Evaluation of Cost Efficiency in Finnish Electricity Distribution

Transcription

1 Jue 4, 2002 Evaluatio of Cost Efficiecy i Fiish Electricity Distributio Pekka Korhoe ad Mikko Syrjäe (May 2002) Helsiki School of Ecoomics P.O. Box 1210, Helsiki, FINLAND Tel , Fax The results are based o a empirical research project fuded by the Miistry of Trade ad Idustry, ad the Eergy Market Authority. The theoretical research was also supported, i part, by grats from the Academy of Filad, the Foudatio of the Helsiki School of Ecoomics, the Foudatio for Ecoomic Educatio, the Foudatio for Commercial ad Techical Scieces, ad IVO-foudatio. We would like to thak the project co-ordiator Mr Kari Lavaste from the Eergy Market Authority, the members of the steerig group of the project, ad the members of the expert group for their pleasat ad productive co-operatio durig the project. We would also like to thak the two aoymous referees who helped us to improve the paper. All rights reserved. This study may ot be reproduced i whole or i part without the authors' permissio. \\Beta\meeyht\Mikko\EMV-artikkeli\EMV Prosessi Aals revisio.doc, , 14:41

2 1 ABSTRACT This paper describes the process of developig a approach to evaluatig the cost-efficiecy of Fiish electricity distributio compaies for regulatio purposes. The process cosisted of three mai stages 1) describig of the problem ad explorig the key factors, 2) fidig measurable quatities for the most essetial factors, ad 3) selectig the fial model to be used i the regulatio. The efficiecy evaluatio is based o Data Evelopmet Aalysis (DEA). The fial model icludes operatioal costs as a iput variable, ad amout of distributed eergy ad quality of distributio (iterruptio time) as output variables. The geographic dispersio of customers (legth of lies) ad the umber of customers are used as evirometal variables so that distributio compaies operatig i differet eviromets ca be compared. Based o data from year 1998, 21 out of 102 compaies are classified as efficiet. The average efficiecy score is 76.9 % ad the lowest oe is 42.6 %. The Eergy Market Authority uses the selected model i supervisig the reasoableess of distributio pricig. Keywords: Data Evelopmet Aalysis, Cost Efficiecy, Electricity Distributio 1 Itroductio The deregulatio of the electricity sector i may Europea ad other coutries has divided the previously vertically itegrated sector ito differet busiesses. I most cases, trasmissio ad distributio are cosidered as atural moopolies ad the price level is regulated. Quite frequetly, Data Evelopmet Aalysis (DEA) is used as a part of the regulatio scheme. There are a umber of articles i OR ad ecoomics jourals ad other reports that describe the use of DEA i the assessmet of electricity distributio. For example, see Bagdadioglu et al. [1996], Försud ad Kittelse [1998], Hjalmarsso ad Veiderpass [1992a, b], Kittelse [1993], Lagset ad Torgerse [1997], Lodo Ecoomics [1999a, b], ad Weyma-Joes [1992]. I Filad, the Electricity Market Act liberalised electricity markets i Sales, productio, trasmissio ad distributio are curretly separate fuctios (but ot ecessarily i separate compaies). Trasmissio ad distributio are defied to be atural moopolies ad oe distributio compay operates o each geographic area. Based o the Electricity Market Act, the compaies are obliged to coect all customers i the area to the etwork ad to deliver electricity for a reasoable compesatio. Also, the compaies have to maitai, use ad develop the etwork so that the eeds of the customers are met, ad a adequate quality is esured. The Electricity Market Act further obliges the authorities to supervise the distributio busiess ad the reasoableess of the distributio pricig. The task of supervisio has bee assiged to the Eergy Market Authority (EMA). Oe of the tasks of the EMA is to defie the cost level that a compay ca achieve by efficiet operatio. The reasoable price level is allowed to cover these costs ad a reasoable retur o ivestmet. The compaies are obliged to report the data eeded by the EMA i the evaluatio.

