ASSESSMENT OF REGIONAL EFFICIENCY IN CROATIA USING DATA ENVELOPMENT ANALYSIS

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1 ASSESSMENT OF REGIONAL EFFICIENCY IN CROATIA USING DATA ENVELOPMENT ANALYSIS Danijela Rabar Juraj Dbrila University f Pula Department f Ecnmics and Turism Dr. Mij Mirkvić Preradvićeva 1, Pula, Cratia danijela.rabar@unipu.hr Abstract In this paper, reginal efficiency f Cratian cunties is measured in three-year perid ( ) using Data Envelpment Analysis (DEA). The set f inputs and utputs cnsists f seven sciecnmic indicatrs. Analysis is carried ut using mdels with assumptin f variable returns-t-scale. DEA identifies efficient cunties as benchmark members and inefficient cunties that are analyzed in detail t determine the surces and the amunts f their inefficiency in each surce. T enable prper mnitring f develpment dynamics, windw analysis is applied. ased n the results, guidelines fr implementing necessary imprvements t achieve efficiency are given. Analysis reveals great disparities amng cunties. In rder t alleviate naturally, histrically and plitically cnditined unequal cunty psitins ver which ecnmic plicy makers d nt have ttal cntrl, categrical apprach is intrduced as an extensin t the basic DEA mdels. This apprach, cmbined with windw analysis, changes relatins amng efficiency scres in favr f cntinental cunties. Key wrds: Data envelpment analysis, Reginal efficiency, Cunty, Windw analysis, Categrical variables 1. INTRODUCTION Reginal efficiency and pssibilities f its imprvement have becme ne f the leading imperatives f all wrld ecnmies. This paper is the result f a research related t multicriterial evaluatin f the achieved reginal develpment level in Cratia. 76

2 The purpse f this paper is t present the results f the analysis f reginal efficiency in Cratia using Data Envelpment Analysis (DEA) investigating the pssibility f applicatin f different extensins t DEA mdels in the treatment f the same prblem. DEA is a nn-parametric prductive efficiency measurement methd fr peratins with multiple inputs and multiple utputs. This apprach first establishes an efficient frntier frmed by a set f decisin making units (DMUs) that exhibit best practices and then assigns the efficiency level t ther nn-frntier units accrding t their distances t the efficient frntier. In this way the methd cmbines and transfrms multiple inputs and utputs int a single efficiency index. The study f Liu et al. (2013) surveys the DEA literature by applying a citatin-based apprach and rates Charnes, Cper and Rhdes (1978, 1981), anker, Charnes and Cper (1984) and Charnes et al. (1985) as fur mst influential papers in DEA develpment. The same study identifies five majr branches f DEA literature, r in ther wrds, five active DEA subareas: tw-stage cntextual factr evaluatin framewrk, extending mdels, handling special data, examining the internal structure and measuring envirnmental perfrmance. While the papers in the first fur subareas are mstly studies f theretical rientatin, the papers in the last subarea are basically applicatin wrks that, amng thers, include the applicatins f DEA n reginal perfrmance evaluatin. An interesting and ften cited example in the internatinal literature is evaluatin f the relative achievement f reginal develpment in 23 administrative regins f Taiwan in 1990, in which the use f DEA was extended by merging with the Malmquist prductivity apprach t determine whether the relative change f their reginal develpment mved frwards r backwards between 1983 and 1990 (Chang, Hwang and Cheng, 1995). DEA is relatively rarely used in the measurement f reginal efficiency in Cratia. Amng the first t address this issue were abić and Grčić (1999) wh evaluated relative reginal develpment level fr Cratian cunties and macrregins in 1991 cmparatively using tw multicriterial analysis methds PROMETHEE and DEA. Althugh the DEA methd itself is present in the literature cncerning the assessment f reginal efficiency, the cmbinatin f categrical apprach and windw analysis is riginal as well as the use f unique cmbinatin f inputs and utputs. The results f the study underline the imprtance f cmbining categrical apprach and windw analysis fr future research. 77

