Efficiency of public and private service delivery: the case of secondary education

ERIES Jou nal olume 15 issue 1 P in ed ISSN 2336-2375 33 Elec onic ISSN 1803-1617 EFFICIENCY OF PUBLIC AND PRIVATE SERVICE DELIVERY: THE CASE OF SECONDARY EDUCATION ABSTRACT A cu en issue is he e alua ion o he e iciency o a ious ypes o educa ion se ice p o ide s. This pape aims o e alua e he e iciency o he se ices o seconda y educa ion p o ided by a a ie y o ypes o p o ide s. The e alua ion o seconda y educa ion is pe o med on a sample o 26 g amma schools in he P ešo egion o he Slo ak Republic. The me hod o da a en elopmen analysis (DEA) is used. The esul s o he e iciency o 26 g amma schools in he pe iod 2012- 2013 o 2016-2017 showed ha g amma schools om he sample es ablished by all p o ide s (public, p i a e, chu ch en i y) eached he ull e iciency sco e. By con as , six g amma schools we e e alua ed as he leas e icien . The e alua ion o he se o g amma schools based on he a e age e iciency sco e also showed ha , om he iewpoin o he ypes o p o ide s, public g amma schools each highe e iciency sco es, in compa ison wi h chu ch and p i a e g amma schools. These indings expand on he heo y o public goods wi h espec o hei p oduc ion and ende aluable in o ma ion o no only educa ion p o ide s bu also c ea o s o egional s a egic plans in educa ion policies. KEYWORDS Da a En elopmen Analysis, e iciency, g amma schools, seconda y educa ion, Slo ak Republic HOW TO CITE Halásko á R., Mikušo á Me ičko á B., Halásko á M. (2022) ‘E iciency o Public and P i a e Se ice Deli e y: The Case o Seconda y Educa ion’, Jou nal on E iciency and Responsibili y in Educa ion and Science, ol. 15, no. 1, pp. 33-46. h p://dx.doi. o g/10.7160/e iesj.2022.150104 Rena a Halásko á1* Beá a Mikušo á Me ičko á2 Ma ina Halásko á3 1Uni e si y o Os a a, Facul y o Educa ion, Depa men o Technical and Voca ional Educa ion, Czech Republic 2Ma ej Bel Uni e si y, Facul y o Economics, Depa men o Public Economics and Regional De elopmen , Slo akia 3VŠB-Technical Uni e si y o Os a a, Facul y o Economics, Depa men o Public Economics, Czech Republic * ena a.halasko [email p o ec ed] A icle his o y Recei ed May 26, 2021 Recei ed in e ised o m Augus 30, 2021 Accep ed Janua y 6, 2022 A ailable on-line Ma ch 22, 2022 Highligh s • E alua ion o he e iciency o g amma schools by use o da a en elopmen analysis. • The e alua ion o he e iciency o g amma schools e lec s he o m o inancing and olume o ecei ed inancial esou ces. • Compa ison o he public and p i a e p o ision o seconda y educa ion ailed o a i e a a clea conclusion ha would p omo e any o he o ms. INTRODUCTION E iciency has been a equen ly discussed opic o e he pas ew decades also in he public sec o . The easons behind a e no only h ea s, such as de ici s in budge s o public-sec o o ganisa ions, bu also public demand associa ed wi h an inc eased in e es in he quali y o public se ices p o ided by public-sec o o ganisa ions om he iewpoin o ci izens in he ole o consume s o public se ices (Ch is l, Köppl- Tu yna and Kucse a, 2020). Unde he pe manen p essu e o he public, hese o ganisa ions a e o ced o inc ease he e iciency o he p o ision o public se ices wi h he aim o secu e a long- e m exis ence. As a esul , hei ac i i ies mus unde go an e alua ion o hei e iciency. E iciency is de ined as ex en o which o ganisa ion p oduces a gi en ou pu , o ex en he goals de ined by he o ganisa ion a e ul illed wi h leas possible use o esou ces. When e alua ing he ul ilmen o goals, a mo e complex app oach mus be adop ed in e ms o he p o ision o public se ices, namely 3Es, s anding o economy, e iciency, and e ec i eness (Chan and Lynn, 1991; Lewis and Fall, 2017; López-To es and P io , 2020). The eason is ha i economy o e iciency a e e alua ed, e ec i eness mus also be conside ed, since i plays a signi ican ole in a complex e alua ion (Kaplan and No on, 2000; López-To es and P io , 2020). A he same ime, he e alua ion o e ec i eness is ine i ably ela ed o he e alua ion o economy and e iciency, since when analysing he ex en o he ul ilmen o he de ined goals, economy and an e icien use o esou ces mus also be aken in o accoun Full esea ch pape P in ed ISSN 2336-2375 34 ERIES Jou nal olume 15 issue 1 Elec onic ISSN 1803-1617 (I ne and La cke , 2003; Kuwai i, 2004). I mus also be said ha despi e a complex e alua ion o economy, e iciency and e ec i eness, hese c i e ia may collide (A ms ong, 2015; Flo ina, 2017). As a ule, only a speci ic ype o educa ional p o ide s is conside ed wi h espec o he e alua ion o he e iciency o educa ional ins i u ions (Coulson, 2009; Che chye e al., 2010; C espo-Cebada, Ped aja-Chapa o and San ín, 2013; Naza ko and Šapa auskas, 2014; Sil e nail and Johnson, 2014; Rao, 2015; Mikušo á, 2017). Resea ch s udies al eady ca ied ou dealing wi h he e alua ion o e iciency in educa ion on he egional le el in he Czech o Slo ak Republics ocused on a ious ypes o seconda y schools, howe e only om he pe spec i e o public p o ide s (Chlebouno á, 2019; Mališo á and Š ang eldo á, 2020). Ou come o he p esen esea ch is e alua ion he e iciency o he deli e y o educa ional se ices by di e en ype o p o ide s (public, p i a e, chu ch en i y) wi h a speci ic ocus on high-school educa ion (g amma schools) in egional con ex he Slo ak Republic. On he heo e ical le el, he a icle con ibu es o he b oadening o cu en knowledge ega ding he use o non-pa ame ic e alua ion o echnical e iciency