3 2 Whe the EMA fids that a compay violates the Electricity Market Act, it ca oblige the compay to chage its behaviour, e.g. to lower its distributio price level. If the compay is ot satisfied with the decisio it ca appeal from it to the Supreme Admiistrative Court. For details of the cases, see a example by the EMA [1999]. I the begiig of the year 2000, there were 106 local distributio compaies i Filad. The abudace of the compaies eables a relative efficiecy compariso. However, the compaies do ot work i similar coditios, which makes the compariso more complicated. The coditios deped o the geographic areas where the compaies operate, ad they are very differet e.g. for urba ad rural compaies. To make the compariso possible, we eed to take ito accout those differetiatig coditios. I this study, efficiecy compariso has bee made by meas of DEA. I DEA, the umerical iputs ad outputs of the uits (compaies) are the basic data for evaluatio. I additio, the umerical idicators that characterise the evirometal coditios of the compaies are icluded i the aalysis. Prior to this study, DEA has bee used i the assessmet of the electricity distributio i Filad i a prelimiary study commissioed by the EMA from the Research Istitute of the Fiish Ecoomy (ETLA). The goal was to study the techical efficiecy of the Fiish distributio busiess (Hokatukia ad Sulamaa [1999]). Based o the prelimiary study, the EMA decided to use DEA as the method for efficiecy evaluatio. To develop the model to be used i the regulatio, EMA commissioed the project described i this paper. The objective of the project was to create a DEA based method of assessig the cost-efficiecy of the Fiish distributio busiess. A special feature was the eed to achieve broad acceptace for the approach amog the distributio compaies. That is why the represetatives of the compaies played a very importat role through the whole developmet process. Especially, i explorig factors affectig the operatio eviromet, their expertise was a ecessity. The model, developed together with the represetatives of the distributio compaies ad those of the EMA, has bee adopted as a part of the moitorig system of the EMA. I this paper, we describe the successful process ad the model that was developed. We especially cocetrate o the key questios related to specifyig the model i.e. determiig the factors that describe the electricity distributio busiess; specifyig idicators for differet factors; ad selectig the idicators to be icluded i the DEA model. O the other had, techical aspects of DEA ad the use of the results i regulatio are ot discussed extesively. The aalysis is aturally preseted here i a simplified way sice, as usual, it cosisted of a umber of iteratios ad feedback loops. The developmet process ca be divided i three mai phases: 1) describig the problem ad explorig the key factors, 2) fidig measurable quatities for the most essetial factors, ad 3) selectig the fial model. The paper cosists of five sectios. I Sectio 2, we itroduce the developmet process ad essetial factors. The selectio of the idicators ad the model is described i Sectio 3, ad

4 3 the results are give i Sectio 4. Cocludig remarks are made i Sectio 5. DEA-models discussed i the text ad used i this study are mathematically formulated i Appedix A. 2 Developmet Process ad Exploratio of Potetial Factors A special aim of the project was to thoroughly aalyse the distributio busiess, ad based o this aalysis itroduce relevat measures eeded i the efficiecy evaluatio. It is especially importat to take ito accout so-called evirometal factors sice the compaies operate i sigificatly differet operatioal eviromets. The EMA had chose DEA as the assessmet method based o previous studies. However, the acceptace of the distributio compaies for the DEA-based approach was oe importat goal. To achieve the goals, two iterest groups were established. The first oe, a steerig group, icluded represetatives from the authorities: the Miistry of Trade ad Idustry, the EMA, ad the Competitio Authority. The first two of these also fiaced the project. Idustry experts costituted the other group, the group of experts, which played a key role i the selectio of factors ad idicators that were use to characterise the distributio busiess. They especially cotributed to explorig evirometal factors that affect the costs of the compaies. The developmet process ca be divided ito three stages. The objective of the first stage was to map potetial factors that could be icluded i the evaluatio of the distributio busiess. For this purpose it was ecessary to get acquaited with the ature of the distributio busiess, the techical structure of the distributio etwork, ad the orgaisatios i the electricity distributio idustry. Durig the secod stage, data was collected ad the best umerical idicators for the potetial factors were sought. Fially, the variables were first examied usig umerical data, o the basis of which a model was selected for the evaluatio of efficiecy. Further, the results produced by the selected model were aalysed. The first stage is described i this sectio ad the other two i the subsequet sectio. The outputs of the distributio busiess are related to the service it provides to the customers, the relatioship with the authorities, ad the effect o the eviromet ad the society. The possible output factors were approached through a aalysis of iterests. The iput side o the other had describes how the compay processes the moetary iput (turover) to physical iputs ad resources. To use costs as the iputs seemed to be the most relevat way to deal with iputs, because the priciples of operatio of the compaies are differet. For istace, some compaies have outsourced their maiteace activities, ad they have miimal labour costs. Thus the labour costs are ot comparable with the costs of the compaies that have ot outsourced their maiteace activities. Moreover, it also makes dealig with the iput simpler. The iitial factors related to the operatig eviromet were aalysed usig the followig bottom-up approach. At the first stage, altogether 37 potetial factors were foud usig a braistormig approach. May of these factors describe relatively detailed aspects ad effects related to the operatioal eviromet. To defie more geeral factors that could be used i the assessmet of efficiecy, these factors were ext classified ito groups with a similar backgroud. The factors were further aalysed based o their sigificace ad the meas of

