Directory UMM :Data Elmu:jurnal:I:International Journal of Educational Management:Vol12.Issue2.1998:

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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]

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

Constantinos Papanastasiou

De partme nt o f Educ atio n, Unive rsity o f Cyprus, Nic o sia, Cyprus

M anolis S. Diakourakis

This study utilizes the methodology of data envelop-ment analysis (DEA) to assess the efficiency of secondary schools in Cyprus. Apart from evaluating the relative effi-ciency of schools, the study provides recommendations for improvement to inefficient schools and discusses man-agerial implications. Further-more, empirical fi ndings based on an approach to estimate efficiency environ-mental effects suggest that no efficiency differences exist between schools operating in rural areas compared to those operating in urban areas.

Introduction

Assessin g t h e p er for m a n ce of a n ed u ca t ion a l sy st em is a n im p or t a n t bu t d ifficu lt t o a ccom -p lish t a sk . E d u ca t ion a l ser v ices fea t u r e a ll t h e d ist in ct ive ch a r a ct er ist ics of ser v ices v is-à -v is m a n u fa ct u r in g, su ch a s p er ish a b ilit y, h et er ogen eit y a n d sim u lt a n eit y (F it zsim -m on s a n d F it zsi-m -m on s, 1994; Sa sser et a l., 1978). Desp it e t h e d ifficu lt ies in volved , sch ool p er for m a n ce a ssessm en t ca n , a m on g ot h er s, b e u sed t o set p er for m a n ce t a r get s, t o m a k e r esou r ce a lloca t ion d ecision s, a n d t o im p r ove over a ll sch ool p er for m a n ce.

Sch ool u n it s b ea r fu r t h er sim ila r it ies t o ser v ice or ga n iza t ion a l u n it s in t h e sen se t h a t t h ey u t ilize m u lt ip le in p u t s t o p r od u ce m u lt i-p le ou t i-p u t s (Ca m er on , 1978). A n u m b er of com m on p r oblem s em er ge w h en a t t em p t in g t o a ssess ser v ice or ga n iza t ion a n d sch ool p er for m a n ce. F ir st , n o u lt im a t e cr it er ion of effect iven ess exist s, sin ce a u n it (ser v ice or ga n iza t ion or sch ool) m ay t y p ica lly p u r su e m u lt ip le, a n d oft en con t r a d ict or y goa ls. Releva n t cr it er ia m ay a lso ch a n ge over t h e lifecy -cle of t h e u n it . Differ en t u n it s m ay a ssign p a r t icu la r im p or t a n ce t o d iffer en t or ga n iza -t ion a l a sp ec-t s a -t d iffer en -t -t im es. Mor eover, cr it er ia a t on e or ga n iza t ion a l level m ay n ot b e t h e sa m e a s t h ose a t a n ot h er or ga n iza -t ion a l level, w h ile r ela -t ion sh ip s a m on g va r i-ou s effect iven ess d im en sion s m ay b e d ifficu lt t o d iscover.

Differ en t cr it er ia h ave t r a d it ion a lly b een d efi n ed for a ssessin g sch ool p er for m a n ce. Ty p ica lly, sch ool effect iven ess h a s b een m ea -su r ed in t er m s of t h e p er for m a n ce of st u d en t s in exa m in a t ion s (see Gr ay, 1981), for a d iscu s-sion on sch ool ou t com es). Ot h er con t ext u a l fa ct or s su ch a s t h e st u d en t s’ socioecon om ica l b a ck gr ou n d a n d ot h er en v ir on m en t a l va r i-a bles i-a r e i-a lso con sid er ed . In t h is p i-a p er w e follow a (p op u la r in t h e lit er a t u r e) p r od u ct ion or “va lu e-a d d ed ” a p p r oa ch in w h ich t h e sch ool u t ilizes som e in p u t s (i.e. n u m b er of

in str u ctor s, exper ien ce of in str u ctor s, socioe-con om ic ba ck gr ou n d of stu den ts, etc.) to pr o-du ce som e ou tpu ts (i.e. exa m in a tion scor es). On e of t h e m et h od ologies u sed in p r ev iou s st u d ies of sch ool p er for m a n ce eva lu a t ion b a sed on in p u t -ou t p u t a n a ly sis h a s b een or d i-n a r y lea st sq u a r es (OLS) r e gr essioi-n a i-n a ly sis. Su ch st u d ies h ave, h ow ever, t wo m a jor d isa d -va n t a ges (Ray, 1991). F ir st , p r ed ict ed -va lu es r esu lt in g fr om a r e gr ession m od el p r ov id e t h e aver a ge or exp ect ed level of ou t com e given cer t a in in p u t s, in st ea d of t h e m a xim u m a ch ieva ble ou t com e. Secon d , t h e in p u t / ou t -p u t -p r od u ct ion fu n ct ion s-p ecifi ed by su ch m od els m ay b e p r oblem a t ic. Most r e gr ession m od els u se a sin gle ou t p u t p r od u ct ion fu n c-t ion , w h ich m ay b e u n r ea lisc-t ic w h en a ssess-in g sch ool p er for m a n ce[1].

In t h is p a p er w e focu s on t h e a ssessm en t of t h e efficien cy of secon d a r y sch ools in Cy p r u s. In a r ecen t st u dy by t h e In t er n a t ion a l Associ-a t ion for t h e E vAssoci-a lu Associ-a t ion of E d u cAssoci-a t ion Associ-a l Ach ievem en t , t h e sch ools of Cy p r u s r a n k ed low com p a r ed t o 41 ot h er cou n t r ies w h ich a lso p a r t icip a t ed in t h e st u dy. How ever, exa m -in -in g on ly t h e sch ools’ ou t p u t d oes n ot p r ov id e a com p let e p ict u r e r e ga r d in g p er for -m a n ce. It is i-m p or t a n t t o k n ow w h et h er sch ools a r e a ct u a lly u t ilizin g t h eir r esou r ces in t h e m ost efficien t w ay t o p r od u ce t h e ob ser ved r a n k in gs. In a d d it ion , it is a lso im p or t a n t t o p r ov id e gu id elin es on h ow sch ools ca n im p r ove fu r t h er.

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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 t ive efficien cy of secon d a r y sch ools, t h is st u dy p r ov id es r ecom m en d a t ion s for im p r ove-m en t t o in efficien t sch ools a n d d iscu sses m a n a ger ia l im p lica t ion s.

T h e p a p er is or ga n ized a s follow s. We n ext p r ov id e a d escr ip t ion of t h e d a t a en velop m en t a n a ly sis m et h od ology. A b r ief lit er a t u r e r ev iew on t h e DE A a p p lica t ion s in ed u ca -t ion a l se-t -t in gs follow s. N ex-t , w e d escr ib e a n em p ir ica l st u dy w h ich u t ilizes DE A t o a ssess t h e efficien cy of secon d a r y sch ools in t h e cou n t r y of Cy p r u s. Ad d it ion a l in sigh t s t o t h e p r oblem of sch ool eva lu a t ion a r e p r esen t ed by b en ch m a r k in g t h e effect of t h e ext er n a l en v i-r on m en t t h i-r ou gh t h e com p a i-r ison of u i-r b a n a n d r u r a l sch ool efficien cy. Ma n a ger ia l im p li-ca t ion s, lim it a t ion s a n d fu t u r e r esea r ch a r e a lso d iscu ssed . Con clu d in g r em a r k s follow.