3 2. DATA AND MODEL SETUP Cratian cunties represent 21 entities whse relative sci-ecnmic efficiency is evaluated in this paper. The chice f indicatrs fr the purpses f this study fllwed the subsequent line f thught: capturing human and material cmpnents and living standards as three utstanding criteria fr determining the degree f sci-ecnmic develpment; exact measurability f indicatrs; availability and accessibility f data n indicatrs. In additin, in any DEA applicatin, it is suggested as rule f thumb that the number f entities shuld be at least three times the number f indicatrs (anker et al., 1989). Accrdingly, seven sci-ecnmic indicatrs 1 are included int analysis. The inputs are represented by registered unemplyment rate and number f supprt allwance users. The utputs are share f the secndary sectr in grss value added (GVA), grss fixed capital frmatin in fixed assets (by headquarter f investr), level f imprt cverage by exprt 2, number f graduated students (by residence) and grss dmestic prduct (GDP). Data fr these indicatrs are relating t the perid and were taken frm the Cratian Emplyment Service, the Cratian ureau f Statistics and the Ministry f Health and Scial Welfare f the Republic f Cratia 3. asic DEA mdels cmmnly used in applicatins are CCR (Charnes, Cper and Rhdes, 1978) and CC (anker, Charnes and Cper, 1984). CCR mdel is built n the assumptin f cnstant and CC mdel n the assumptin f variable (either increasing r decreasing) returns t scale activities. In additin, the DEA mdel can be adjusted t the strategy chsen by management and therefre riented n input reductin (input-riented mdel) r n utput augmentatin (utput-riented mdel). Let us cnsider the set f n DMUs. Each f them (DMU j, j = 1, 2,..., n) prduces s utputs and fr their prductin uses m inputs. Let us dente xj = { xij, i = 1,2,..., m} the vectr f inputs and { y, r = 1,2 s} yj = rj,..., the vectr f utputs fr the DMU j. Then the data set is given by tw matrices the matrix f inputs: X ( xij, i = 1,2,..., m, j = 1,2,..., n) Y = ( yrj, r = 1,2,..., s, j = 1,2,..., n). = and the matrix f utputs: The basic principle f DEA mdels in evaluatin f efficiency f the DMU, { 1, 2,..., n} 4 cnsists in lking fr a virtual DMU with inputs and utputs defined as the linear cmbinatin f inputs and 1 The variables fr which smaller amunts are preferable will be cnsidered inputs, while thse fr which larger amunts are preferable will be cnsidered utputs. 2 level f imprt cverage by exprt = (ttal exprts / ttal imprts) *100 3 The data were adjusted as fllws: numbers f supprt allwance users and graduated students were taken per 100,000 inhabitants while capital frmatin and GDP were taken per capita at cnstant prices f the year The fllwing prcedure is based n Cper, Seifrd and Tne, 2006, pp

4 utputs f the ther DMUs in the decisin set, i.e. Xλ and Yλ, where λ ( λ λ,..., ) =, λ > 0 is the vectr f weights (cefficients f linear cmbinatin) f the DMUs. The virtual DMU shuld be better (r at least nt wrse) than the analysed DMU. The prblem f lking fr a virtual DMU can generally be frmulated as standard linear prgramming prblem: 1, 2 λ n Input-riented mdel Output-riented mdel (CC I ) min θ (CC O ) max η subject t θ x Xλ 0 subject t Xλ x (1) Yλ y η y Yλ 0 (2) e λ = 1 e λ = 1 (3) λ 0 λ 0 (4) where e is a rw vectr with all elements equal t 1. Cnditins (1) cnsist f m, cnditins (2) f s, and cnditins (4) f n cnstraints. In ur case, n = 21, m = 2, s = 5. Vectr λ shws the prprtins cntributed by efficient DMUs t the prjectin f DMU nt efficient frntier. The ptimal bjective value θ ( 0 θ * 1) in the input-riented mdel is the efficiency result, and fr inefficient DMU * < als the input reductin rate. In the utput-riented mdel, the ptimal bjective value η ( η * 1) is the reciprcal f the efficiency result, and fr inefficient DMU als the utput enlargement rate. This makes the mst imprtant difference between input-riented and utput-riented CC mdels. It is bvius frm cnstraints (1) and (2) that in the input-riented mdel ( X λ, Yλ ) utperfrms ( θ x, y ) + shrtfalls s R when * < θ 1. With regard t this prperty, the input excesses s s + with s 0, 0 are defined and identified as slack vectrs by s = θ x Xλ s fr any feasible slutin ( λ) s = Yλ y +,, θ, f (CC I ). R m * and the utput T discver the pssible input excesses and utput shrtfalls, a tw-phase prcedure is used. In the first phase, θ is minimized and, in the secnd phase, the sum f the input excesses and utput * shrtfalls is maximized keeping θ = θ (the ptimal bjective value btained in the first phase). Definitin 1 (CC-Efficiency): 79