5 4 impact. The aalysis led to a re-groupig of the factors so that the umber of factors was further reduced. Figure 1 presets a example of a factor ad a umber of effects it covers. Similar aalysis was used for all evirometal factors. Geographical dispersio of customers Distributio distace Size of the territory Need for cablig Urba coditios Difficult costructio coditios Rural coditios Overhead lies Frequet chages i the etwork Log distaces Figure 1 Geographical distributio of customers ad the factors it covers We compared our ideas to previous iteratioal studies. Lodo Ecoomics [1999a, b] presets a comprehesive literature review ad a thorough aalysis based o a study commissioed by the Australia regulator. For other studies, see for example Hjalmarso ja Veiderpass [1992a, b], Försud ad Kittelse [1998]. Most of these previous studies measure oly techical efficiecy ad are based o physical measures of iputs. I our case the goal was to aalyse cost level. Usig physical iputs i the aalysis of cost efficiecy would brig alog the problem of fidig the uit prices. Aother frequet problem seems to be the evaluatio of the capital iput i.e. either the amout of capital or the cost of capital. The most commo outputs i literature are the amout of distributed eergy, the umber of customers, the peak demad ad the service area. These are characterised usig differet idicators ad differet levels of aggregatio. Correspodigly, usual iputs are etwork size, labour, geeral expeses, ad etwork losses i.e. the eergy lost i trasmissio. I some cases, average of the iterruptio time i customer hours is proposed to be icluded i the aalysis. There is o agreemet o which factors are cotrollable ad which are ot. Some of the studies also call some of these factors or some combiatio of them evirometal factors. However the studies do ot usually describe the selectio of factors or the process exhaustively. For oe exceptio, see Kittelse [1993]. Cotrary to most of the earlier studies DTE [2000] uses total operatioal expediture as iput i the DEA-model. The measuremet of iput is thus based o accoutig data - ot physical measures. I our project, the followig factors were cosidered potetially sigificat based o the qualitative aalysis discussed above. The abstractio level of the factors varied at this stage of the process. Some of the factors are more directly related to the expeditures, ad some are

6 5 more abstract ad have a idirect or less clear effect o the cost level. The expert group approved the list as a startig poit for further aalysis. Iputs: Operatioal expediture Cost of capital Outputs: Distributed eergy Quality Evirometal factors: Geographical dispersio of customers Number of customers Forest cover Witer Chage i the cosumptio of electricity Isular areas Urbaisatio 3 Idicators ad selectio of the model 3.1 Selectio of Idicators The ext step was to fid the umerical idicators for the potetial factors. The idicators that were fially used i the aalyses are listed i Table 1. Table 1 Factors ad umerical idicators used i the aalyses Factor Selected idicator (Abbreviatio) Iput: Operatioal expediture Amout of operatig costs, cotrolled by the compay (OpEx) Outputs: Distributed eergy Amout of distributed eergy weighted by the average atioal voltage-levelbased distributio prices (value of distributed eergy) (EergyV) Evirometal factors: Quality Geographical dispersio of customers Number of customers Witer Forest cover Movig average of customers total iterruptio time (h) (Iter3y) Total etwork legth of the differet voltage levels (km) (Lies) Number of users (Customers) Average sow depth i the witer (cm) (Sow) Forest cover (km 2 ) (Forest)