in public se ices wi h espec o he co ec ion o inpu s and ou pu s in he in e es o an e ec i e p o ision o he analysed se ices seconda y educa ion. This pape aims o e alua e he e iciency o he se ices o seconda y educa ion p o ided by a a ie y o ypes o p o ide s. The e alua ion is pe o med a he egional le el on a sample o 26 g amma schools in egion o in he Slo ak Republic P ešo . The au ho s o he pape in end answe he esea ch ques ion (RQ), which s ems om heo e ical bases o he deli e y o public se ices and esul s o s udies pe o med in he gi en a ea. RQ: A e e icien g amma schools in he P ešo egion ela ed o he pa icula ype o educa ion p o ide s (a public, p i a e, chu ch en i y)? A esea ch ques ion is sui ed o explo a o y esea ch, because he ela ionships be ween a iables e iciency and a ious ypes o educa ion se ice p o ide s a e mo e unce ain. The pape is di ided in o six pa s. The i s pa is in oduc ion, which p esen s he gi en opic in b oade con ex om he pe spec i e o he e iciency o public se ices, ollowed by heo e ical backg ound and o e iew o li e a u e on he opics o e iciency o educa ion and e iciency o seconda y educa ion. The hi d pa desc ibes he applied me hod and da a used. The ou h pa p esen s he esul s abou he e alua ion o he e iciency o g amma schools in he Slo ak Republic using he example o he P ešo egion and ende s sugges ions and measu es o he leas e icien schools. The nex pa is discussion, whe e he esul s a e discusses in a wide con ex . The las pa is conclusion, which summa ises he ob ained ou comes and o e s a heme o u he esea ch. Li e a u e e iew E iciency is de ined as he ela ionship be ween he quan i y o inpu s in an implemen a ion o a p ocess, and he quan i y o ou pu s (Flo ina, 2017). E iciency and e ec i eness pu sues he ela ionship be ween inpu s, ou pu s and ou comes (Mihaiu, Op eana and C is escu, 2010:133). The highe is he esul (ou pu ) ob ained in e ms o p esc ibed esou ces (inpu s), he g ea e is he e iciency o an ac i i y (A onso, Schuknech and Tanzi, 2003: 8). E iciency can be e alua ed in a ious a eas o economy. Educa ion ep esen s an a ea o he public sec o . The sec o o educa ion includes schooling a schools a all le els and in simila acili ies ha a e pa ly o ully unded om public esou ces. In gene al, i is impossible o de ine which educa ional se ices all unde he public sec o and which do no , because sys ems o educa ion a y ac oss coun ies and so does he ange o educa ional se ices ha a e co e ed om public esou ces (S igli z and Rosenga d, 2015). O e he pas yea s, app oaches owa ds he e alua ion o e iciency ha e been inc easingly discussed in he sec o o educa ion (Lockheed and Hanushek, 1994; Bohm and Bohmo a, 2016; De Wi e and López-To ez, 2017; Johnes, Po ela and Thanassoulis, 2017; López-To es and P io , 2020). Educa ional e iciency is equen ly con used wi h educa ional e ec i eness, and a imes he wo e ms a e (inapp op ia ely) used in e changeably. Educa ional e ec i eness is whe he o no a speci ic se o esou ces has a posi i e e ec on achie emen and, i so, how la ge his e ec is. Clea ly, since e ec i eness does no di ec ly compa e esou ce uses o cos s, wha is e ec i e is no necessa ily wha is mos e icien (Lockheed and Hanushek, 1994: 2). Thus, in he con ex o educa ion, e icien use o esou ces (be ha inancial o he inna e abili y o s uden s) occu s when he obse ed ou pu s om educa ion (such as es esul s o alue added) a e p oduced a he lowes le el o esou ce; e ec i e use o esou ces ensu es ha he mix o ou comes om educa ion desi ed by socie y a e achie ed. I is e iciency ( a he han e ec i eness) o educa ion (Johnes, Po ela and Thanassoulis, 2017: 331). Educa ional ins i u ions a e seen as mul i-p oduc o ganisa ions p oducing an a ay o ou pu s om a ious inpu s (Johnes, Po ela and Thanassoulis, 2017: 332). Acco ding o a numbe o au ho s, he e iciency o educa ional ins i u ions is a cu en ly discussed opic (Naza ko and Šapa auskas, 2014; Mikušo á, 2017; Agasis i and Zoido, 2018). Besides, he e a e di e en iews on he e alua ion o e iciency in educa ion. Me ičko á e al. (2020) deal wi h measu ing and e alua ing o he pe o mance o seconda y educa ion in he Slo ak Republic and p oposed possible pe o mance indica o s in e ms o public g amma schools. Also o he au ho s (Fe o and D’Elia, 2020; De La Hoz, Zuluaga and Mendoza, 2021) add ess he ques ion o measu ing e iciency in educa ion om a a ie y o pe spec i es. Co de o- Fe e a, Ped aja-Chapa o and Salinas-Jimenez (2008) ocused on di e en possibili ies o measu ing e iciency in he educa ion sec o , aiming o de ine he mos app op ia e model o he e alua ion o schools. De Wi e and López-To es (2017) ca ied ou an ex ensi e e iew o li e a u e on he opic o e iciency in educa ion, summing up selec ed a iables and adop ed app oaches owa d he e alua ion o e iciency in educa ion. A numbe o esea ch s udies deal wi h he e iciency o seconda y educa ion in Eu opean coun ies. A is o nik and Obadić (2014) esea ched echnical e iciency o seconda y educa ion in he EU and OECD coun ies. The esul s con i med ha echnical e iciency in seconda y educa ion di e s ERIES Jou nal olume 15 issue 1 P in ed ISSN 2336-2375 35 Elec onic ISSN 1803-1617 signi ican ly ac oss he majo i y o he analyzed coun ies. Dincă e al. (2021) e alua e he e iciency o he educa ion sec o using a sample o 28 EU coun ies. An e alua ion o alloca ion and echnical e iciency was pe o med a di e en le els o educa ion. Based on he esul