5 + If an ptimal slutin ( θ λ, s, s ), btained in this tw-phase prcess satisfies θ * = 1 and has n + slack ( s = 0, s = 0 ), then the DMU is called CC-efficient, therwise it is CC-inefficient. Definitin 2 (Reference Set): Fr a CC-inefficient DMU, its reference set E = An ptimal slutin can be expressed as E is defined based n an ptimal slutin { j λ > 0 } j { 1, 2,..., n } j ( ) θ * x = x j λ j + s, j E + y = y j λ j s. j E. λ by These relatins suggest that the efficiency f ( x, y ) fr DMU can be imprved if the input values are reduced radially by the rati θ * (thus remving technical inefficiency) and the input excesses recrded in s are eliminated, and if the utput values are augmented by the utput shrtfalls in (thus remving mix inefficiency). Described imprvement can be expressed by the fllwing frmula knwn as the CC-prjectin: xˆ * = θ x s, + y ˆ = y + s. Using an analgus prcedure, the slack ( t, t + ) f the utput-riented mdel is defined by + s t = x + Xλ and t = Yλ ηy, while the prjectin is expressed by: x ˆ = x t, + y ˆ = η y + t. ased n the freging, it is evident that efficiency scres, reference sets and prjectins f inefficient DMUs depend n mdel rientatin, while the efficient frntier des nt. The need fr the mnitring f reginal develpment dynamics, which is extremely imprtant fr ecnmic plicy makers, leads t the use f windw analysis as ne f the extensins t DEA mdels. 80

6 In that case, data fr several perids fr each DMU are included int analysis, and each DMU is regarded as if it were a different DMU in each f the reprting perids. Anther issue in evaluating the relative efficiency is dealing with situatins when DMUs perate under different cnditins ver which they d nt have ttal cntrl. In such cases, the evaluatin f all DMUs n equal fting wuld be unfair t thse in wrse psitin. The slutin is prpsed with the use f categrical apprach that prvides apprpriate cmparisns by dividing DMUs int L categries. Thus, DMUs in categry 1 are in the mst disadvantageus cnditin and will be cmpared nly amng themselves. DMUs in categry 2 are in a better psitin than thse in categry 1, and will be cmpared with reference t DMUs in categries 1 and 2 and s n. In cnclusin, DMUs in categry L will be cmpared with reference t all DMUs. This way, evaluating the efficiency by cmparing DMUs in wrst psitin with thse in better psitin is avided. 3. MODEL APPLICATION AND EMPIRICAL RESULTS Knwledge f the prductin frntier characteristics fr the prcess t be analyzed is crucial fr mdel type selectin. Since that culd nt be determined with certainty in the case f reginal perfrmance, the analysis was carried ut under bth (cnstant and variable returns-t-scale) assumptins. It appeared that differences between the results btained by CCR and CC mdel were significant. They may be attributed t the return effect with respect t the range f activities thus making the CC mdel mre suitable fr describing the analyzed sci-ecnmic activity. Since ecnmic grwth is aimed at decreasing all here selected inputs and increasing all here selected utputs at the same time, bth rientatins are utilized and the btained results are cmpared. The assessment f Cratian cunties relative efficiency is perfrmed in tw steps, based n empirical data n seven sci-ecnmic indicatrs, and cmputed by prgram package DEA-Slver-Pr 7.0F (Saitech, Inc.). Due t the nature f selected indicatrs, cmparisns f the cunties were made n a yearly basis. The first step f this research was carried ut using windw analysis. Since a three-year perid is chsen, the windw (i.e. the perid within which the cmparisns are perfrmed) ranges frm ne t three years. Fr the purpses f this study, ne windw which includes all three years is used. The relative efficiency results are listed in Table 1. Amng 63 bserved entities, 15 turned ut t be efficient. The highest efficiency results were achieved in 2007 tward bth rientatins. Nne f the 21 cunties were efficient during the entire perid. The wrst efficiency results accrding t the number f efficient cunties were achieved in 2006, while the lwest average efficiency was achieved 81

7 in Average efficiency scres fr all three perids are greater in utput rientatin than in input rientatin. The differences related t rientatin are extreme in certain aspects, fr instance, in minimum efficiency scres. Hwever, it des nt mean that the efficiency is easier t achieve tward utput-rientatin because that depends n the specific situatin in which particular cunty perates. Large differences between the average and wrst efficiency results give evidence f great reginal disparities in Cratia. Table 1: Windw analysis results ne windw ( ) Surce: Authr s calculatins Surces and amunts f relative inefficiency and prpsed imprvements are extremely valuable infrmatin n which authrities can set gals and make decisins that will lead t them. The imprtance f reference set shuld als be emphasized because it prvides infrmatin n the rle mdels fr each inefficient cunty. Since windw analysis, unlike basic DEA mdels, des nt bring these results, a new mdel will be cnstructed as fllws. Three data sets n seven selected indicatrs, ne fr each f the bserved years, are included int a basic CC mdel fr each cunty. In this way, 82