7 6 The selectio of the idicators from a group of potetial oes was based o a umber of prelimiary aalyses ad discussios with the expert group. Next we summarise the discussio o the selectio of idicators. Operatioal expediture ad cost of capital A atural measure of operatioal expediture is available i the accoutig data. We oly eed to subtract the costs that are outside the cotrol of the compaies from their total costs. For example the price paid for the atioal grid is such a cost item. Oe possible idicator for the cost of capital is ivestmets. The EMA uses the movig average of ivestmet as a proxy for depreciatio i their moitorig activities. However, the reported ivestmet expeditures fluctuated remarkably from year to year, causig high fluctuatio i efficiecy scores. Thus, whe usig ivestmets as a iput, the efficiecy scores did ot characterise the efficiecy of the compay but rather the amout of the ivestmet expeditures durig the period. Furthermore, icludig ivestmets to a model that is used to assess the performace durig a particular year is coceptually questioable sice the ivestmets are plaed for a lifetime of tes of years. A decisio was therefore made to discard ivestmets as a measure. Other available idicators for capital expediture, such as depreciatio, were foud to be poor as well. Fially, a decisio was made to exclude capital expediture from further aalysis. Distributed eergy ad quality The key questio that is related to measurig distributed eergy is the potetial aggregatio of voltage levels. A weighted sum of differet voltage levels was foud to be a good approach. The extet of the value added of the differet voltage levels was characterised by the average atioal distributio price of each voltage level. This seems to be more atural tha icludig each voltage level as a separate variable, which would icrease the umber of dimesios. The movig average of customers total iterruptio time was foud to be the best available idicator for quality. I this output idicator small values are preferred. Thus, techically we iclude it i the DEA-models as a iput, as suggested by Dyso et al. [2001]. However, the EMA ca oly make decisios cocerig the cost level of the compaies. Thus we eed to preserve the cost iterpretatio of the results, ad Quality is treated as a so-called odiscretioary factor. Geographical dispersio of customers ad umber of customers Network legth was used as a idicator for the geographical dispersio of customers. Eve if etwork legth is ot a perfect idicator, its beefit is that it describes the actual distace to each customer. A drawback is that the compaies ca cotrol the legth of etwork. Three differet idicators of etwork legth were compared. First, differet voltage levels were directly summed up. Secod, a weighted sum based o stadardised operatig costs was used, ad third, ivestmet costs were used as alterative weights. Neither weightig model, however, correlated better with the operatig costs tha the direct summig. Overhead

8 7 lies ad cables i the low-voltage (0,4 kv) grid were ot separated i the data, ad thus exact weightig was impossible. Cosequetly, a decisio was made to give up weightig. Both the geographical dispersio of customers ad the umber of customers are such that higher values of the idicators are assumed to cause higher costs, ceteris paribus, ad thus the evirometal factors are treated as outputs. This also applies to Witer ad Forest cover. Witer ad forest cover We foud forest cover i square kilometres i the distributio area be a reasoable proxy for icreased costructio costs, added risk for iterruptio etc. The problem is, of course, that the compay does ot always eed to build the lies ito the forest although there would be forest i the distributio area. Similarly Sow is a proxy for all the coditios that are liked to witer coditios. The problem here is that there is o atural scale (size of the compay) icluded i the average sow depth, which was cosidered the best idicator. Thus, this idicator ca oly be used i a variable returs to scale DEA-model. Other factors No useful umerical idicator could be foud for isular coditios, therefore a decisio was made to examie the impacts of isular coditios i retrospect, based o the results produced by DEA. No special idicator was derived for urbaisatio, either, but it was assumed that the geographical dispersio of customers ad the umber of customers, amog others, would together serve to characterise desely populated areas with a sufficiet degree of accuracy. Also here, the impact was aalysed afterwards. Furthermore, i the prelimiary aalysis all the possible idicators of chage i the cosumptio of electricity were foud to characterise the additioal costs ad ivestmets poorly. 3.2 DEA models The aim of the project was to build a suitable DEA model for the EMA. I this sectio the basic priciples ad cocepts i DEA are discussed. The startig poit of DEA is to perform a compariso of a uit relative to the other uits i the populatio. The uits are compared to productio plas that are based o existig uits ad their combiatios. Baker, Chares ad Cooper [1984] preset the followig priciples for modellig feasible productio possibilities: - All the observed productio plas are feasible - If a productio pla is feasible, the ay pla cosumig more iput or producig less output is feasible - Covex combiatios of ay existig productio plas are feasible These priciples lead to a variable returs to scale model origially preseted by Baker et al. [1984], which is ofte called the BCC model. The uits that defie the boudary of the productio possibility set are called efficiet. Efficiecy of a uit is measured as a maximal proportioal decrease i the iputs or a maximal proportioal icrease i the outputs. The efficiecy score presets the chage i the iputs or outputs that would make the uit efficiet.