Data envelopment analysis

T h e m et h od ology of d a t a en velop m en t a n a ly -sis, in it ia lly in t r od u ced by Ch a r n es et a l. (1978), is a m a t h em a t ica l p r ogr a m m in g t ech -n iq u e u sed t o eva lu a t e t h e r ela t ive efficie-n cy of h om ogen eou s u n it s. T h is efficien cy eva lu a t ion d er ives fr om a n a ly sin g em p ir ica l ob ser -va t ion s ob t a in ed fr om d ecision -m a k in g u n it s (DMUs), a t er m coin ed by Ch a r n es et a l. (1978) t o d efi n e p r od u ct ive u n it s w h ich a r e ch a r a c-t er ized by com m on m u lc-t ip le ou c-t p u c-t s a n d com m on d esign a t ed in p u t s.

Rela t ive h om ogen eit y of or ga n iza t ion a l u n it s su ch a s sch ools, b a n k b r a n ch es or h os-p it a ls, os-p r ov id es in st a n ces for im os-p lem en t a t ion of t h e DE A m et h od ology. 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 w h er e a ccou n t in g a n d fi n a n cia l r a t ios a r e of lit t le va lu e, m u lt ip le ou t p u t s a r e p r od u ced t h r ou gh t h e t r a n sfor m a t ion of m u lt ip le in p u t s, a n d t h e in p u t ou t p u t t r a n sfor m a t ion r ela t ion -sh ip s a r e n ot k n ow n (Ch a r n es et a l., 1978).

In a b r oa d sen se, efficien cy of a sin gle DMU k₀op er a t in g in a h om ogen eou s set of N DMUs, u t ilizin g m u lt ip le in p u t s It o p r od u ce m u lt ip le ou t p u t s R, ca n b e d efi n ed a s follow s :

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w h er e, E_K

0 = efficien cy of u n it K0, y_{r K}

0 = a m ou n t of ou t p u t r= 1, …, Rp r od u ced by DMU K₀,

x_iK

0 = a m ou n t of in p u t i= 1, …, Icon su m ed by DMU K₀,

u_{r K}

0 = w eigh t given t o ou t p u t r, v_iK

0 = w eigh t given t o in p u t i, R = n u m b er of ou t p u t s, I = n u m b er of in p u t s.

As lon g a s t h e u n it u n d er con sid er a t ion r em a in s a sin gle DMU, w e cou ld r et a in t h e p r eced in g d efi n it ion . How ever, a n a t t em p t of d efi n in g efficien cy for a gr ou p of DMUs sim u lt a n eou sly is n ot p ossible u sin g ju st d efi n it ion (1), sin ce a com m on set of w eigh t s is d ifficu lt t o b e set a m on g a ll DMUs of a ser -v ice or ga n iza t ion or sy st em .

E a ch DMU ca n b e a llow ed t o ch oose it s ow n set of w eigh t s b a sed on it s ow n va lu e sy st em (Ch a r n es et a l., 1978) in a n a t t em p t t o a p p ea r a s efficien t a s p ossible. T h e follow in g m od el is for m ed b a sed on d efi n it ion (1):

(M 1 )

Ma xim ize (2)

su b ject t o:

(3)

u_{r K}

0, viK0≥0 for a ll r= 1, …, R, a n d i= 1, …, I, (4) T h r ou gh M 1, ea ch DMU K₀a n a ly sed w ill sp ecify t h e p a r t icu la r in p u t a n d ou t p u t w eigh t s (ua n d vr esp ect ively ), w h ich m a xi-m ize it s ow n r a t io of w eigh t ed ou t p u t t o w eigh t ed in p u t , su b ject t o t h e con st r a in t t h a t n o ot h er u n it u t ilizin g t h e sa m e w eigh t s cou ld exceed a n efficien cy r a t in g of 1. A DMU w it h efficien cy r a t in g of 1 w ill b e given t h e ch a r a ct er iza t ion of efficien t r ela t ive t o ot h er DMUs. Vice ver sa , a n efficien cy r a t in g of less t h a n 1 w ill lea d u s t o ch a r a ct er izin g t h is sp e-cifi c u n it a s in efficien t in r ela t ion t o ot h er s.

(M 1 ) r e p r esen t s a fr a ct ion a l lin ea r p r o-gr a m m in g (LP ) m od el. T h is ca n b e ea sily t r a n sfor m ed in t o a sim p le lin ea r p r ogr a m , a s follow s:

(M 2 )

Ma xim ize (5)

su b ject t o:

(3)

(7)

(8) w h er e,

E_K

0 = efficien cy of u n it K0, y_rK

0 = a m ou n t of ou tpu t rpr odu ced by DMU K₀,

x_iK

0 = a m ou n t of in p u t icon su m ed by DMU K₀,

u_{r K}

0 = w eigh t given t o ou t p u t r, v_iK

0 = w eigh t given t o in p u t i,

T h e t r a n sfor m a t ion is ob t a in ed by set t in g t h e d en om in a t or of (2) t o a n a r b it r a r ily select ed con st a n t . A sim ila r m a n ip u la t ion of eq u a t ion (2) ca n r esu lt in a n in p u t m in im iza t ion or i-en t ed lin ea r p r ogr a m m in g m od el[2].

T h e d u a l for m u la t ion of (M2) ca n p r ov id e a d d it ion a l in sigh t s a n d is com p u t a t ion a lly less exp en sive:

(M 3 )

Min im ize (9)

su b ject t o:

for a ll i= 1, 2, …, I, (10)

for a ll r= 1, 2, …, R, (11)

(12) (13) w h er e s_r+_{a n d}_s

i–r e p r esen t t h e sla ck va r ia bles

cor r esp on d in g t o t h e ou t p u t s a n d in p u t s r esp ect ively.

Ba sed on m od el (M 3 ) w e ca n ch a r a ct er ize DMU K₀efficien t a s lon g a s t h e va lu e of H_K

0is eq u a l t o 1. If H_K

0exceed s t h e low er lim it of 1, t h e DMU u n d er a ssessm en t is ch a r a ct er ized in efficien t in com p a r ison t o ot h er DMUs. T h a t is, t h er e exist s a w eigh t ed com b in a t ion of a ct u a l p er for m a n ce of ot h er u n it s, su ch t h a t n o ou t p u t of u n it K₀exceed s t h a t of t h e w eigh t ed ou t p u t of t h e w eigh t ed com b in a -t ion . A-t -t h e sa m e -t im e, w e cou ld r ed u ce a ll in p u t s of K₀by t h e p r op or t ion H_K

0w it h ou t a n y in p u t fa llin g b elow t h a t of t h e

cor r esp on d in g w eigh t ed com b in a t ion of ot h er u n it s. If DMU K₀is d eem ed in efficien t , m a n -a gem en t cou ld d ecr e-a se -a ll t h e in p u t s of K₀in t h e sa m e p r op or t ion , in or d er t o a ch ieve t h e d esir ed w eigh t ed com b in a t ion p er for m a n ce.