s, he au ho s s a e ha “old” membe s a es each a highe e iciency sco e compa ed o “new” membe s a es. Agasis i and Zoido (2018) measu ed he e iciency in 8,000 schools in 30 coun ies (using PISA indica o s). Following he esul s o he pe o mance o high schools in 36 coun ies using PISA indica o s, Co de o e al. (2018) also came o he conclusion ha he e exis s a highe he e ogenei y be ween coun ies han be ween schools. Di e ences be ween schools a e asc ibed mainly o economic indica o s and cul u al alues. O he au ho s (Sa ico and Rosa, 2009; Hen iques and Ma cena o-Gu ie ez, 2021) o e an image o he educa ion sys em by e alua ing he e iciency o seconda y educa ion in selec ed coun ies. In pa icula , Hen iques and Ma cena o-Gu ie ez (2021) concen a ed on he pe o mance o high schools in Po ugal, conside ing he a ia ion o di e en indica o s. The indings indica e ha an a e age e icien public school eaches an a e age sco e, bu is s ill below he OECD a e age. A signi ican aspec ha is e lec ed in he e alua ion o e iciency a high schools is he manne o inancing and he o al olume o ecei ed inancial esou ces wi h espec o he achie ed esul s (A onso and Aubyn, 2006; Agasis i, 2014; Bohm and Bohmo á, 2016; Ga u o a e al., 2017). Agasis i (2014) and Ga u o a e al. (2017) e alua ed he e iciency o public expendi u es on seconda y educa ion in Eu opean coun ies and he quali y o educa ion by use o PISA indica o s. E alua ion o educa ion e iciency is associa ed also wi h he ul ilmen o educa ion goals in ela ion o an e icien use o public esou ces (Ma eso a and Kuca, 2019; Ople alo a, No ako a and Balaban, 2019). As ega ds o he au ho s, Haele mans and De Wi e (2012), o ins ance, assessed he impac o inno a ion in educa ion on seconda y school pe o mance in he Ne he lands. Thei esul s con i m ha inno a ion in p o iling, eaching, p ocesses and educa ion chains is signi ican ly ela ed o e iciency, whe eas inno a ion in highe quali ica ion o eache s has an insigni ican e ec on schools’ e iciency. In a b oade con ex , he e iciency o seconda y educa ion is analysed also in ela ion o compe i ion be ween schools. B adley, Johnes and Milling on (2001) calcula ed he echnical e iciency o all seconda y schools in England in he pe iod 1993-1998 on he basis o a ange o ou pu s (execu ion o exams and isi a e). The esul s indica e ha compe i ion co ela es wi h e iciency. The esul s also showed ha compe i ion is a signi ican de e minan o changes o e iciency in ime. Holmbe g (2017) pe o med he measu emen o ela i e e iciency o high schools in Sweden in he pe iod 2006-2007 h ough 2015-2016 by means o s ochas ic on ie analysis. The signi ican ac o s we e he impac o compe i ion on he school pe o mance and ela i e e iciency o public and independen schools. Also Agasis i (2013) did esea ch in o he e alua ion o e iciency in ela ion o compe i ion, using he example o schools in I aly. The esul s showed ha compe ing schools each highe pe o mance and be e esul s. In connec ion wi h he e iciency o seconda y educa ion, o he au ho s ha e examined he e iciency o public and p i a e schools (Waldo, 2007; Millime and Collie , 2008; Che chye e al., 2010; Rao, 2015) o e iciency o cha e schools (Sil e nail and Johnson, 2014). Millime and Collie (2008) analysed whe he compe i ion amongs public schools in luences he e iciency in which hese schools ope a e. The ob ained indings sugges ha he e a e un esol ed in e ac ions be ween compe i ion, e iciency and inances o school. Waldo (2007) s a es ha he e alua ion o e iciency in Swedish public high schools a he local le el is a ec ed by compe i ion and local policies. Howe e , he au ho is o he opinion ha e iciency o p i a e schools is un ela ed o compe i ion. Che chye e al. (2010) sugges ed addi ional c i e ia (e iciency and equi y) o p i a e (bu publically unded) and public schools in Belgium (Flande s) o compa e he pe o mance o di e en school ypes. Thei app oach includes conside a ions, o ob aining “ ai ” pe o mance compa isons in he public sec o con ex . The gi en opic p o ides an app oach o he e alua ion o he e iciency o seconda y educa ion (g amma schools) om he iewpoin o a ious p o ide s in he egional con ex o he Slo ak Republic. This iew on he e iciency o seconda y educa ion (g amma schools) is signi ican ly ela ed o no only he manne schools a e unded, bu also an ou line o compe i ion condi ions be ween he indi idual ypes o schools. In he economic en i onmen , he aim o non-p ice compe i ion is o a ac demand wi h me hods o he han p ice (Mankiw, 2009). In he p esen case, seconda y schools (g amma schools), when iden ical educa ional se ices a e o e ed by a ious p o ide s o educa ion (public, p i a e, chu ch en i ies), apply me hods o non-p ice compe i ion, such as inc eased quali y o educa ion o inno a ion o educa ional se ices. The use o his compe i ion be ween schools mo i a es he schools o inc ease e iciency. MATERIALS AND METHODS Da a Da a om he S a is ical O ice o he Slo ak Republic om he yea s 2012-2019 we e used o documen he numbe o schools (g amma schools) by ype o educa ion au ho i y in he egions o he Slo ak Republic. The da abase o he e alua ion o e iciency is ep esen ed by seconda y da a ob ained om he epo on educa ional ac i i ies o e he pe iod o i e school yea s, 2012-2013 o 2016-2017. The chosen ime pe iod o e alua ing he e iciency o schools is in luenced by he a ailabili y o da a o all analysed a iables a he ime o s udy p ocessing. The sou