9 8 For the efficiet uits the score is 1 or 100 % ad for the iefficiet uits betwee 0 ad 1. These ideas are illustrated i Figure 2, where the solid lie illustrates efficiet productio plas i the case of variable returs to scale. The mathematical formulatio is available i Appedix A, model (A2). I the case of costat returs to scale the productio plas defied above ca be scaled proportioally. Thus ay feasible productio pla leads to aother feasible pla if we multiply all iputs ad all outputs by ay positive coefficiet. Thus for a efficiet uit, a p % icrease i all iputs is assumed to lead to a p % icrease i all outputs. Efficiecy is ow measured i relatio to this set i the same way as above. This leads to the so-called CCR model, origially preseted by Chares, Cooper ad Rhodes [1978], which is preseted mathematically i Appedix A, model (A1). The dashed lie i Figure 2 illustrates efficiet productio plas i this case. 6 5 D Output 4 3 B F' C F 2 E'' E' E 1 A Iput Figure 2 Illustratio of priciples behid basic DEA models I Figure 2, the models are illustrated i a oe iput ad oe output case. I the mathematical formulatio of the DEA models, this idea is geeralised to the case of multiple iputs ad outputs. DEA models also have a coectio to the classical defiitio of productivity i.e. output per iput. From Figure 2 we see that i the case of costat returs to scale this ratio is the slope of the lie from origi to a uit. I the case of multiple iputs ad outputs, this ratio is geeralised as a weighted sum of outputs per weighted sum of iputs. Furthermore, i the case of costat returs to scale the maximal productivity is assumed to be depedet of the size. I stadard DEA models discussed above, we assume that all iputs (outputs) ca be proportioally decreased (icreased). I our case, Quality was treated as a o-discretioary

10 9 iput. Hece, we eed to modify the model i such way that quality is ot assumed to be improved. I this model, the feasible productio plas are defied as above but we oly seek to decrease the use of oe iput factor. This model, origially itroduced by Baker ad Morey [1986], is mathematically preseted i Appedix A as model (A3). This model was used i this study both as a costat ad as a variable returs to scale variat. 3.3 Selectio of the model The selectio of the factors or the idicators to be icluded i the DEA model was maily based o the results of two kids of aalyses. First, the prelimiary data aalysis was based o correlatio ad regressio aalyses ad a graphic examiatio of variables. Secod, the focus was o the results produced by the differet combiatios of idicators. Afterwards, the statistical tests ad the stepwise procedure suggested by Kittelse [1993] for the selectio of variables were used i a comparative aalysis. The selectio of variables was discussed both with domestic ad iteratioal experts. Prelimiary data aalysis First, the correlatio of variables was examied, after which the mutual ifluece of variables was studied usig graphical presetatios. A liear regressio model was used i the exploratory aalysis of the joit effects of the variables. Results of these aalyses are preseted i Table 2 ad Table 3. Table 2 Correlatios of the selected idicators OpEx Iter3y EergyV Lies Customers Sow Forest OpEx 1.00 Iter3y EergyV Lies Customers Sow Forest Table 3 Results of a liear regressio (OpEx as depedet variable) Coefficiet Std Error t Stat P-value (two sided) Iter3y EergyV Lies Customers Sow Forest