T h e size of t h e n ecessa r y d ecr ea se is in d i-ca t ed by t h e va lu e of H_K

0.

F r om t h e scop e of com p u t a t ion a l effor t , t h e fa ct t h a t (M 3 ) h a s on ly (I+ R) con st r a in t s com p a r ed t o (N+ R+ I+ 1) con st r a in t s of m od el (M 2 ) a n d Nis t y p ica lly m u ch la r ger t h a n I+ R, d eem s (M 3 ) ea sier t o solve in com p a r ison t o (M 2 ). An a d d it ion a l a dva n t a ge of (M 3 ) is t h e p r ov ision of t a r get va lu es for in efficien t u n it s by com p a r in g t h em a ga in st a com p osit e u n it con st r u ct ed by t h e a ct u a l p er for m a n ce of t h e r est of t h e u n it s (Bou ssofi -a n e et a l., 1991). T h ese t a r get s ca n p r ov id e gu id elin es for im p r ovem en t t o in efficien t u n it s. At op t im a lit y, t h e follow in g in p u t / ou t p u t va lu es occu r :

for a ll i= 1, 2, …, n (14)

for a ll r= 1, 2, …, m (15)

w h er e * in d ica t es op t im a lit y. T h ese a r e in p u t -or ien t ed t a r get s sin ce t h e a t t em p t h er e is t o m in im ize in p u t s. Ou t p u t -or ien t ed t a r get s ca n a lso b e d er ived by d iv id in g b ot h

Mod el (M 3 ) w a s in t r od u ced by Ch a r n es et a l. (1978) b a sed on t h e a ssu m p t ion of con st a n t r et u r n s t o sca le. H ow ever, w h ile t h is a ssu m p -t ion cou ld of-t en b e le gi-t im a -t e, i-t m ay n o-t b e va lid in ca ses w h er e t h e sca le of op er a t ion s cou ld in fl u en ce a DMU’s efficien cy r a t in g, su ch a s, for exa m p le, w h en a ssessin g sch ool p er for m a n ce. Mor eover, in for m a t ion con -cer n in g t h e a m ou n t of in efficien cies ow in g t o t h e sca le of op er a t ion s wou ld p r ove t o b e ver y u sefu l for m a n a ger ia l d ecision s. Ap p en d ix 1 p r esen t s a m od el d escr ib ed by Ba n k er et a l. (1984) t o cover t h e issu e of in efficien cies d u e t o sca le of op er a t ion s, t h r ou gh a n ext en sion of m od el (M 3 ).

Applications of DEA in education

Ap p lica t ion s of DE A t o m ea su r e t h e efficien cy of ed u ca t ion a l p r od u ct ion h ave ext en sively b een r e p or t ed in lit er a t u r e, b e gin n in g w it h t h e in t r od u ct or y p a p er of DE A (Ch a r n es et a l., 1978), wh ich in t r od u ced t h e DE A m et h od ology by d em on st r a t in g it in a sch ool set t in g. T h e a im of t h is sect ion is n ot t o p r esen t a t h or ou gh lit er a t u r e r ev iew of DE A a p p lica t ion s in ed u -ca t ion , bu t r a t h er t o p r esen t som e of t h e m or e r eleva n t st u d ies t o t h is wor k .

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t h r ou gh (P F T) a n d n on follow t h r ou gh (N F T) sch em es for p r im a r y sch ool ch ild r en in t h e USA. P a r t icip a n t s in P F T w er e ch ild r en w h o ca m e fr om less a dva n t a ged b a ck gr ou n d s, w h ile t h e exp er im en t a lso in clu d ed a con t r ol gr ou p of N F T ch ild r en for ea ch d ist r ict t h a t p a r t icip a t ed in t h e P F T. DE A w a s u sed in or d er t o a ssess t h e efficien cies of p olicies w it h in w h ich m a n a ger s op er a t e w h ile elim i-n a t ii-n g t h e ii-n efficiei-n cies or igii-n a t ii-n g fr om t h e m a n a ger s t h em selves.

An a lt er n a t ive u se of DE A is p r esen t ed by Bessen t a n d Bessen t (1983). Mor e sp ecifi ca lly, DE A is u sed for r esou r ce a lloca t ion of va r iou s p r ogr a m s in t h e en v ir on m en t of a com m u n it y colle ge. T h e m a in con t r ibu t ion of t h e st u dy w a s t h e r ecogn it ion t h a t , in sp it e of som e lim it a t ion s, DE A cou ld p r ove h elp fu l in r esou r ce a lloca t ion . DE A ca n n ot , h ow ever, p r ov id e a n a n sw er t o t h e q u est ion of a lloca t -in g t ot a l or ga n iza t ion a l r esou r ces -in or d er t o ob t a in m a xim u m ou t p u t fr om t h e u n it s.

Bou ssofi a n e et a l. (1991) u t ilize t h e con t ext of com p a r in g sch ools for t h e p u r p ose of d em on st r a t in g p r a ct ica l issu es en cou n t er ed in select in g a n d q u a lify in g in p u t s a n d ou t -p u t s. Sch ools w er e ch osen a s a n illu st r a t ion m a in ly d u e t o t h e im p or t a n ce of en v ir on m en -t a l fa c-t or s in -t h eir op er a -t ion . An im p or -t a n -t ob ser va t ion of t h e a u t h or s is t h e effect of t h e select ion of in p u t s a n d ou t p u t s in t h e d is-cr im in a t or y p ow er of DE A, w h ich m or e sp ecifi ca lly is r ela t ed t o t h e n u m b er of select ed in p u t s a n d ou t p u t s. As a m in im u m n u m b er of u n it s t h a t w ill b e given t h e t a g of efficien t , a u t h or s set t h e p r od u ct of t h e n u m -b er of in p u t s a n d ou t p u t s.

In a sim ila r m a n n er, Gola n y a n d Ta m ir (1995), u t ilize h y p ot h et ica l d a t a t a k en fr om a n eva lu a t ion of som e elem en t a r y sch ools in a sch ool d ist r ict . Aim of t h e illu st r a t ion is t h e d ist in ct ion b et w een d iffer en t a sp ect s eva lu -a t ed by efficien cy, effect iven ess -a n d eq u -a lit y, in a d d it ion t o sp ecify in g p ot en t ia l t r a d e-off a m on g t h em . In a n ot h er r ecen t st u dy, T h a n a s-sou lis (1996) d em on st r a t ed h ow t o u se DE A t o set t a r get s for d iffer en t ia lly effect ive sch ools. J oh n es a n d J oh n es (1993) r efer t o a n a p p li-ca t ion of t h e m et h od ology in u n iver sit ies. In t h e p a r t icu la r st u dy, DE A is u sed for a ssessin g t h e r esea r ch p er for m a n ce of UK d e p a r t -m en t s of econ o-m ics d u r in g 1984-88. DE A w a s esp ecia lly va lu a ble sin ce n o u n iver sa lly a cce p t ed im p or t a n ce w eigh t s exist r e ga r d in g t h e r eleva n t in p u t s a n d ou t p u t s. T h e p r oblem w a s a d d r essed t h r ou gh t h e a llow a n ce of DE A for ea ch u n it t o d et er m in e it s ow n set of in p u t a n d ou t p u t w eigh t s su ch t h a t it m a xim izes it s efficien cy. H ow ever, ea ch u n it is n ot com -p let ely fr ee t o d efi n e it s set , sin ce it is su b ject t o t h e con st r a in t t h a t n o ot h er u n it cou ld a ccom p lish a n efficien cy r a t in g t h a t exceed s

u n it y, b a sed on t h e sa m e set of w eigh t ed in p u t s a n d ou t p u t s.