ces ha e been chosen om selec ed s a is ics and da abases o he Slo ak Republic. Speci ically, da a a e d awn om he Regis e o Schools and School Facili ies, School Repo s, Eduzbe (collec ion o da a o he pu poses o no ma i e inancing), Managemen Repo s, he NÚCEM da a po al, he INEKO (Ins i u e o Economic and Social Re o ms) p ima y and seconda y schools po al and he S a is ics o he Cen e o Social A ai s and Families. The pape is ocused on he e alua ion o comple e seconda y gene al educa ion (uppe seconda y), which acco ding o Ac no. 245/2008 Coll. (Na ional Council o he Slo ak P in ed ISSN 2336-2375 36 ERIES Jou nal olume 15 issue 1 Elec onic ISSN 1803-1617 Republic, 2008) “applies o he success ul comple ion o he las yea o a leas a ou -yea and a maximum o eigh yea s o he g amma school educa ional p og amme”. The esea ch sample a e selec ed g amma schools in he Slo ak Republic, speci ically in he P ešo egion. Acco ding o he Eu opean Commission/ EACEA/Eu ydice (2020: 2) and Ac no. 245/2008 Coll. (Na ional Council o he Slo ak Republic, 2008), a g amma school “is a gene al, in e nally di e en ia ed seconda y school which educa es pupils in 4-yea , 5-yea o 8-yea educa ional p og ammes and p o ides uppe seconda y gene al educa ion ISCED 344. Educa ional p og ammes o g amma schools ocus pa icula ly on p epa a ion o s udy a highe educa ion ins i u ions; hey may also p epa e o he pu sui o some ac i i ies in public adminis a ion and cul u e“. Fo he esea ch, 26 g amma schools ha e been chosen wi h h ee di e en educa ion p o ide s in he P ešo egion. These g amma schools a e loca ed in he ci ies o he P ešo egion. The g amma schools ha e been selec ed on he basis o andom selec ion. A leas one ep esen a i e was selec ed o each ci y, p o ided i had i s da a published and a ailable. G ea e ep esen a ion o g amma schools is seen in la ge and egional ci ies, such as P ešo . The se o g amma schools includes public (s a e), p i a e and chu ch ou -yea g amma schools. Public g amma schools (Pu), a o al o 15, es ablished by he P ešo sel -go e ning egion ( egion), eigh g amma schools es ablished by chu ch o a chu ch communi y (Ch), and h ee g amma schools which ep esen p i a e es ablishe s (P ). See Table 1 o mo e de ails. School Educa ion p o ide Municipali y G amma school JIRASKOVA 12 BJ public Ba dejo G amma school LIPANY public Lipany G amma school J. A. RAYMAN PO public P ešo G amma school T. VANSOVA SL public S a á Ľubo ňa G amma school DR. C. DAXNER VT public V ano nad Toľou G amma school GIRALTOVCE public Gi al o ice G amma school GEN. L. SVOBODA HE public Humenné G amma school SNINA public Snina G amma school J. F. RIMAVSKY LE public Le oča G amma school P.O. HVIEZDOSLAV KK public Kežma ok G amma school MEDZILABORCE public Medzilabo ce G amma school KUKUCINOVA PP public Pop ad G amma school SABINOV public Sabino G amma school DUKL. HRDINOV public S idník G amma school STROPKOV public S opko P i a e g amma school BJ p i a e Ba dejo P i a e g amma school PP p i a e Pop ad G amma school SUKROMA SPOJENA SKOLA PO p i a e P ešo G amma school SV. MONIKA PO chu ch P ešo E angelical g amma school - EV. SPOJ. SKOLA PO chu ch P ešo G amma school SV. J. ZLATOUSTY HE chu ch Humenné Chu ch g amma school SV. MIKULAS SL chu ch S a á Ľubo ňa G amma school SV. MIKULAS PO chu ch P ešo G amma school SV. F. Z ASSISI LE chu ch Le oča G amma school CIRKEVNA SPOJENA SKOLA HE chu ch Humenné G amma school P.P. GOJDIC PO chu ch P ešo Table 1: Se o g amma schools in he P ešo egion (sou ce: INEKO, 2020a) Inpu and ou pu indica o s ha e been selec ed o e alua e he e iciency o g amma schools. Inpu ac o s: he numbe o eache s pe 100 s uden s and Con ibu ion o one s uden pe school yea . Ou pu ac o s: Ra e o s uden s admi ed o uni e si ies and Uni e si y admission success a e (see Table 2). The inpu and ou pu indica o s in his pape ha e been aken om he o icial da abase INEKO (INEKO, 2020b, 2020c). A ce ain limi a ion in connec ion o he applied ou pu indica o s is he admission a e o applican s o uni e si ies ab oad. This he admission a e o applican s is no moni o ed in e ms o indi idual seconda y schools in Slo akia. Howe e , we do no conside i se ious limi a ion, because he o al pe cen age o all applican s om all schools who manage o s udy a uni e si ies ab oad accoun s ep esen only 17% (OECD, 2018). The esul s o he co ela ion analysis using Pea son’s co ela ion coe icien (Cohen e al., 2013) ha e shown ela ions be ween inpu and ou pu alues in he pe iod 2012- 2013 o 2016-2017. A low o medium co ela ion can be seen be ween he inpu alues in he e alua ed yea s (maximum alue o 0.44); a medium o s ong co ela ion be ween ou pu alues (maximum alue o 0.67); and a nega i e low o medium co ela ion be ween inpu and ou pu alues (maximum alue ERIES Jou nal olume 15 issue 1 P in ed ISSN 2336-2375 37 Elec onic ISSN 1803-1617 o -0.49). A medium o s ong co ela ion was only obse ed be ween ou pu alues in he e alua ed pe iod. Howe e , bo h ou pu indica o s a e conside ed necessa y o he ollowing analysis o he e iciency o schools by use o he DEA me hod, which is he eason why none o he ou pu indica o s has been excluded. Me hods The p esen esea ch applies he me hod o da a en elopmen analysis (DEA) o e alua ion o echnical e iciency o public se ices in he educa ion sec o . DEA is among he mos equen ly used non-pa ame ic me hods in he e alua ion o echnical e iciency o p oduc ion uni s. The e alua ion o he e