cou ld br in g it in lin e w ith its peer
gr ou p. Accor din g to th e ta ble, a n oth er sch ool
(or com bin a tion of oth er sch ools) exists, in
wh ich th e tea ch er s a r e on aver a ge you n ger,
th e pa r en ts’ edu ca tion , th e socioecon om ic
sta tu s a n d th e tea ch er s’ edu ca tion is lower,
bu t th e aver a ge scor e on th e TIMSS exa m w a s
equ a lly good. Th e m odel poin ts tow a r ds a r ea s
wh ich m ay n eed im pr ovem en t, su ch a s, for
exa m ple, th e qu a lity of th e tea ch er s a s it
r ela tes to th eir a ge a n d edu ca tion , a n d th e
r esu ltin g im plica tion s for on -goin g tea ch er
tr a in in g.
Clea r ly, n ot a ll th e r ecom m en da tion s of th e
m odel a r e fea sible. Im pr ovin g th e stu den ts’
socioecon om ic sta tu s is n ot a sh or t-ter m
effor t, n eith er is a fea sible effor t by th e
pr in cipa l of th e sch ool a lon e. Oth er r ecom m en da tion s, su ch a s th e qu a lity of th e tea ch er s ca n be im plem en ted w ith th e colla bor a tion of th e a u th or ities. Su ch a possible str a te gy cou ld in volve th e r ota tion of tea ch er s
a m on g differ en t sch ools[4]. Th e fea sibility of
th e m odels’ r ecom m en da tion s m u st be exa m in ed on a sch ool ba sis in colla bor a tion w ith
th e pr in cipa l of th e sch ool a n d th e pr oper
a u th or ities. Th e ou tpu t m a xim iza tion ver sion of th e m odel ca n a lso pr ovide th e exa m
scor e level wh ich cold be a ch ieved by th e
sch ool, given its cu r r en t in pu ts.
We a lso obser ve in Ta ble IV th a t th e ta r get
sch ool con str u cted by th e m odel – wh ich is a
lin ea r com bin a tion of existin g sch ools – is
sm a ller in size com pa r ed to sch ool X. Th is
ca n , to som e exten t, expla in wh y th e vir tu a l
sch ool per for m s better sin ce sm a ller sch ools
m ay per for m “better ”. On th e oth er h a n d,
su ch size differ en ce m ay deem th e com pa r ison u n fa ir. E xa m in a tion of th e peer sch ools of
sch ool X ca n h elp iden tify “well-beh aved”
sch ools a n d pr ovide th e m ea n s for a m or e fa ir
com pa r ison . For exa m ple, Ta ble V pr esen ts
a ctu a l da ta fr om sch ool Y, on e of th e peer
Table IV
Ac tual and targe t value s fo r all variable s as
indic ate d by DEA fo r sc ho o l X
School X
Actual value
Target value
Socioeconomic status
Teachers’ age
Teachers’ education
Parents’ education
Students’ population
International
mathematics score
10.00
4.50
6.00
4.10
344.00
8.60
3.00
5.00
3.20
69.00
450.10
450.10
Table V
Co mpariso n o f an ine ffic ie nt sc ho o l with a
sc ho o l similar in size
Socioeconomic status
Teachers’ age
Teachers’ education
Parents’ education
Students’ population
International
mathematics score
School X
(actual)
Peer for X
(actual)
10.00
4.50
6.00
4.10
344.00
8.90
4.00
5.00
3.90
337.00
450.10
463.10
sch ools of sch ool X. Th e two sch ools a r e sim ila r in size.
We obser ve th a t th e aver a ge edu ca tion of
tea ch er s, for exa m ple, a t th e peer of sch ool X
is lower th a n th a t obser ved a t X. F u r th er
investiga tion in to h ow ca n sch ool X ca pita lize
on th e a dva n ta ge of its tea ch er s to in cr ea se
th e TIMSS exa m in a tion scor e sh ou ld be
in itia ted.
Benchmarking the ef fects of the
environment
On e of th e pr im a r y goa ls of th e stu dy is to
ben ch m a r k th e possible en vir on m en ta l effect
on th e efficien cies of sch ools. Ba sed on th e
distin ction of ou r da ta set in to two h om ogen eou s su bgr ou ps – u r ba n a n d r u r a l a r ea
sch ools – we w ill u tilize a n a ppr oa ch pr oposed by Ch a r n es et a l. (1981) wh ich isola tes
a n d eva lu a tes sch ool pr ogr a m m e efficien cy.
Her e, we follow th e a ppr oa ch in a sim ila r
m a n n er to isola te a n d a ssess th e en vir on m en ta l im pa ct on sch ool efficien cy.