11 10 These results are aturally oly idicative. Our fial goal is ot to try to describe the average relatioship ad especially ot with a liear fuctio. These results however suggest that Sow ad Forest are ot related to the operatioal costs. Selectio of the fial combiatio of factors Whe selectig the fial combiatio, we aalysed the effect of each factor by addig ad removig factors from the DEA-model. At the early stages of the process both costat ad variable returs to scale models were compared. Fial comparisos were based o the variable returs to scale model (model (A3) i Appedix A) ad the results preseted here are based o this model versio. The startig poit was a combiatio, which icludes OpEx ad the four other factors, EergyV, Iter3y, Lies ad Customers, that were suggested to have a sigificat effect o the cost level. We call this model the basic model. I the selectio of the fial combiatio of factors, graphical aalysis was used to study the effects o the efficiecy scores whe idicators were excluded from or icluded i the basic model. For example, Figure 3 presets the decreases i efficiecy whe the quality idicator Iter3y was excluded, ad Figure 4 presets the icreases i the efficiecy scores whe the idicator Forest was icluded Chage i Efficiecy Score Iter3y/Customer Figure 3 Decreases i efficiecy scores whe excludig Iter3y from the basic model

12 11 Chage i Efficiecy Score Forest Figure 4 Icreases i efficiecy scores whe icludig Forest to the basic model The selectio of the factors to be icluded i the model was maily based o aalysig the umber of uits clearly affected by the chage i the model. This was cosidered as a idicator of the average effect of the factor o the costs. As ca be see from Figure 3, Iter3y affects a large umber of compaies ad it thus seems that there is a coectio betwee the cost level ad the iterruptios. O the other had, Figure 4 illustrates how Forest affects oly a relatively small umber of uits ad ot eve all the compaies that have a large forest cover. The selected combiatio of factors is aturally a result of a compromise betwee the coverage of the factors ad the discrimiatig power of the model. Accordig to statistical aalyses, all of the selected factors have a impact either o the cost level or efficiecy. o the other had, it has ot bee possible to show that the factors excluded from the model have a statistical coectio to costs, which would ot have bee take ito accout i coectio with the other factors. The key issue related to the selectio of factors was the cotradictig results of the chages i the efficiecy scores of idividual compaies ad the chages i the average scores based o statistical tests. Although a factor may ot sigificatly affect the results o the average, it may affect the efficiecy of a idividual compay. These problems are especially related to the idicators Witer ad Forest that were excluded from the model i the fial selectio of variables. These factors were excluded, because the average depedece of efficiecy or costs o them could ot be show ad also because the weight of these factors o the efficiecy of idividual compaies would have rise to a questioably high level. This correspods to a case where the effect of these factors is highly o-liear ad thus with high costs coected to the extreme values of these idicators. Simultaeously, there was o clear evidece of the real cost effects of these factors to support this view.