iciency o he gi en p oduc ion uni ende s he e iciency ega ding he ans o ma ion o i s inpu s o ou pu s ela i e o o he uni s. Unlike he usual calcula ion o e iciency (p oduc i i y) a e, he DEA me hod applies ma hema ical p og amming, which enables he inclusion o a as amoun o inpu s and ou pu s in he model. Unlike he o dina y calcula ion, he weigh s a e a iable and se o maximise he ela i e e iciency a e o he e alua ed uni agains he o he uni s (Coope , Sei o d and Zhu, 2011; Dlouhý, Jablonský and Zýko á, 2018; Melecký, S aníčko á and Hančlo á, 2019). E iciency is exp essed by he ans o ma ion p ocess o inpu s o ele an ou pu s. Fo he analysis, he BCC-O (ou pu - o ien ed model) is applied, which op imises he ou pu s. The abb e ia ion BCC is de i ed om he ini ials o i s au ho s who we e he i s o o mula e i : Banke , Cha nes and Coope (1984). This model conside s a iable e u ns o scale. I is a adial model compa ing he e iciency o se e al n-decision uni s (Decision Making Uni s - DMU) in he ans o ma ion o m inpu s o he same ype o s ou pu s o he same ype (Zhu, 2016). As he e can be a la ge numbe o uni s whose e iciency is analysed, i is mo e sui able o ope a e wi h dual models. A mo e de ailed cha ac e is ic o he BCC model is ende ed by e.g. Banke , Cha nes and Coope (1984), Toloo (2014) o Zhu (2016). N is he numbe o uni s – in ou case g amma schools ( , 1, 2, ..., j DMU j n= ), whe e each consumes m di e en inpu s ( , ij x 1, 2, ..., im= ) and p oduces s di e en ou pu s ( j y , 1, 2, ..., s= ). The ma ix o inpu s may be ma ked as X = { ij x , 1, 2 , ,im= … ; 1, 2 , ,jn= … }, while he ma ix o ou pu s may be ma ked as Y = { , j y 1, 2 , , s= … ; 1, 2 , ,jn= … }. The ou pu -o ien ed BCC model (dual) can be w i en in he ollowing o m (Coope , Sei o d and Zhu, 2011 o Dlouhý, Jablonský and Zýko á, 2018: 33). Maximise () 11 ms q i i ss ϕε −+ = = ++ ∑∑ (1) Subjec o 1 1,..., n j j q q j y s y s λϕ + = −= = ∑ 1 1,..., n ij j i iq j x sx i m λ − = += = ∑ 1 1 n j j λ = = ∑ 0 1,..., jjn λ ≥= 0 1,..., i s im − ≥= 0 1,..., s s + ≥= Whe e ij x a e inpu s, 1, 2, ..., im= is he alue o he i- h inpu o he uni DMUj, m - numbe o inpu s; j y a e ou pu s, 1, 2, ..., s= is he alue o he - h ou pu o he uni DMUj, s - numbe s o ou pu s; and whe e q is e alua ed DMUq, yq is he ou pu o e alua ed DMUq, xq is he inpu o e alua ed DMUq, q ϕ − e iciency a e o he e alua ed uni (DMUq). Depending on he cha ac e o e u ns o scale, a condi ion has been added in he model. The condi ion, p esuming a iable e u ns o scale, is as ollows: 1 1 n j j λ = = ∑ s+ , 1, 2..., s= , and i s− , 1, 2..., ,im= a e dual a iables a ibu ed o low cons ain s o weigh s o inpu s and ou pu s. In he limi ing condi ions, hese a e slack a iables o inpu s ( ) s+ and ou pu s ( ) s− and he ε is an in ini esimal cons an by means o which he model secu es a posi i e alue o all weigh s o inpu s and ou pu s. Componen s o ec o 12 ( , , , ), 0 n jj λ λλ λ λ =…≥ as weigh s (coe icien s o linea combina ion) assigned o he espec i e uni s o he e alua ed se (Coope , Sei o d and Zhu, 2011; Dlouhý, Jablonský and Zýko á, 2018). DEA models p o ide he use s wi h ou pu in o ma ion no only ega ding he e iciency a e bu also abou how he e alua ed uni s (g amma schools in he p esen Va iable Desc ip ion Uni Sou ce Inpu s Numbe o eache s pe 100 s uden s The numbe o eache s pe 100 s uden s a he school. Fo he pu poses o his indica o , in e nal eache s, ex e nal eache s and eache s o p ac ical subjec s a e conside ed. Numbe s a e acked as o Sep embe 15 h o he espec i e school yea . numbe School po al INEKO Con ibu ion o one s uden pe school yea The olume o inancial esou ces a he school’s disposal o one yea . The sums a e p o ided in he amoun pe s uden and pe school yea , beginning wi h espec o he yea de ined. eu os School po al INEKO Ou pu s Ra e o s uden s admi ed o uni e si ies The sha e o seconda y school g adua es accep ed o a leas one uni e si y in he ollowing school yea in Slo akia agains he o al numbe o g adua es. pe cen age School po al INEKO Uni e si y admission success a e The sha e o seconda y school g adua es accep ed o a leas one uni e si y in he ollowing school yea in Slo akia agains he o al numbe o candida es who applied o a a leas one uni e si y. pe cen age School po al INEKO Table 2: Inpu and ou pu a iables o he analysis (sou ce: INEKO, 2020b, 2020c) P in ed ISSN 2336-2375 38 ERIES Jou nal olume 15 issue 1 Elec onic ISSN 1803-1617 esea ch) imp o e hei ac i i ies o each he e iciency on ie (Dlouhý, Jablonský and Zýko á, 2018: 35). Some ad an ages o he DEA app oach a e: he sou ces o ine iciency can be analysed and quan i ied o e e y e alua ed uni ; capable o being used wi h any inpu - ou pu measu emen , al hough o dinal a iables emain icky (Coope , Sei o d and Zhu, 2011). By using he DEA SOLVER so wa e o p ocessing he analysis, he inal o de o e icien g amma schools is ob ained along wi h he answe o he ques ion which schools (g amma schools) a e e icien and which a e no . E icien uni s a e on he e ge o e iciency while e iciency is equal o 1. The ou come o he DEA analysis is a se o ecommenda ions o ine icien uni s (in he p esen s udy o g amma schools) on how o s eamline he p oduc ion o hei educa ional se ices. RESULTS Rep esen a ion o he numbe o g amma schools by ypes o educa ion p o ide in egions o he Slo ak Republic Acco ding o he Eu opean Commission/ EACEA/EURYDICE (2020) g amma schools in he Slo ak Republic a e es ablished by he s a