Th e a ppr oa ch (a lso descr ibed in Zen ios et
a l., 1995), pr oceeds in th r ee steps:
S tep 1. Ru n th e DE A m odel on two gr ou ps
oper a tin g in two differ en t en vir on m en ts.
S tep 2. P r oject in efficien t u n its on th eir
cor r espon din g efficien t fr on tier. Com bin e
pr ojected a n d efficien t u n its fr om both
gr ou ps a n d r u n th e DE A a ga in on th e pooled
da ta set.
S tep 3. E xa m in e wh eth er th e r esu ltin g efficien cy distr ibu tion s in ea ch gr ou p a r e differ en t. Th is ca n be don e by u sin g Ma n n -Wh itn ey
n on -pa r a m etr ic tests, sin ce th e r esu ltin g
distr ibu tion s a r e n ot lik ely to follow n or m a lity.
Th e u r ba n a n d r u r a l a r ea sch ools wer e
pooled togeth er a n d th e a bove pr ocedu r e w a s
followed. Th e r esu ltin g efficien cies su ggest
th a t th er e is n o sta tistica lly sign ifica n t efficien cy differ en ces between u r ba n a n d r u r a l
a r ea sch ools (p < 0.001).
[ 71 ]
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
Th e TIMSS scor es sh ow n in Ta ble II su ggest
th a t u r ba n sch ools in deed ou tper for m ed r u r a l
sch ools (p < 0.05). Th e a bove r esu lt, h owever,
su ggests th a t differ en ces in in efficien cy of
sch ools ca n n ot be attr ibu ted to envir on m en ta l
in flu en ces. Th u s, a n y cor r ective a ction s
sh ou ld be a im ed at ch a n gin g th e in ter n a l
r a th er th a n th e exter n a l envir on m en t.
Limitations and future research
Th e m odels developed in th e stu dy we
descr ibed a bove wer e lim ited by da ta ava ila bility, a n d th u s m yopic in n a tu r e. On ly a
sin gle ou tpu t w a s con sider ed, ba sed on a
sin gle exa m on a sin gle su bject, given to
eigh th gr a der s. Th e ou tpu t set sh ou ld be
expa n ded to r efl ect m or e desir a ble sch ool
ou tcom es. Th u s, ou tpu ts wh ich in clu de oth er
su bjects sh ou ld a lso be in cor por a ted in th e
set, r epr esen ta tive of th e wh ole body of stu den ts. Mu sic a n d a th letics ou tpu ts sh ou ld
a lso be con sider ed. Th e in pu t set sh ou ld a lso
in clu de fu r th er in for m a tion on th e tea ch er s’
tr a in in g a n d qu a lity, th e sch ools’ r esou r ces,
a n d th e socioecon om ic en vir on m en t.
F u r th er m or e, th is w a s a cr oss-section a l
stu dy con du cted a t a sin gle poin t in tim e.
Stu dies of a dyn a m ic n a tu r e sh ou ld a lso con sider ch a n ges over tim e. As da ta ava ila bility
th r ou gh stu dies su ch a s TIMSS in cr ea ses,
su ch dyn a m ic stu dies w ill a lso be m a de
possible.
F in a lly, of extr em e in ter est w ill be stu dies
wh ich w ill focu s on in ter n a tion a l com pa r ison s. Th e focu s of TIMSS for exa m ple w a s to
pr ovide th e m ea n s to com m u n ica te k n ow ledge a cr oss cou n tr ies. Sch ool per for m a n ce
ca n gr ea tly ben efi t fr om in ter n a tion a l stu dies
wh ich w ill exa m in e both th e in pu t a n d th e
ou tpu t side of th e sch ool effectiven ess pictu r e. It wou ld be of gr ea t in ter est to exa m in e
h ow th e efficien cy of sch ools ch a n ge a s th ey
a r e com pa r ed a ga in st sch ools oper a tin g in
differ en t edu ca tion a l system s.
Conclusion
In th is pa per we develop DE A m odels to
a ssess th e efficien cy of secon da r y sch ools in
Cypr u s. We dem on str a te h ow in efficien t
u n its ca n ben efi t fr om su ch a n a lysis a n d be
dir ected tow a r ds a r ea s wh ich m ay r equ ir e
im pr ovem en t.
On e of th e m a jor fi n din gs w a s th a t in th e
ca se of Cypr u s, r oom for sch ool efficien cy
im pr ovem en t exists, even th ou gh n ot gr ea t.
Despite th e low r a n k in gs sch ools in Cypr u s
obta in ed du r in g th e TIMSS, m ost of th e
sch ools fin d th em selves ver y close to th e
efficien t fr on tier. Th ese r esu lts em ph a size th e
existin g h om ogen eity between sch ools a s fa r
[ 72 ]
a s efficien cy is con cer n ed, a n d u n der lin e th e
im por ta n ce of fu tu r e in ter n a tion a l efficien cy
stu dies. As in ter n a tion a l da ta ava ila bility
th r ou gh stu dies su ch a s TIMSS in cr ea ses,
su ch stu dies w ill a lso be m a de possible.