Ray (1991) u t ilized t h e DE A m et h od ology in com b in a t ion t o r e gr ession a n a ly sis in or d er t o a ssess r ela t ive efficien cy in p u blic sch ool d ist r ict s in Con n ect icu t , USA. T h r ou gh h is a n a ly sis h e p oin t ed ou t t h e effect of socioecon om ic va r ia bles in p r od u ct iv it y va r ia -t ion s. A r ela -t ive p a p er, in -t h e sen se -t h a -t i-t r efer s t o com b in ed u se of DE A w it h r e gr es-sion a n a ly sis, is p r esen t ed by Sext on a n d Slee p er (1994), a im in g a t fa cin g t h e la ck of h om ogen eit y b et w een DMUs in volved .

Assessing the ef fectiveness of

schools in Cyprus

M odel description

St u d ies of ed u ca t ion a l p r od u ct ion fu n ct ion d efi n e t wo m a jor w ay s of d escr ib in g t h e in fl u -en ces of sch oolin g on st u d -en t a ch ievem -en t . E it h er t a k e in t o a ccou n t t h e cu m u la t ive in fl u -en ce of fa m ily b a ck gr ou n d , p eer s, sch ool in p u t a n d in n a t e a b ilit ies on st u d en t a ch ieve-m en t a t cer t a in t iieve-m e p oin t s or ieve-m ea su r e t h ese fa ct or s d u r in g t h e p er iod st u d en t is a t t en d in g sch ool.

Ou r st u dy u ses t h e secon d a lt er n a t ive, a lso k n ow n a s t h e v a lu e a d d edm od el. T h is m od el is con ven ien t in t h e sen se t h a t it r ed u ces d a t a r eq u ir em en t s, sin ce sch ool-level a ggr e ga t ed d a t a ca n b e u sed . Mor eover, ed u ca t ion a l a ch ievem en t is a p r od u ct of b ot h in p u t s con -t r olla ble by -t h e sch ool bu -t a lso of o-t h er fa c-t or s su ch a s fa m ily b a ck gr ou n d , in n a c-t e a b ili-t ies, p eer s a n d for m er ou ili-t com es.

F igu r e 1 p r esen t s t h e t h eor et ica l fr a m e-wor k u n d er ly in g t h e d evelop ed m od els.

T h r ee gen er ic d et er m in a n t s d r ive sch ool p er for m a n ce (Th a n a ssou lis, 1996). F ir st , sch ool-sp ecifi c fa ct or s su ch a s t h e size of t h e sch ool, a n d t h e n u m b er a n d q u a lit y of t h e t ea ch er s; secon d , fa ct or s wh ich a r e fa m ily a n d ext er n a l en v ir on m en t sp ecifi c, su ch a s for exa m p le, t h e st u d en t s’ socioecon om ic b a ck -gr ou n d or t h e loca t ion of t h e sch ool; a n d fi n a lly, t h e a b ilit ies of t h e st u d en t h im / h er self.

T h r ee m od els, a s p r esen t ed in Ta ble I w er e con st r u ct ed , b a sed on t h e a b ove fr a m ewor k a n d on d a t a ava ila b ilit y. T h e sm a ll n u m b er of

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

Figure 1

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sch ools ava ila ble lim it ed t h e n u m b er of in p u t a n d ou t p u t va r ia bles, in or d er t o p r eser ve t h e DE A m od el’s d iscr im in a t or y p ow er. T h e m od -els p r esen t ed in Ta ble I p r oceed fr om a sim p le (Mod el 1) t o a m or e com p lica t ed in p u t set (Mod el 3). All m od els in clu d e a sin gle, com -m on ou t p u t , con sist in g of t h e scor e fr o-m st a n d a r d ized exa m in a t ion s su ch a s t h e TIMSS, t o b e d iscu ssed in t h e n ext sect ion .

T h e fi r st m od el u ses in p u t s wh ich ca n b e ob t a in ed fr om t ea ch er s’ a n d st u d en t s’ q u es-t ion n a ir es. Mor e sp ecifi ca lly, ies-t in clu d es es-t h e a ge a n d ed u ca t ion a l level of t ea ch er s, in a d d i-t ion i-t o i-t h e p a r en i-t s’ ed u ca i-t ion a n d i-t h e socio-econ om ic st a t u s of t h e fa m ily. Mod el 2 a lso in clu d es sch ool d a t a . Th a t is, t h e size of t h e sch ool, d efi n ed a s t h e st u d en t s’ p op u la t ion w a s in clu d ed . An a d d it ion a l in p u t is con sid-er ed by Mod el 3 t o ca p t u r e t h e socioecon om ic b a ck gr ou n d of st u d en t s. T h e n u m b er of b ook s a t st u d en t ’s h om e w a s u sed a s a p r oxy for t h a t . A d escr ip t ion of a ll t h e va r ia bles in clu d ed in a ll t h e m od els is sh ow n in Ap p en d ix 2.

Data

T h e T h ir d In t er n a t ion a l Ma t h em a t ics a n d Scien ce St u dy (TIMSS) w a s con d u ct ed d u r in g t h e m on t h s of May J u n e 1995. TIMSS is con -d u ct e-d by t h e In t er n a t ion a l Associa t ion for t h e E va lu a t ion of E d u ca t ion a l Ach ievem en t (IE A), in a t ot a l of 45 cou n t r ies, cover in g m or e t h a n h a lf a m illion st u d en t s a t fi ve gr a d es levels in m or e t h a n 15,000 sch ools. T h e m a in goa l of TIMSS is t o p r ov id e in t er n a t ion a l b en ch m a r k s r e ga r d in g sch ool p er for m a n ce. Da t a w er e collect ed u sin g st a n d a r d ized q u est ion n a ir es, a d ju st ed t o r efl ect cu lt u r a l d iffer en ces, com p let ed by sch ool p r in cip a ls, t ea ch er s a n d st u d en t s.

TIMSS p r ov id es t h e va r iou s p a r t icip a t in g cou n t r ies a veh icle w it h w h ich t o in vest iga t e a va r iet y of issu es, in clu d in g w h a t con ce p t s st u d en t s u n d er st a n d , h ow w ell t h ey ca n a p p ly t h eir k n ow led ge in p r oblem solv in g sit u a -t ion s, a n d w h e-t h er -t h ey ca n com m u n ica -t e t h eir u n d er st a n d in gs. In for m a t ion r e ga r d in g

t h ese issu es is ver y im p or t a n t . Sk ills in m a t h -em a t ics a n d scien ce a r e b ecom in g cr it ica l t o econ om ic p r ogr ess d u e t o t h e t r a n sfor m a t ion of m od er n societ ies in t o m or e t ech n ologica lly b a sed , w h er e h igh er levels of t ech n ica l com -p et en ce a n d fl exible t h in k in g a r e r eq u ir ed [3].