e ep esen ed by a sel -go e ning egion, o a egional o a dis ic au ho i y (61.7%), p i a e en i ies (16.6%), he chu ch (21.7%). I is he e o e a speci ic combina ion o public/ p i a e mix o p oduc ion and inancing o educa ion se ices wi h a speci ic ocus on g amma schools. The o e iew o g amma schools by he ype o educa ion p o ide in egions o he Slo ak Republic is seen in Table 3. Yea s 2012, 2015 and 2019 ha e been chosen o he sake o compa ing he end o he numbe o high schools (g amma schools). Slo akia/ egions** 2012 2015 2019 schools* schools* schools* Public P i a e Chu ch To al Public P i a e Chu ch To al Public P i a e Chu ch To al Slo akia 152 39 55 245 149 40 57 246 145 39 51 235 BR egion 21 13 9 43 21 15 945 20 16 9 45 TRN egion 16 2 4 22 16 3 3 22 16 3 2 21 TRE egion 12 3 4 19 12 3 4 19 11 3 4 18 NI egion 17 2 8 27 17 1 8 26 16 0 6 22 ZI egion 21 2 6 29 21 2 730 21 2 6 29 BB egion 20 5 5 30 19 5 5 29 18 6 4 28 PR egion 21 6 13 40 21 513 39 21 512 38 KO egion 23 6 6 35 22 6 8 36 22 4 8 34 No e:* Numbe o schools as o Sep embe 15 h o he espec i e yea , No e:** BR- B a isla a egion; TRN- T na a egion; TRE-T enčín egion; NI- Ni a egion, ZI-Žilina egion, BB- Banská Bys ica egion, PR- P ešo egion, KO- Košice egion. Table 3: Numbe o g amma schools by ype o educa ion p o ide in egions o he Slo ak Republic (sou ce: au ho s acco ding o he S a is ical O ice o he Slo ak Republic, 2021) E alua ing he numbe o g amma schools in he Slo ak Republic, a no iceable educ ion in he numbe o g amma schools can be seen, namely 235 g amma schools in 2019 compa ed o 245 in 2012, o 246 in 2015. Compa ing he ep esen a ion o g amma schools in he indi idual egions o he Slo ak Republic, he la ges numbe o g amma schools is ound in he B a isla a egion (app oxima ely 18%), ollowed by he P ešo egion (app oxima ely 16%), and he hi d la ges numbe o g amma schools (14%) is loca ed in he Košice egion. On he o he hand, he lowes numbe o g amma schools om he egions o he Slo ak Republic is ep esen ed in he T enčín egion (app oxima ely 8%), wi h 19 g amma schools in 2012 and 2015, and 18 g amma schools in 2019. As ega ds g amma schools by he ype o educa ion au ho i y, public g amma schools accoun o he majo i y in egions o he Slo ak Republic, ollowed by chu ch g amma schools (wi h he excep ion o he B a isla a egion). P i a e g amma schools a e he leas ep esen ed in mos egions. The numbe o g amma schools acco ding o he speci ic educa ion au ho i ies (public, p i a e, chu ch) di e s sligh ly in he espec i e egions, especially in he B a isla a egion (p i a e g amma schools) and in he P ešo egion (chu ch g amma schools). The esul s clea ly show ha , speci ically in he P ešo egion, ou o he o al o 38 g amma schools 21 a e public g amma schools (55.5%), 5 a e p i a e g amma schools (13.2%), and 12 a e chu ch g amma schools (31.6%). Using he example o selec ed g amma schools in he P ešo egion, an analysis o he e iciency o seconda y educa ion is ca ied ou in he nex pa o he esul s. E alua ion o he e iciency o g amma schools in he condi ions o he Slo ak Republic using he example o he P ešo egion In his pa is p esen ed he e iciency o 26 g amma schools in he P ešo egion in he school yea s 2012- 2013 o 2016-2017, using he BCC-O model. The sco e e iciency in he espec i e yea s is seen in Table 4. ERIES Jou nal olume 15 issue 1 P in ed ISSN 2336-2375 39 Elec onic ISSN 1803-1617 Based on he o e all esul s o success a e o e he school yea s 2012-2013 o 2016-2017, G amma school J. A. Rayman, ha ing achie ed he e iciency sco e o 1 in all e alua ed yea s, can be conside ed he bes e iciency model. G amma school Ji asko a 12 in Ba dejo and G amma school Medzilabo ce, bo h e icien ou imes in he cou se o he i e yea s, achie ed he second bes esul s in e iciency in he e alua ed yea s. G amma school Lipany, G amma school P. P. Gojdic and G amma school T. Vanso a in S a a Lubo na achie ed h ee ull e iciency sco es. On he con a y, six g amma schools we e ine icien in all e alua ed yea s. These we e wo g amma schools es ablished by he sel -go e ning P ešo egion, h ee g amma schools es ablished by he chu ch, and one es ablished by a p i a e en i y (see Table 4). On he whole, mos ly g amma schools es ablished by he egion and chu ch eached he ull sco e (=1), whe eas p i a e g amma schools eached ull e iciency only in he school yea 2013-2014. In 2012-2013, 10 g amma schools we e e icien : se en public and h ee chu ch. In 2014-2016, only i e g amma schools we e e icien each yea , ou o which we e public and one chu ch. The highes numbe o e icien g amma schools, 11, was obse ed in he school yea 2016- 2017. The numbe o e icien g amma schools in he obse ed pe iod by he ype o educa ion p o ide is seen in Table 5. Schools E iciency sco e 2012-2013 2013-2014 2014-2015 2015-2016 2016-2017 G amma school JIRASKOVA 12 BJ (Pu) 1 1 1 1 0.8812 G amma school LIPANY (Pu) 0.9666 0.9724 1 1 1 G amma school J. A. RAYMAN PO (Pu) 1 1 1 1 1 G amma school T. VANSOVA SL (Pu) 1 0.9647 1 0.9823 1 G amma school DR. C. DAXNER VT (Pu) 0.9731 0.9554 1 0.9100 0.9868 G amma school GIRALTOVCE (Pu) 1 0.9078 0.9952 0.9282 1 G amma school GEN. L. SVOBODA HE (Pu) 1 1 0.9928 0.9960 0.9527 G amma school SNINA (Pu) 0.9438 0.9972 0.9789 0.9907 1 G amma school J. F. RIMAVSKY LE (Pu) 0.957 0.9718 0.9782 0.9161 0.9208 G amma school P.O. HVIEZDOSLAV KK (Pu) 1 1 0.9773 0.9700 0.9627 G amma school MEDZILABORCE (Pu) 1 1 0.9753 1 1 G amma school KUKUCINOVA