F u r th er m or e, we fou n d n o efficien cy differ en ces wh ich ca n be a ttr ibu ted solely to th e
en vir on m en t, despite th e lower scor es
obser ved in r u r a l a r ea s. Th is is a n im por ta n t
fin din g for sch ools in Cypr u s, sin ce th e
effor ts tow a r ds im pr ovem en t ca n n ow focu s
on th e sch ool level a lon e.
Notes
1 E ven th ou gh n ot a s popu la r, sim u lta n eou s
equ a tion m odels to estim a te m u ltiple ou tpu t
pr odu ction tech n ologies, a n d th u s over com e
th is pr oblem , h ave been pr oposed by Levin
(1970) a n d Mich elson (1970).
2 Th is ca n be a ch ieved by settin g th e n u m er a tor
of (2) to a con sta n t a n d m in im izin g th e
den om in a tor
(Min im ize
3 F u r th er in for m a tion on th e TIMSS stu dy is
pr ovided in th e follow in g In ter n et a ddr ess
h ttp:/ / w w w csteep.bc.edu / tim ss
4 Alth ou gh tea ch er r ota tion a m on g differ en t
sch ools is cu r r en tly obser ved, efficien cy fin din gs su ch a s th e on es obta in ed h er e a r e n ot
con sider ed wh en m a k in g decision s on th ese
r ota tion s.
References and further reading
Ba n k er, R.D., Ch a r n es, A. a n d Cooper, W.W. (1984),
“Models for estim a tion of tech n ica l a n d sca le
in efficien cies in da ta en velopm en t a n a lysis”,
M a n a gem en t S cien ce, Vol. 30, pp. 1078-92.
Bessen t, A. a n d Bessen t, W. (1983), “E va lu a tion of
edu ca tion a l pr ogr a m pr oposa ls by m ea n s of
da ta en velopm en t a n a lysis”, Ed u ca tion a l
A d m in istra tion Qu a r terly, Vol. 19 N o. 2,
pp. 82-107.
Bou ssofi a n e, A., Dyson , R.G. a n d Th a n a ssou lis, E .
(1991), “Applied da ta en velopm en t a n a lysis”,
Eu ropea n J ou r n a l of Opera tion a l R esea rch ,
Vol. 52, pp. 1-15.
Ca m er on , K. (1978), “Mea su r in g or ga n iza tion a l
effectiven ess in in stitu tion s of h igh er edu ca tion ”, A d m in istra tiv e S cien ce Qu a r terly,
Vol. 23, pp. 604-32.
Ch a r n es, A., Cooper, W.W. a n d Rh odes, E . (1978),
“Mea su r in g th e efficien cy of decision m a k in g
u n its”, Eu ropea n J ou r n a l of Opera tion a l
R esea rch , Vol. 2, pp. 429-44.
Ch a r n es, A., Cooper, W.W. a n d Rh odes, E . (1981),
“E va lu a tin g pr ogr a m a n d m a n a ger ia l efficien cy: a n a pplica tion of da ta en velopm en t
a n a lysis to pr ogr a m follow th r ou gh ”, M a n a gem en t S cien ce, Vol. 27, pp. 668-97.
F itzsim m on s, J .A. a n d F itzsim m on s, M.J . (1994),
S er vice M a n a gem en t for Com petitiv e A dva n ta ge, McGr aw -Hill, N ew Yor k , N Y.
Andre as C. So te rio u,
Ele na Karahanna,
Co nstantino s Papanastasio u
and Mano lis S. Diako urakis
Using DEA to e valuate the
e ffic ie nc y o f se c o ndary
sc ho o ls: the c ase o f Cyprus
Inte rnatio nal Jo urnal o f
Educ atio nal Manage me nt
1 2 / 2 [1 9 9 8 ] 6 5 –7 3
Gola n y, B. a n d Ta m ir, E . (1995), “E va lu a tin g efficien cy-effectiven ess-equ a lity tr a de-offs: a da ta
en velopm en t a n a lysis a ppr oa ch ”, M a n a gem en t S cien ce, Vol. 41 N o. 7, pp. 1172-84.
Gr ay, J . (1981), “Sch ool effectiven ess r esea r ch : k ey
issu es”, Ed u ca tion a l R esea rch , Vol. 24 N o. 1,
pp. 49-54.