TIMSS u t ilized in for m a t ion fr om st u d en t s, t ea ch er s a n d sch ool p r in cip a ls a s follow s: • Pr in cip a l qu estion n a ire. T h is in st r u m en t

w a s a d m in ist er ed t o t h e sch ool’s p r in cip a l. It ob t a in ed gen er a l in for m a t ion a b ou t t h e sch ool, i.e. sch ool size, n u m b er of t ea ch er s t ea ch in g a t sch ool for fi ve or m or e yea r s, in for m a t ion on t h e sch ool’s com m u n it y a n d on t h e n u m b er of d e p a r t m en t h ea d s. • T ea ch er of m a th em a tics a n d scien ce qu

es-tion n a ire. Da t a collect ed t h r ou gh t h is in st r u m en t , w h ich w a s a d m in ist er ed t o t ea ch er s, in clu d e t h e t ea ch er ’s ed u ca t ion a l b a ck gr ou n d , coop er a t ion w it h ot h er t ea ch -er s for lesson en h a n cem en t , a n d t ea ch in g m et h od ologies.

• S tu d en t in for m a tion. In for m a t ion on su ch va r ia bles a s t h e socioecon om ic st a t u s of st u d en t ’s fa m ily, p a r en t s’ ed u ca t ion a n d n u m b er of b ook s a t h om e w a s ga t h er ed v ia a q u est ion n a ir e. F u r t h er m or e, m a t h t est s w h ich cover ed six con t en t a r ea s (fr a ct ion s a n d n u m b er s (34 p er cen t ), m ea su r em en t (12 p er cen t ), p r op or t ion a lit y (7 p er cen t ), d a t a r e p r esen t a t ion , a n a ly sis, a n d p r ob a b il-it y (14 p er cen t ), geom et r y (15 p er cen t ), a n d a lgeb r a (18 p er cen t )) w er e a lso a d m in is-t er ed is-t o seven is-t h a n d eigh is-t h gr a d e sis-t u d en is-t s. Ou r st u dy w a s b a sed on t h e Ma t h em a t ics TIMSS d a t a a s collect ed in Cy p r u s w it h t h e colla b or a t ion of t h e Min ist r y of E d u ca t ion a n d Cu lt u r e, t h e P ed a gogica l In st it u t e, a n d t h e Un iver sit y of Cy p r u s. Da t a w er e ga t h er ed fr om 55 h igh sch ools, w h ich r efl ect s t h e t ot a l of low er secon d a r y sch ools (gy m n a siu m s) in Cy p r u s. In t er m s of st u d en t s p op u la t ion , 5,852 ou t of a t ot a l of 19,694 st u d en t s p a r t icip a t ed in t h e st u dy, fr om b ot h t h e seven t h a n d eigh t h gr a d es of h igh sch ool (a ges 13-14 yea r s old ). Da t a a r e a ggr e ga t ed t o t h e sch ool level. F u r -t h er m or e, n o d a -t a w er e u sed in -t h is s-t u dy fr om t h e p r in cip a ls’ q u est ion n a ir e b eca u se of t h e ver y low r esp on se r a t e ob ser ved , r e ga r d -in g fu lly com p let ed q u est ion n a ir es (less t h a n 10 p er cen t ). Sch ool size w a s ob t a in ed fr om secon d a r y sou r ces t h r ou gh t h e Min ist r y of E d u ca t ion a n d Cu lt u r e.

For t h e p u r p oses of t h is st u dy, a d ist in ct ion w a s m a d e b et w een sch ools loca t ed in u r b a n a r ea s (33 sch ools) a n d t h ose loca t ed in r u r a l a r ea s (22 sch ools). T h u s, t wo se p a r a t e gr ou p s w er e for m ed , a n d a ssessed se p a r a t ely. T h is d ist in ct ion p r ov id es t wo d esir a ble ou t com es. F ir st , t h e cover a ge of DE A’s h om ogen eit y of u n it s r eq u ir em en t is m a in t a in ed . Secon d , t h e Table I

Variable s use d in the DEA e ffic ie nc y me asure me nt

M odel 1 M odel 2 M odel 3

Inputs

Age of teacher ✓ ✓ ✓

Education level of teacher ✓ ✓ ✓

Parents’ education ✓ ✓ ✓

Socioeconomic status ✓ ✓ ✓

School size ✓ ✓

Number of books at student’s home ✓

Output

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t wo gr ou p s w ill b e u sed t o d em on st r a t e p ossi-ble en v ir on m en t a l effect s on t h e efficien cies of sch ools t h r ou gh a b en ch m a r k in g a p p r oa ch w h ich w ill b e d iscu ssed la t er. Ta ble II p r e-sen t s d escr ip t ive st a t ist ics on t h e d a t a col-lect ed fr om t h e t wo gr ou p s.

Results and discussion

All t h r ee m od els w er e r u n u n d er b ot h con -st a n t r et u r n s t o sca le (CRS) a n d va r ia ble r et u r n s t o sca le (VRS), se p a r a t ely for t h e u r b a n a n d r u r a l gr ou p. F u r t h er m or e, b ot h in p u t m in im iza t ion a n d ou t p u t m a xim iza t ion DE A m od els w er e r u n for ea ch sch ool in ea ch gr ou p, in or d er t o id en t ify in efficien t a n d b est p r a ct ice sch ools. T h e ou t p u t m a xim iza -t ion m od el p r ov id es in for m a -t ion on h ow m u ch t h e aver a ge st u d en t p er for m a n ce on

t h e TIMSS t est cou ld b e im p r oved , given it s in p u t s. T h e in p u t m in im iza t ion m od el p r o-v id es in for m a t ion on h ow m u ch a n in effi-cien t sch ool cou ld fu r t h er r ed u ce som e of it s in p u t s w h ile m a in t a in t h e cu r r en t level of p er for m a n ce. Ta ble III p r ov id es d escr ip t ive st a t ist ics on t h e r esu lt in g efficien cy d ist r ibu -t ion s of in p u -t m in im iza -t ion m od els.

It is n ot ewor t h y t h a t even t h ou gh som e in efficien cies a r e ev id en t , t h e over a ll efficien cies ob ser ved a r e h igh . Assu m in g, for exa m -p le, CRS a n d u sin g Mod el 2, w e h ave a m ea n efficien cy va lu e of 96.56 for u r b a n a r ea sch ools a n d 94.82 for r u r a l a r ea sch ools. A p ossible exp la n a t ion of t h is m ay in volve t h e t igh t con t r ol exh ib it ed by t h e Min ist r y of E d u ca t ion w it h r esp ect t o t ea ch in g cu r r icu la , sch ool a ct iv it ies a n d over a ll p er for m a n ce.