13 12 We also checked that if there is a coectio betwee the efficiecy scores ad the evirometal factors that were left out of the model. Table 4 presets the result i the case of Sow. As ca be oticed there is o clear differece i the average efficiecy or the umber of efficiet uits betwee the whole populatio ad the compaies with highest values of Sow. Table 4 Coectio betwee Sow ad the efficiecies based o the fial model Average efficiecy Number of efficiet (%) All with highest values of Sow with highest values of Sow The coectios of isular coditios ad the degree of urbaisatio to the efficiecy of compaies were studied based o the selected model. The results produced by the selected model idicate that the proportio of efficiet uits ad the average efficiecy of the uits is o the same level i urba compaies as i the whole populatio. The results also show that the compaies operatig uder isular coditios are classified as efficiet whe the selected model is used. Furthermore, the results seem to be idepedet of the chage i the amout of distributed eergy. It ca therefore be cocluded that the factors are sufficietly take ito accout i coectio with the combiatios of the other factors icluded i the model. The fial model icludes Operatioal expediture as the iput; Distributed eergy ad Quality as the outputs; ad Geographical dispersio of customers ad Number of customers as the evirometal factors. The correspodig umerical idicators were itroduced i Table 1. To compare the selectio of factors icluded i our model, we used the stepwise approach suggested by Kittelse [1993]. The approach is based o the idea to test, if addig a ew factor to a DEA model causes a statistically sigificat chage i the efficiecy scores. The procedure starts with a simple model. Potetial additioal factors are iserted i the model oe at a time ad the factor causig the most sigificat chage is added. New factors are added i this maer as log as the sigificace exceeds a predefied risk level. Thus the idea is aalogical to stepwise regressio. Statistical testig is based o F-tests ad a Kolmogorov- Smirov type o-parametric test suggested by Baker [1993], ad ormal t-test. For more discussio o statistical testig i DEA, see also Baker [1996]. The stepwise approach supports the selectio of factors icluded i the fial model, if risk is cotrolled at 10 % level. Model versio Because the compaies are uable to cotrol the amout of eergy distributed ad the evirometal factors, ad because the EMA wated to assess the cost efficiecy of the compaies, a iput-orieted model was used i all the aalyses. As cost level is the oly discretioary variable, the model measures the amout of potetial cost savigs. To make the selectio cocerig returs to scale, scale iefficiecy was aalysed usig graphical illustratios of efficiecies versus differet scale idicators. It was observed that scale disadvatages were coected especially to the operatio of the very smallest compaies, as

14 13 well as to that of the large compaies with the logest etworks. Because distributio compaies caot, i the short ru, affect the scale of their operatio, a decisio was made to select a model based o a variable returs to scale assumptio. O the other had, also the use of costat returs to scale would be motivated sice i that case the customers would ot be affected by the wrog size of the operatio. 4 Results The iitial populatio cosisted of 106 distributio etwork operators who were active at the begiig of year At the time of the study, the latest available ad most comprehesive data was from the year The cost data of oe etwork operator was missig, ad a decisio was made to exclude three so-called idustrial etwork compaies from the fial evaluatio. The idustrial etworks clearly differ from the rest e.g. due to their differet customer structure. All the idustrial etworks appeared to be efficiet i the prelimiary calculatios. However, it is impossible to coclude from the data whether they are really efficiet, because there are ot eough compaies of the same type to make a compariso. Thus, the fial populatio used i the calculatios comprised of 102 etwork operators. Based o the selected model, 21 out of the 102 etwork operators are classified as efficiet. Correspodigly, the average efficiecy score is 76.9 ad the lowest is Figure 5 presets the distributio of the efficiecy scores Number of DMUs Efficiecy Score Figure 5 Distributio of the efficiecy scores The results show that efficiet uits are distributed all over Filad. They operate i differet operatioal eviromets, for example both i urba ad rural areas, ad the size of the efficiet uits varies alog the whole rage. Also from this poit of view, it seems that the model characterises the differeces i the operatioal eviromet.

15 14 The optimal scale of operatio varies a lot, ad disecoomies of scale are primarily related to very log etworks ad to very small amouts of distributed eergy. As the umber of compaies icluded i the aalysis is relatively large, we were uable to aalyse the results i detail from each idividual compay's poit of view. The efficiecy potetial calculated o the basis of the efficiecy scores amouts to a total of EUR 68 millio. This amout accouts for 15% of the total costs of the uits ivolved ad for 7.3% of the total turover. After comparig the results produced by the selected model to the previous studies of the Fiish etwork operators, it ca be stated that our results are cosistet with the earlier oes. 5 Discussio This paper cocetrates o the practical aspects of determiig ad selectig the factors icluded i a efficiecy aalysis. We have itetioally left out may aspects related to for example the techical aspects of DEA that are extesively discussed i literature. Others also discuss e.g. the theoretical aspects of the use of DEA i regulatio. For example see Bogetoft [1997] ad Agrell et al. [2002]. A compariso of the above-preseted results to the results form the years revealed that there are uexplaied fluctuatios i the operatig costs that were used as a iput factor. Clear problems related to the reliability of the data were thus discovered. The routies for gatherig data must therefore be further developed i order to esure the quality of it. Whe reliable data have bee gathered over a period of several years, it may also be iterestig to evaluate chages i productivity usig e.g. the Malmquist idex. There is also reaso to cotiue the developmet of the idicator of quality icluded i the model. The adopted idicator of quality is first of all limited to the aspect of supply iterruptios. Secod, it has bee defied through trasformer districts, which provides a potetial source of error. However, quality has bee cosidered so sigificat that a decisio was made to iclude it i the model, i spite of the shortcomigs of the idicator. Cost of capital was excluded from the fial model sice reliable data could ot be gathered. As electricity distributio is a capital-itesive busiess, there are good grouds to ivestigate further the possibility of icludig e.g. the level of ivestmets i the model. Solvig this problem is oe of the most importat future eeds ad the EMA has cotiued to work o this aspect. Furthermore, some of the factors that the group of experts iitially cosidered sigificat did ot reveal a sigificat effect o costs i the aalyses. Further research is welcomed also i this matter. The total-cost-based model used i this study for aalysig cost efficiecy has ot traditioally bee used i DEA-based efficiecy evaluatios. The approach is based o the accoutig iformatio reported by the compaies ad ot o the traditioal physical quatities ad