PP (Pu) 0.883 0.8653 0.9716 0.8466 1 G amma school SABINOV (Pu) 0.9362 0.8936 0.9195 0.9400 1 G amma school DUKL. HRDINOV SVIDNIK (Pu) 0.9362 0.9265 0.9636 0.8212 0.9889 G amma school STROPKOV (Pu) 0.9574 0.9091 0.9507 0.9253 1 P i a e g amma school BJ (P ) 0.8511 0.9732 0.9263 0.8500 0.9493 P i a e g amma school PP (P ) 0.8617 1 0.9263 0.8900 0.9300 G amma school - souk oma spojena skola PO (P ) 0.8511 1 0.8316 0.9800 0.8600 G amma school SV. MONIKA PO (Ch) 0.9409 0.9689 0.9876 0.9618 0.9083 E angelical g amma school - EV. SPOJ. SKOLA PO (Ch) 0.8936 0.8386 0.9674 0.7900 0.9878 G amma school SV. J. ZLATOUSTY HE (Ch) 0.9761 1 0.9368 0.9400 1 Chu ch g amma school SV. MIKULAS SL (Ch) 0.9985 0.9535 0.9368 0.9830 1 G amma school SV. MIKULAS PO (Ch) 0.8191 0.9263 0.9847 0.8900 0.9501 G amma school SV. F. Z ASSISI LE (Ch) 1 0.978 0.8931 0.9146 0.9296 G amma school CIRKEVNA SPOJENA SKOLA HE (Ch) 1 1 0.8842 0.8300 0.9467 G amma school P.P. GOJDIC PO (Ch) 1 1 0.8842 1 0.9606 No e: Pu – public g amma school, P – p i a e g amma school, Ch – chu ch g amma school Table 4: E iciency sco e in g amma schools in he P ešo egion in he school yea s 2012-2013 o 2016-2017 (sou ce: au ho s by use o DEA SOLVER) To al numbe o g amma schools by educa ion p o ide E icien g amma schools in he obse ed school yea s 2012-2013 2013-2014 2014-2015 2015-2016 2016-2017 Public (15) 7 5 5 4 9 Chu ch (8) 3 3 0 1 2 P i a e (3) 0 2 0 0 0 Table 5: Numbe o e icien g amma schools in he P ešo egion by educa ion p o ide (sou ce: au ho s) Table 6 shows he a e age e iciency sco e o g amma schools in he P ešo egion. I can be seen ha he in he pe iod 2012-2013 o 2016-2017 he a e age e iciency sco e o he 26 g amma schools in he P ešo egion anged om 0.91 o 1 in 15 public g amma schools, om 0.90 o 0.92 in h ee p i a e g amma schools, and om 0.90 o 0.97 in eigh chu ch g amma schools. P in ed ISSN 2336-2375 40 ERIES Jou nal olume 15 issue 1 Elec onic ISSN 1803-1617 Recommenda ions o ine icien g amma schools in he P ešo egion by he ype o educa ion p o ide Now, ecommenda ions and sugges ions a e p esen ed o he ine icien g amma schools in he school yea s 2012-2013 o 2016-2017, using he da a p esen ed in he ou pu o he DEA analysis. The absolu e alues and ecommended pe cen age changes o inc ease and achie e e iciency a e p o ided o selec ed ine icien uni s (ine icien g amma schools). The s a ed alues and pe cen age changes depend on he selec ion o inpu and ou pu ac o s as well as on he selec ion o he model and i s o ien a ion. In all i e e alua ed school yea s, 2012-2013 o 2016-2017, six g amma schools we e ine icien . These a e wo g amma schools es ablished by a public educa ion p o ide (G amma school in S idnik and G amma school J. F. Rima sky in Le oca), h ee chu ch g amma schools (G amma school s . Mikulas, G amma school s . Monika in P ešo , and E angelical g amma school - E anjelicka spojena skola in P ešo ), and one p i a e g amma school (P i a e G amma school Ba dejo ). The lis o he ine icien g amma schools acco ding o he ype o educa ion p o ide is shown in Tables 7-9. Recommenda ions o ine icien public g amma schools Recommenda ions based on he BBC-O ou pu -o ien ed model o he imp o emen o ine icien public g amma schools in he P ešo egion a e cap u ed in Table 7. schools a e age sco e schools a e age sco e G amma school JIRASKOVA 12 BJ (Pu) 0.98 G amma school DUKL. HRDINOV SVIDNIK (Pu) 0.93 G amma school LIPANY (Pu) 0.99 G amma school STROPKOV (Pu) 0.95 G amma school J. A. RAYMAN PO (Pu) 1 P i a e g amma school BJ (P ) 0.91 G amma school T. VANSOVA SL (Pu) 0.99 P i a e g amma school PP (P ) 0.92 G amma school DR. C. DAXNER VT (Pu) 0.97 G amma school - souk oma spojena skola PO (P ) 0.90 G amma school GIRALTOVCE (Pu) 0.97 G amma school SV. MONIKA PO (Ch) 0.95 G amma school GEN. L. SVOBODA HE (Pu) 0.99 E angelical g amma school - EV. SPOJ. SKOLA PO (Ch) 0.90 G amma school SNINA (Pu) 0.98 G amma school SV. J. ZLATOUSTY (Ch) 0.97 G amma school J. F. RIMAVSKY (Pu) 0.95 Chu ch g amma school SV. MIKULAS SL (Ch) 0.97 G amma school P.O. HVIEZDOSLAV KK (Pu) 0.98 G amma school SV. MIKULAS PO (Ch) 0.91 G amma school MEDZILABORCE (Pu) 0.99 G amma school SV. F. Z ASSISI LE (Ch) 0.94 G amma school KUKUCINOVA PP (Pu) 0.91 G amma school CIRKEVNA SPOJENA SKOLA HE (Ch) 0.93 G amma school SABINOV (Pu) 0.94 G amma school P.P. GOJDIC PO (Ch) 0.97 No e: Pu – public g amma school, P – p i a e g amma school, Ch – chu ch g amma school Table 6: A e age e iciency sco e o g amma schools in he P ešo egion in he pe iod 2012-2013 o 2016-2017 (sou ce: au ho ’s calcula ions) School yea G amma school J. F. Rima sky in Le oca I1 I2 O1 O2 Sco e E 2012-2013 -15.6 -6.3 4.5 4.5 0.95 2013-2014 0 0 2.9 2.9 0.97 2014-2015 0 0 2.4 2.2 0.97 2015-2016 -9.2 0 11.3 9.2 0.92 2016-2017 -1.8 0 8.6 8.6 0.92 School yea G amma school Duklianskych h dino in S idnik I1 I2 O1 O2 Sco e E 2012-2013 -8.1 -5.6 10.8 6.8 0.93 2013-2014 0 -1.2 9.4 7.9 0.92 2014-2015 -7.2 0 3.8 4.5 0.96 2015-2016 -30. 