8 each f 63 f them is treated as separate entity. Such mdel cnstructin is justified because it des nt affect relative efficiency scres identified by windw analysis using ne three-year windw 5 and yet calculates additinal crucial results. Cunty that was rated efficient usually appears in the reference sets f inefficient cunties. The frequency f its ccurrence in thse sets can be cnsidered as an indicatin f whether it is a rle mdel t ther cunties. Table 2 displays these frequencies fr every efficient cunty. Table 2: The reference set frequency accrding t windw analysis ne windw ( ) Surce: Authr s calculatins Istria-2007 sets a gd example fr the input-riented case (32) and City f Zagreb-2007 leads in the utput-riented case (39). While the City f Zagreb stands ut due t the perfrmances in 2007, the Cunty f Istria excels in tw years (2006 and 2007) and it makes it relatively mst successful cunty. The average differences per inefficient cunty between empirical and prjected values in every input and utput are displayed in Table 3. Grss fixed capital frmatin in fixed assets has far the strngest influence n inefficiency during the whle perid and tward bth rientatins. On the ther hand, mstly the number f graduated students least affects relative efficiency. Anther issue in evaluating the perfrmance f Cratian cunties is their great disparities caused by reasns ver which ecnmic plicy makers d nt have cmplete cntrl. In that cntext, the evaluatin carried ut in the first step f this research seems unfair t cntinental cunties and t indulgent t castal cunties and particularly t the City f Zagreb. Therefre, it appears mst 5 Fr example, the Cunty f Istria is represented by three entities which, due t the need f mutual distinguishing, are marked as Istria-2005, Istria-2006 and Istria Thus the efficiency scre in the rw relating t the Cunty f Istria and in the clumn relating t the year 2006 is in fact the efficiency scre f the entity named Istria

9 apprpriate t classify Cratian cunties int three categries. Hence, the City f Zagreb is placed in categry 3 (gd), all 7 cunties f Adriatic Cratia in categry 2 (average) and the rest f 13 cunties in categry 1 (pr). Table 3: Surces and average amunts f inefficiency accrding t windw analysis ne windw ( ) Surce: Authr s calculatins The secnd step f this research was therefre carried ut using a categrical apprach. The rle f categrical mdels in measuring reginal efficiency in Cratia is t alleviate the impact f naturally, histrically and plitically cnditined unequal psitin f its cunties. At the same time, the primary rle f windw analysis mdels is t mnitr the dynamics f achieving sci-ecnmic efficiency f the cunties. Thse extensins t basic DEA mdels slve tw independent prblems but there is the questin f mdel chice in the case f their simultaneus reslutin. A satisfactry slutin is prvided by the cmbinatin f categrical mdel and windw analysis. Since n existing mdel meets these requirements, the new mdel is cnstructed based n the previus windw analysis mdel by assigning crrespnding categries t all f 63 entities. This means that the categry f a particular cunty is assigned t each f three entities that represent the cunty. S designed mdel will be hereafter referred t as the cmbined CC mdel. Its results are identical t the results f windw analysis using ne three-year windw with the categrical apprach. This pens the pssibility f their cmparisn with the results f afre described windw analysis mdel (with n categrical variables). 84

10 Table 4: Cmbined CC mdel results ne windw ( ) and three categries Surce: Authr s calculatins Applicatin f the cmbined CC mdel using bth rientatins led t the results shwn in Table 4. Cmparisns f the results listed in Tables 1 and 4 shw their significant differences, with the 85