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 5 3 3 .8 5 7 4 0 .5 7 1

Education level of teacher 8 5 6 .0 1 8 6 0 .5 2 3

Parents’ education 7 .8 5 2 3 .4 8 4 5 .3 3 0 5 .1 2 8 1 .2 5 5

Socioeconomic status 1 2 .0 7 3 9 .0 2 0 1 0 .5 7 2 1 0 .5 8 2 0 .7 3 0

School size 6 2 5 1 6 0 3 9 0 .9 3 9 4 0 8 1 1 9 .7 2 0

Number of books at student’s home 3 .9 7 7 2 .8 4 6 3 .3 9 3 3 .4 0 8 0 .2 7 1

Output

International mathematics score 5 2 7 .5 9 8 4 3 9 .1 8 4 4 8 2 .7 2 7 4 8 2 .2 3 3 2 6 .8 5 2

Rural area schools Inputs

Age of teacher 4 .5 3 3 .5 5 3 .5 0 .4 8 6

Education level of teacher 6 .5 5 5 .7 8 9 6 0 .4 4 5

Parents’ education 4 .8 5 3 2 .5 3 .5 1 8 3 .4 0 .6 9 0

Socioeconomic status 1 0 .7 3 2 8 .6 7 4 9 .6 6 5 9 .7 5 3 0 .6 0 5

School size 5 0 4 1 3 4 3 0 8 .7 7 3 3 4 5 1 4 6 .0 0 5 3

Number of books at student’s home 3 .4 1 3 2 .8 3 9 3 .1 5 8 3 .1 7 9 0 .1 8 4

Output

International mathematics score 4 8 4 .5 1 1 4 1 8 .9 6 9 4 5 5 .7 4 0 4 5 4 .1 2 3 1 8 .3 2 7 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 M odel 2 M odel 3

CRS VRS CRS VRS CRS VRS

Urban Rural Urban Rural Urban Rural Urban Rural Urban Rural Urban Rural

M ean 9 5 .9 5 9 4 .3 4 9 7 .0 0 9 6 .7 1 9 6 .5 6 9 4 .8 2 9 7 .9 4 9 6 .7 1 9 7 .1 0 9 6 .7 8 9 8 .1 1 9 8 .5 0 M inimum 8 6 .8 2 8 3 .6 8 8 8 .9 6 8 6 .6 7 8 7 .3 1 8 3 .6 8 9 2 .3 3 8 6 .6 7 9 0 .3 0 8 8 .1 3 9 1 .7 5 9 0 .0 4

M aximum 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0

Percentage share of

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Ta ble IV p r esen t s in p u t m in im iza t ion sa m p le r esu lt s a n d su ggest ed im p r ovem en t gu id e-lin es for on e of t h e in efficien t sch ools, sch ool X, t h a t cou ld b r in g it in lin e w it h it s p eer gr ou p. Accor d in g t o t h e t a ble, a n ot h er sch ool (or com b in a t ion of ot h er sch ools) exist s, in w h ich t h e t ea ch er s a r e on aver a ge you n ger, t h e p a r en t s’ ed u ca t ion , t h e socioecon om ic st a t u s a n d t h e t ea ch er s’ ed u ca t ion is low er, bu t t h e aver a ge scor e on t h e TIMSS exa m w a s eq u a lly good . T h e m od el p oin t s t ow a r d s a r ea s w h ich m ay n eed im p r ovem en t , su ch a s, for exa m p le, t h e q u a lit y of t h e t ea ch er s a s it r ela t es t o t h eir a ge a n d ed u ca t ion , a n d t h e r esu lt in g im p lica t ion s for on -goin g t ea ch er t r a in in g.

Clea r ly, n ot a ll t h e r ecom m en d a t ion s of t h e m od el a r e fea sible. Im p r ov in g t h e st u d en t s’ socioecon om ic st a t u s is n ot a sh or t -t er m effor t , n eit h er is a fea sible effor t by t h e p r in cip a l of t h e sch ool a lon e. Ot h er r ecom m en d a t ion s, su ch a s t h e q u a lit y of t h e t ea ch er s ca n b e im p lem en t ed w it h t h e colla b or a t ion of t h e a u t h or it ies. Su ch a p ossible st r a t -e gy cou ld in volv-e t h -e r ot a t ion of t -ea ch -er s a m on g d iffer en t sch ools[4]. T h e fea sib ilit y of t h e m od els’ r ecom m en d a t ion s m u st b e exa m -in ed on a sch ool b a sis -in colla b or a t ion w it h t h e p r in cip a l of t h e sch ool a n d t h e p r op er a u t h or it ies. T h e ou t p u t m a xim iza t ion ver -sion of t h e m od el ca n a lso p r ov id e t h e exa m scor e level w h ich cold b e a ch ieved by t h e sch ool, given it s cu r r en t in p u t s.

We a lso ob ser ve in Ta ble IV t h a t t h e t a r get sch ool con st r u ct ed by t h e m od el – w h ich is a lin ea r com b in a t ion of exist in g sch ools – is sm a ller in size com p a r ed t o sch ool X. T h is ca n , t o som e ext en t , exp la in w h y t h e v ir t u a l sch ool p er for m s b et t er sin ce sm a ller sch ools m ay p er for m “b et t er ”. On t h e ot h er h a n d , su ch size d iffer en ce m ay d eem t h e com p a r i-son u n fa ir. E xa m in a t ion of t h e p eer sch ools of sch ool X ca n h elp id en t ify “w ell-b eh aved ” sch ools a n d p r ov id e t h e m ea n s for a m or e fa ir com p a r ison . For exa m p le, Ta ble V p r esen t s a ct u a l d a t a fr om sch ool Y, on e of t h e p eer

sch ools of sch ool X. T h e t wo sch ools a r e sim i-la r in size.

We ob ser ve t h a t t h e aver a ge ed u ca t ion of t ea ch er s, for exa m p le, a t t h e p eer of sch ool X is low er t h a n t h a t ob ser ved a t X. F u r t h er in vest iga t ion in t o h ow ca n sch ool X ca p it a lize on t h e a dva n t a ge of it s t ea ch er s t o in cr ea se t h e TIMSS exa m in a t ion scor e sh ou ld b e in it ia t ed .

Benchmarking the ef fects of the

environment

On e of t h e p r im a r y goa ls of t h e st u dy is t o b en ch m a r k t h e p ossible en v ir on m en t a l effect on t h e efficien cies of sch ools. Ba sed on t h e d ist in ct ion of ou r d a t a set in t o t wo h om oge-n eou s su b gr ou p s – u r b a oge-n a oge-n d r u r a l a r ea sch ools – w e w ill u t ilize a n a p p r oa ch p r o-p osed by Ch a r n es et a l. (1981) w h ich isola t es a n d eva lu a t es sch ool p r ogr a m m e efficien cy. H er e, w e follow t h e a p p r oa ch in a sim ila r m a n n er t o isola t e a n d a ssess t h e en v ir on m en -t a l im p a c-t on sch ool efficien cy.

T h e a p p r oa ch (a lso d escr ib ed in Zen ios et a l., 1995), p r oceed s in t h r ee st e p s:

S tep 1.Ru n t h e DE A m od el on t wo gr ou p s op er a t in g in t wo d iffer en t en v ir on m en t s.

S tep 2.P r oject in efficien t u n it s on t h eir cor r esp on d in g efficien t fr on t ier. Com b in e p r oject ed a n d efficien t u n it s fr om b ot h gr ou p s a n d r u n t h e DE A a ga in on t h e p ooled d a t a set .