0 30.3 21.8 0.82 2016-2017 0 -1.8 1.1 1.1 0.98 No e: inpu indica o I1 – sha e o eache s pe 100 s uden s; inpu indica o I2 – con ibu ion o s uden in EUR; ou pu indica o O1 – a e o g adua es admi ed o uni e si y in %; ou pu indica o O2 – uni e si y admission success a e in % Table 7: P ojec ion o ine icien g amma schools (educa ion p o ide is a public en i y) (sou ce: au ho s using DEA SOLVER) I he sugges ions o inc easing he e iciency o public g amma schools a e e alua ed acco ding o he BBC-O model (Table 7), a p oblem occu ed in he case o G amma school J. F. Rima sky in Le oca in he analysed pe iod ega ding he numbe o eache s pe 100 s uden s, and in each yea an inc ease in he a e o admi ed s uden s (O1) and he pe cen a e o admission (O2). Fo he las wo yea s analysed, he equi ed inc ease anges om 8 o 11%. To inc ease and ERIES Jou nal olume 15 issue 1 P in ed ISSN 2336-2375 41 Elec onic ISSN 1803-1617 a he same ime app oach he pa e ns o e iciency, i is ecommended o o e p epa a o y cou ses o uni e si ies led by eache s and p o esso s om he equi ed uni e si ies, which could inc ease in e es and mo i a e s uden s o be mo e in e es ed in p epa ing o en ance exams. Fo he i s and he las wo yea s analysed, a educ ion o he numbe o eache s pe 100 pupils (I1) is ad ised, caused by he g adual educ ion o he o al numbe o pupils and school eache s o e he las h ee yea s om 199 pupils o 176, and he numbe o eache s dec eased by one each yea . This phenomenon may ha e been caused by he lack o in e es on he pa o elemen a y-school lea e s and hei pa en s due o p ejudices abou he quali y o chu ch high schools in he Slo ak Republic. G amma school in S idnik was ine icien in he analysed pe iod as a esul o a high, subop imal numbe o eache s pe 100 pupils, and also ailed o achie e a su icien pe cen age o success ul admission o uni e si ies and he a e o g adua es admi ed o uni e si ies. In 2016-2017, compa ed o 2015- 2016, he g amma school inc eased he e iciency sco e om 0.82 o 0.98, because he o al numbe o school s uden s had been educed om 219 o 197, and also educed he numbe o eache s om 24 o 22, and in u n, he numbe o success ully admi ed g adua es inc eased. In he school yea 2015-2016, 44 ou o 66 g adua es we e admi ed and in he ollowing yea 56 ou o 63 g adua es. To inc ease e iciency, we ecommend o inc ease (O1) he sha e o admi ed g adua es a uni e si ies and (O2) he admission a e using p epa a o y cou ses which can help g adua es in uni e si y en ance exams. Recommenda ions o ine icien p i a e g amma schools Sugges ions o he ou pu -o ien ed model (BCC-O) o inc ease he e iciency o one p i a e g amma school in he P ešo egion a e lis ed in Table 8. School yea P i a e g amma school Ba dejo I1 I2 O1 O2 Sco e E 2012-2013 -54.0 -17.5 26 17.5 0.85 2013-2014 -14.4 0 12.5 2.8 0.97 2014-2015 -24.6 -0.99 124.4 8.0 0.92 2015-2016 -39.6 -2.0 28.9 17.7 0.85 2016-2017 -21.32 0 5.3 5.3 0.94 No e: inpu indica o I1 – sha e o eache s pe 100 s uden s; inpu indica o I2 – con ibu ion o s uden in EUR; ou pu indica o O1 – a e o g adua es admi ed o uni e si y in %; ou pu indica o O2 – uni e si y admission success a e in % Table 8: P ojec ion o an ine icien g amma school (educa ion p o ide is a p i a e en i y) (sou ce: au ho s using DEA SOLVER) In he e alua ed yea s, he P i a e g amma school Ba dejo was ine icien . I came closes o he e iciency limi in he school yea 2013-2014 wi h he sco e o 0.97. Table 8 shows sugges ions o inpu and ou pu co ec ions o each yea . Following he analysis h ough an ou pu -o ien ed model, i can be seen ha a yea -on-yea educ ion (I1) o he numbe o eache s pe 100 s uden s is ecommended. A he same ime, an inc ease o he sha e o uni e si y g adua es admi ed o uni e si ies (O1) and o he pe cen age o uni e si y admission success (O2) is ecommended on an annual basis. Based on hese indings, i is ecommended o educe he high p opo ion o eache s pe 100 s uden s while i would be sui able o use he se ices o ex e nal eaching s a o inc ease he a ac i eness o he school, e.g. o eign eache s, exchange s ays and an inc ease in he numbe o pupils a he school and hus inc ease i s e iciency. Once he numbe o s uden s admi ed o he g amma school has inc eased, he sha e o eache s pe 100 pupils will dec ease, and he g amma school will app oach he limi o e iciency. The sha e o s uden s admi ed o uni e si y can be inc eased h ough p epa a o y cou ses. Recommenda ions o ine icien chu ch g amma schools Following he ou pu -o ien ed model (BCC-O), Table 9 p o ides sugges ions o imp o ing he e iciency o h ee g amma schools, which a e es ablished by he chu ch o chu ch communi y. Based on he ou pu -o ien ed BCC-O model, educ ion o inpu s as well as ou pu s is ecommended o G amma school s . Mikulas. Rega ding ou pu s, i is ecommended o engage in educa ion h ough clubs, communica ion and exchange s ays wi h o eign s uden s, o c ea e pa ne schools and pa icipa e in o eign p ojec s and hus inc ease he chances o admission o uni e si ies. The model o he imp o emen o e iciency also ecommends a educ ion (I2) in he con ibu ion pe s uden . This phenomenon may be caused by he poo ly s a ed eal amoun o he con ibu ion o he s uden con ibu ion comes om se e al sou ces. In he case o G amma school s . Monika in P ešo , o inc ease e iciency, i is ecommended o educe inpu s and inc ease ou pu s. Acco ding o he analysis o he las yea , his g amma school could achie e e iciency i i inc eases bo h ou pu s (O1, O2) by 10%. We sugges pa icipa ing in p ojec s and ge ing mo e poin s o he admission p ocedu e by engaging and w i ing e.g. wo k on p o essional ac i i ies o he school. Based on he model, i is ecommended o he E angelical g amma school in P ešo o educe bo h inpu ac o s (I1, I2), when in 2014-2015 and 2016-2017 he ecommended educ ion o he s uden con ibu ion exceeded 40%. The en i e con ibu ion om public unds is b oken down in o he numbe o s uden s in he school.