11 exclusin f City f Zagreb and Istria 6. With the categrical apprach, amng 63 bserved entities, 19 turned ut t be efficient, which were fur mre than accrding t the previus mdel. Similar t the previus mdel, the best results f average efficiency accrding t all criteria were achieved in the year The wrst results accrding t the efficiency scre were achieved in 2006, while the number f cunties that were efficient in 2005 and 2006 was the same. Mst f the reference set frequencies generated by this mdel (Table 4) are significantly different cmpared t the previus mdel, mainly at the expense f Istria and City f Zagreb. That happened mstly because thse tw cunties nw cannt be members f reference sets f inefficient cunties in the mst numerus categry 1. Table 5: Surces and average amunts f inefficiency accrding t the cmbined CC mdel ne windw ( ) and three categries Surce: Authr s calculatins Average differences per inefficient cunty between empirical and prjected values in every input and utput are displayed in Table 5. Similar t the previus mdel, grss fixed capital frmatin in fixed assets has the strngest influence n inefficiency. On the ther side, this influence is nt nearly as strng as in the previus mdel. That is because capital frmatin in cntinental cunties is generally cnsiderably lw cmpared with the rest f Cratia, thus raising the amunt f average inefficiency in that utput. Since the cmparisn f categry 1 with the ther tw categries is here bypassed, the inefficiency related t capital frmatin is significantly reduced. 6 The reasns f keeping the efficiency unchanged differ fr these tw cunties. The City f Zagreb is in bth mdels cmpared t the same set f cunties and therefre nthing changes. Istria is relatively the best perfrming cunty, s the cmparisn with City f Zagreb des nt threaten its efficiency scre. 86

12 4. CONCLUSION Assessment f relative efficiency f Cratian cunties accrding t windw analysis and t the cmbined mdel was based n their tw cmmn features. Specifically, the cunties were cmpared t ne anther at the level f ne three-year perid and based n the same set f indicatrs. In the windw analysis mdel, which enabled mnitring f develpment dynamics, each cunty was cmpared t all ther cunties. esides the develpment dynamics, specifically cnstructed cmbined mdel tk int accunt unequal psitin f cunties by cmparing each f them nly t the cunties frm the same r lwer categries. Therefre, relative efficiency scres accrding t this mdel were nt lwer than accrding t the previus ne. After classificatin f cunties, a significant number f them imprved the efficiency. Sme even became efficient. Therefre, the ttal average relative efficiency increased, advancing frward the categrical apprach fr mst cunties as preferred. REFERENCES abić, Z. and Grčić,. (1999), Evaluatin f relative develpment level fr Cratian cunties, in: Aganvić, I., Hunjak, T. and Scitvski, R. (editrs), Prceedings f the 7 th Internatinal Cnference n Operatinal Research KOI 98, Rvinj, Cratia, September 30 Octber 2, 1998, Cratian Operatinal Research Sciety, Osijek, pp anker, R.D., Charnes, A. and Cper, W.W. (1984), Sme Mdels fr Estimating Technical and Scale Inefficiencies in Data Envelpment Analysis, Management Science, Vl. 30, pp anker, R.D., Charnes, A., Cper, W.W., Swarts, J. and Thmas, D. (1989), An intrductin t data envelpment analysis with sme mdels and their uses, Research in Gvernmental and Nn-Prfit Accunting, Vl. 5, pp Chang, P., Hwang, S. and Cheng, W. (1995), Using data envelpment analysis t measure the achievement and change f reginal develpment in Taiwan, Jurnal f Envirnmental Management, Vl. 43, pp Charnes, A., Cper, W.W., Glany,., Seifrd, L.M. and Stutz, J. (1985), Fundatins f data envelpment analysis fr Paret-Kpmans efficient empirical prductin functins, Jurnal f Ecnmetrics, Vl. 30, pp Charnes, A., Cper, W.W. and Rhdes, E. (1981), Evaluating prgram and managerial efficiency an applicatin f data envelpment analysis t Prgram Fllw Thrugh, Management Science, Vl. 27, pp Charnes, A., Cper, W.W. and Rhdes, E. (1978), Measuring the Efficiency f Decisin Making Units, Eurpean Jurnal f Operatinal Research, Vl. 2, pp Cper, W.W., Seifrd, L.M. and Tne, K. (2006), Intrductin t Data Envelpment Analysis and Its Uses: With DEA-Slver Sftware and References, Springer, New Yrk. Cratian ureau f Statistics, Statistical Yearbk f the Republic f Cratia, varius issues, Zagreb. Cratian Emplyment Service, Yearbk, varius issues, Zagreb. 87

13 Liu, J.S., Lu, L.Y., Lu, W.-M. and Lin,.J. (2013), Data envelpment analysis : A citatin-based literature survey, Omega, Vl. 41, pp Ministry f Health and Scial Welfare f the Republic f Cratia, Annual statistical reprt n applied scial welfare rights, legal prtectin f children, the yuth, marriage, family and persns deprived f business capacity, and the prtectin f persns with physical r mental disabilities in the Republic f Cratia, varius issues, Zagreb. 88