S tep 3. E xa m in e w h et h er t h e r esu lt in g efficien cy d ist r ibu t ion s in ea ch gr ou p a r e d iffer -en t . T h is ca n b e d on e by u sin g Ma n n -Wh it n ey n on -p a r a m et r ic t est s, sin ce t h e r esu lt in g d ist r ibu t ion s a r e n ot lik ely t o follow n or m a l-it y.

T h e u r b a n a n d r u r a l a r ea sch ools w er e p ooled t oget h er a n d t h e a b ove p r oced u r e w a s follow ed . T h e r esu lt in g efficien cies su ggest t h a t t h er e is n o st a t ist ica lly sign ifi ca n t effi-cien cy d iffer en ces b et w een u r b a n a n d r u r a l a r ea sch ools (p< 0.001).

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 1 0 .0 0 8 .6 0

Teachers’ age 4 .5 0 3 .0 0

Teachers’ education 6 .0 0 5 .0 0

Parents’ education 4 .1 0 3 .2 0

Students’ population 3 4 4 .0 0 6 9 .0 0 International

mathematics score 4 5 0 .1 0 4 5 0 .1 0

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

School X Peer for X

(actual) (actual)

Socioeconomic status 1 0 .0 0 8 .9 0

Teachers’ age 4 .5 0 4 .0 0

Teachers’ education 6 .0 0 5 .0 0

Parents’ education 4 .1 0 3 .9 0

Students’ population 3 4 4 .0 0 3 3 7 .0 0 International

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T h e TIMSS scor es sh ow n in Ta ble II su ggest t h a t u r b a n sch ools in d eed ou t p er for m ed r u r a l sch ools (p < 0.05). Th e a bove r esu lt , h owever, su ggest s t h a t d iffer en ces in in efficien cy of sch ools ca n n ot b e a t t r ibu t ed t o en v ir on m en t a l in fl u en ces. T h u s, a n y cor r ect ive a ct ion s sh ou ld b e a im ed a t ch a n gin g t h e in t er n a l r a t h er t h a n t h e ext er n a l en v ir on m en t .

Limitations and future research

T h e m od els d evelop ed in t h e st u dy w e d escr ib ed a b ove w er e lim it ed by d a t a ava il-a b ilit y, il-a n d t h u s m yop ic in n il-a t u r e. On ly il-a sin gle ou t p u t w a s con sid er ed , b a sed on a sin gle exa m on a sin gle su b ject , given t o eigh t h gr a d er s. T h e ou t p u t set sh ou ld b e exp a n d ed t o r efl ect m or e d esir a ble sch ool ou t com es. T h u s, ou t p u t s w h ich in clu d e ot h er su b ject s sh ou ld a lso b e in cor p or a t ed in t h e set , r e p r esen t a t ive of t h e w h ole b ody of st u -d en t s. Mu sic a n -d a t h let ics ou t p u t s sh ou l-d a lso b e con sid er ed . T h e in p u t set sh ou ld a lso in clu d e fu r t h er in for m a t ion on t h e t ea ch er s’ t r a in in g a n d q u a lit y, t h e sch ools’ r esou r ces, a n d t h e socioecon om ic en v ir on m en t .

F u r t h er m or e, t h is w a s a cr oss-sect ion a l st u dy con d u ct ed a t a sin gle p oin t in t im e. St u d ies of a dy n a m ic n a t u r e sh ou ld a lso con -sid er ch a n ges over t im e. As d a t a ava ila b ilit y t h r ou gh st u d ies su ch a s TIMSS in cr ea ses, su ch dy n a m ic st u d ies w ill a lso b e m a d e p ossible.

F in a lly, of ext r em e in t er est w ill b e st u d ies w h ich w ill focu s on in t er n a t ion a l com p a r -ison s. T h e focu s of TIMSS for exa m p le w a s t o p r ov id e t h e m ea n s t o com m u n ica t e k n ow l-ed ge a cr oss cou n t r ies. Sch ool p er for m a n ce ca n gr ea t ly b en efi t fr om in t er n a t ion a l st u d ies w h ich w ill exa m in e b ot h t h e in p u t a n d t h e ou t p u t sid e of t h e sch ool effect iven ess p ic-t u r e. Iic-t wou ld b e of gr ea ic-t in ic-t er esic-t ic-t o exa m in e h ow t h e efficien cy of sch ools ch a n ge a s t h ey a r e com p a r ed a ga in st sch ools op er a t in g in d iffer en t ed u ca t ion a l sy st em s.

Conclusion

In t h is p a p er w e d evelop DE A m od els t o a ssess t h e efficien cy of secon d a r y sch ools in Cy p r u s. We d em on st r a t e h ow in efficien t u n it s ca n b en efi t fr om su ch a n a ly sis a n d b e d ir ect ed t ow a r d s a r ea s w h ich m ay r eq u ir e im p r ovem en t .

On e of t h e m a jor fi n d in gs w a s t h a t in t h e ca se of Cy p r u s, r oom for sch ool efficien cy im p r ovem en t exist s, even t h ou gh n ot gr ea t . Desp it e t h e low r a n k in gs sch ools in Cy p r u s ob t a in ed d u r in g t h e TIMSS, m ost of t h e sch ools fi n d t h em selves ver y close t o t h e efficien t fr on t ier. T h ese r esu lt s em p h a size t h e exist in g h om ogen eit y b et w een sch ools a s fa r

a s efficien cy is con cer n ed , a n d u n d er lin e t h e im p or t a n ce of fu t u r e in t er n a t ion a l efficien cy st u d ies. As in t er n a t ion a l d a t a ava ila b ilit y t h r ou gh st u d ies su ch a s TIMSS in cr ea ses, su ch st u d ies w ill a lso b e m a d e p ossible.

F u r t h er m or e, w e fou n d n o efficien cy d iffer -en ces w h ich ca n b e a t t r ibu t ed solely t o t h e en v ir on m en t , d esp it e t h e low er scor es ob ser ved in r u r a l a r ea s. T h is is a n im p or t a n t fi n d in g for sch ools in Cy p r u s, sin ce t h e effor t s t ow a r d s im p r ovem en t ca n n ow focu s on t h e sch ool level a lon e.

Notes

1 E ven t h ou gh n ot a s p op u la r, sim u lt a n eou s eq u a t ion m od els t o est im a t e m u lt ip le ou t p u t p r od u ct ion t ech n ologies, a n d t h u s over com e t h is p r oblem , h ave b een p r op osed by Lev in (1970) a n d Mich elson (1970).

2 T h is ca n b e a ch ieved by set t in g t h e n u m er a t or of (2) t o a con st a n t a n d m in im izin g t h e d en om in a t or

(Min im ize

3 F u r t h er in for m a t ion on t h e TIMSS st u dy is p r ov id ed in t h e follow in g In t er n et a d d r ess h t t p :/ / w w w cst ee p.b c.ed u / t im ss

4 Alt h ou gh t ea ch er r ot a t ion a m on g d iffer en t sch ools is cu r r en t ly ob ser ved , efficien cy fi n d -in gs su ch a s t h e on es ob t a -in ed h er e a r e n ot con sid er ed w h en m a k in g d ecision s on t h ese r ot a t ion s.