J oh n es, G. a n d J oh n es, J . (1993), “Mea su r in g th e
r esea r ch per for m a n ce of UK econ om ics
depa r tm en ts: a n a pplica tion of da ta en velopm en t a n a lysis”, Ox ford Econ om ic Pa pers,
Vol. 45, pp. 332-47.
Levin , H.M. (1970), “A n ew m odel of sch ool effectiven ess”, in US Depa r tm en t of Hea lth , E du ca tion a n d Welfa r e, Do T ea ch ers M a k e a Differ en ce?, US Gover n m en t P r in tin g Office, Wa sh in gton , DC.
Mich elson , S. (1970), “Th e a ssocia tion of tea ch er
r esou r ces w ith ch ildr en ch a r a cter istics”, in
US Depa r tm en t of Hea lth , E du ca tion a n d
Welfa r e, Do T ea ch ers M a k e a Differen ce?, US
Gover n m en t P r in tin g Office, Wa sh in gton , DC.
N or m a n , M. a n d Stock er, B. (1991), Da ta En v elopm en t A n a lysis: th e A ssessm en t of Per for m a n ce,
Wiley, Ch ich ester.
Ray, S.C. (1991), “Resou r ce-u se efficien cy in pu blic
sch ools: a stu dy of Con n ecticu t da ta ”, M a n a gem en t S cien ce, Vol. 37 N o. 12, pp. 1620-8.
Sa m m on s, P., N u tta ll, D. a n d Cu tta n ce, D. (1993),
“Differ en tia l sch ool effectiven ess: r esu lts
fr om a r ea n a lysis of th e In n er Lon don Au th or ity’s ju n ior sch ool pr oject da ta ”, B r itish Ed u ca tion a l R esea rch J ou r n a l, Vol. 19, pp. 381-405.
Sa sser, W.E ., Olsen , R.P. a n d Wyckoff, D.D. (1978),
M a n a gem en t of S er vice Opera tion s, Allyn &
Ba con , Boston .
Sexton , T.R. a n d Sleeper, S. (1994), “Im pr ovin g
pu pil tr a n spor ta tion in N or th Ca r olin a ”,
In ter fa ces, Vol. 24 N o. 1, pp. 87-103.
Th a n a ssou lis, E . (1996), “Alter in g th e bia s in
differ en tia l sch ool effectiven ess u sin g da ta
en velopm en t a n a lysis”, J ou r n a l of th e Opera tion a l R esea rch S ociety, Vol. 47, pp. 882-94.
Th a n a ssou lis, E . a n d Du n sta n , P. (1994), “Gu idin g
sch ools to im pr oved per for m a n ce u sin g da ta
en velopm en t a n a lysis: a n illu str a tion w ith
da ta fr om a loca l edu ca tion a l a u th or ity”,
J ou r n a l of th e Opera tion a l R esea rch S ociety,
Vol. 45, pp. 1247-62.
Zen ios, C., Zen ios, A.S., Aga th ocleou s, K. a n d
Soter iou , A.C. (1995), B en ch m a rk s of th e Efficien cy of B a n k B ra n ch es, Repor t 95-10, Depa r tm en t of P u blic a n d Bu sin ess Adm in istr a tion ,
Un iver sity of Cypr u s, N icosia , Cypr u s.
su bject to:
for a ll i = 1, 2, …, I,
(17)
for a ll r = 1, 2, …, R ,
(18)
(19)
(20)
(21)
Com pa r in g (M 4) to (M 3), we n otice th a t th eir
on ly differ en ce is estim a ted in th e in clu sion
of con str a in t (18). Th is con vexity con str a in t
r equ ir es th a t m u ltiplier s λj sh ou ld a dd u p to
1, th u s en su r in g th e com pa r ison of DMUs
a ga in st a com posite u n it of sim ila r size.
Appendix 2
Variables used
Inputs
Age of teacher
Parents’
education
Categories inc lude sec ondary
educ ation, university or postgraduate
studies, etc .
Socioeconomic
status
Data are obtained from questioning
the student about the existenc e of a
variety of things at his home, suc h as
tape rec order, c omputer, speed boat,
satellite antenna
School size
Measured by student population
Number of
books at
student’s
home
Existenc e of five c ategories:
1. 0-10 books
2. 11-25
3. 26-100
4. 101-200
5. More than 200 books
The student is asked to estimate
the number of books at his home,
exc luding sc hool books, newspapers
and magazines
Variable returns to scale model
Min im ize
(16)
Below 25 years
25-29
30-39
40-49
50-59
60 and above
Education level Categories inc lude options suc h as
of teacher
BSc / BA, MA, PhD etc .
Appendix 1
(M 4)
1.
2.
3.
4.
5.
6.
Output
International
mathematics
score
Average sc ore ac hieved at the sc hool
level in the mathematic s sec tion of
the TIMSS study
[ 73 ]