References and further reading

Ba n k er, R.D., Ch a r n es, A. a n d Coop er, W.W. (1984), “Mod els for est im a t ion of t ech n ica l a n d sca le in efficien cies in d a t a en velop m en t a n a ly sis”,

M a n a gem en t S cien ce, Vol. 30, p p. 1078-92. Bessen t , A. a n d Bessen t , W. (1983), “E va lu a t ion of

ed u ca t ion a l p r ogr a m p r op osa ls by m ea n s of d a t a en velop m en t a n a ly sis”, E d u ca tion a l A d m in istra tion Qu a r terly, Vol. 19 N o. 2, p p. 82-107.

Bou ssofi a n e, A., Dy son , R.G. a n d T h a n a ssou lis, E . (1991), “Ap p lied d a t a en velop m en t a n a ly sis”,

E u r op ea n J ou r n a l of Op era tion a l R esea rch, Vol. 52, p p. 1-15.

Ca m er on , K. (1978), “Mea su r in g or ga n iza t ion a l effect iven ess in in st it u t ion s of h igh er ed u ca -t ion ”, A d m in istra tiv e S cien ce Qu a r terly, Vol. 23, p p. 604-32.

Ch a r n es, A., Coop er, W.W. a n d Rh od es, E . (1978), “Mea su r in g t h e efficien cy of d ecision m a k in g u n it s”, E u r op ea n J ou r n a l of Op era tion a l R esea rch, Vol. 2, p p. 429-44.

Ch a r n es, A., Coop er, W.W. a n d Rh od es, E . (1981), “E va lu a t in g p r ogr a m a n d m a n a ger ia l effi-cien cy : a n a p p lica t ion of d a t a en velop m en t a n a ly sis t o p r ogr a m follow t h r ou gh ”, M a n a ge-m en t S cien ce, Vol. 27, p p. 668-97.

F it zsim m on s, J .A. a n d F it zsim m on s, M.J . (1994),

(9)

Gola n y, B. a n d Ta m ir, E . (1995), “E va lu a t in g effi-cien cy -effect iven ess-eq u a lit y t r a d e-offs: a d a t a en velop m en t a n a ly sis a p p r oa ch ”, M a n a ge-m en t S cien ce, Vol. 41 N o. 7, p p. 1172-84. Gr ay, J . (1981), “Sch ool effect iven ess r esea r ch : k ey

issu es”, E d u ca tion a l R esea rch, Vol. 24 N o. 1, p p. 49-54.

J oh n es, G. a n d J oh n es, J . (1993), “Mea su r in g t h e r esea r ch p er for m a n ce of UK econ om ics d e p a r t m en t s: a n a p p lica t ion of d a t a en velop -m en t a n a ly sis”, Ox ford E con om ic Pa p ers, Vol. 45, p p. 332-47.

Lev in , H .M. (1970), “A n ew m od el of sch ool effect iven ess”, in US De p a r effect m en effect of H ea leffect h , E d u ca -t ion 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 t in g Office, Wa sh -in gt on , DC.

Mich elson , S. (1970), “T h e a ssocia t ion of t ea ch er r esou r ces w it h ch ild r en ch a r a ct er ist ics”, in US De p a r t m en t of H ea lt h , E d u ca t ion 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 t in g Office, Wa sh in gt on , DC. N or m a n , M. a n d St ock er, B. (1991), Da ta E n v elop

-m en t A n a lysis: th e A ssess-m en t of Per for -m a n ce, Wiley, Ch ich est er.

Ray, S.C. (1991), “Resou r ce-u se efficien cy in p u blic sch ools: a st u dy of Con n ect icu t d a t a ”, M a n -a gem en t S cien ce, Vol. 37 N o. 12, p p. 1620-8. Sa m m on s, P., N u t t a ll, D. a n d Cu t t a n ce, D. (1993),

“Differ en t ia l sch ool effect iven ess: r esu lt s fr om a r ea n a ly sis of t h e In n er Lon d on Au t h or -it y ’s ju n ior sch ool p r oject d a t a ”, B r itish E d u -ca tion a l R esea rch J ou r n a l, Vol. 19, p p. 381-405. Sa sser, W.E ., Olsen , R.P. a n d Wyck off, D.D. (1978),

M a n a gem en t of S er v ice Op era tion s, Ally n & Ba con , Bost on .

Sext on , T.R. a n d Slee p er, S. (1994), “Im p r ov in g p u p il t r a n sp or t a t ion in N or t h Ca r olin a ”,

In ter fa ces, Vol. 24 N o. 1, p p. 87-103. T h a n a ssou lis, E . (1996), “Alt er in g t h e b ia s in

d iffer en t ia l sch ool effect iven ess u sin g d a t a en velop m en t a n a ly sis”, J ou r n a l of th e Op era -tion a l R esea rch S ociety, Vol. 47, p p. 882-94. T h a n a ssou lis, E . a n d Du n st a n , P. (1994), “Gu id in g

sch ools t o im p r oved p er for m a n ce u sin g d a t a en velop m en t a n a ly sis: a n illu st r a t ion w it h d a t a fr om a loca l ed u ca t ion a l a u t h or it y ”,

J ou r n a l of th e Op era tion a l R esea rch S ociety, Vol. 45, p p. 1247-62.

Zen ios, C., Zen ios, A.S., Aga t h ocleou s, K. a n d Sot er iou , A.C. (1995), B en ch m a rk s of th e E ffi-cien cy of B a n k B ra n ch es, Re p or t 9510, De p a r t -m en t of P u blic a n d Bu sin ess Ad -m in ist r a t ion , Un iver sit y of Cy p r u s, N icosia , Cy p r u s.

Appendix 1

Variable returns to scale model

(M 4 )

Min im ize (16)

su b ject t o:

for a ll i= 1, 2, …, I, (17)

for a ll r= 1, 2, …, R, (18)

(19) (20) (21) Com p a r in g (M 4 ) t o (M 3 ), w e n ot ice t h a t t h eir on ly d iffer en ce is est im a t ed in t h e in clu sion of con st r a in t (18). T h is con vexit y con st r a in t r eq u ir es t h a t m u lt ip lier s λ_jsh ou ld a d d u p t o 1, t h u s en su r in g t h e com p a r ison of DMUs a ga in st a com p osit e u n it of sim ila r size.

Appendix 2

Variables used

Inputs

Age of teacher 1 . Below 2 5 years 2 . 2 5 -2 9 3 . 3 0 -3 9 4 . 4 0 -4 9 5 . 5 0 -5 9 6 . 6 0 and above

Education level Categories inc lude options suc h as of teacher BSc / BA, MA, PhD etc .

Parents’ Categories inc lude sec ondary education educ ation, university or postgraduate

studies, etc .

Socioeconomic Data are obtained from questioning status 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 Existenc e of five c ategories: books at 1 . 0 -1 0 books

student’s 2 . 1 1 -2 5 home 3 . 2 6 -1 0 0

4 . 1 0 1 -2 0 0

5 . More than 2 0 0 books The student is asked to estimate the number of books at his home, exc luding sc hool books, newspapers and magazines

Output

International Average sc ore ac hieved at the sc hool mathematics level in the mathematic s sec tion of