16 15 stadard prices. This approach suits for the eeds of the Fiish regulator as it ca oly make decisios cocerig the cost level. For discussio o the cosideratio of efficiecy i the regulatio i Filad, see Lavaste [2001]. The suggested model is ow adopted by the EMA ad also the compaies have broadly accepted it as a basis for the supervisio. The approach is costatly developed further ad for example the questios of quality ad the cost of capital are studied. Appedix A: Data Evelopmet Aalysis models This appedix itroduces the mathematical formulatios for the DEA models discussed ad used i this paper. It first presets the most commo DEA models, preseted by Chares, Cooper ad Rhodes [1978], ad Baker, Chares ad Cooper [1984]. The it describes the extesios that were used i the aalyses described i this paper. The models are preseted i their simplest forms to improve readability. A more detailed descriptio of may techical aspects ca be foud e.g. i a book by Cooper, Seiford ad Toe [1999]. The startig poit of DEA is to perform a compariso of a uit relative to the other uits i the populatio. Based o the priciples discussed i Sectio 3.2, the basic DEA models aalyse possible decreases i all iputs or possible icreases i all outputs. The efficiecy aalysis i DEA ca also be iterpreted as a geeralisatio of the compariso of productivity, i.e. the ratio of output ad iput, i a multiple iput ad output case. We use a otatio y ki to refer to the observed output k of uit i ad x ji to refer to the observed iput j of uit i. Variables of the DEA model are referred to as λ i, i = 1,,, which is the weight of uit i i the referece poit for the assessed uit, ad θ, which is the efficiecy score for the assessed uit. Subscript 0 refers to the assessed uit, but the uit preserves also its origial idex. Usig this otatio, the stadard costat returs to scale model preseted by Chares, Cooper ad Rhodes [1978], ad thereby ofte referred to as the CCR model, ca be formulated i the followig way. mi s.t. θ θ x j0 λ i x ji 0, j = 1,, p (A1) i=1 λ i y ki y k0, k = 1,, r i=1 λ i 0, i = 1,, The preseted model versio is iput orieted i.e. it seeks to reduce the use of all the iputs. A uit is classified as efficiet whe o reductio is assumed to be possible i.e. the objective fuctio of the problem equals to 1. For iefficiet uits the value is betwee 0 ad 1. This value is ofte multiplied by 100 i.e. preseted i a percetage form. The model determies the efficiecy of oe uit at a time ad thus the optimisatio problem has to be solved separately for each uit. Ofte also the dual of this so-called evelopmet form is aalysed. For more details see Cooper et al. [1999].

17 16 Baker, Chares ad Cooper [1984] preseted a model where the questio of returs to scale is take ito cosideratio. Thus the required level of productivity is depedet of the size of the uit. I the evelopmet model the chage is easily doe by addig a covexity costrait for the combiatios of the uits. Whe these chages are doe, we get the followig model. mi s.t. θ θ x j0 λ i x ji 0, j = 1,, p i=1 i=1 i=1 λ i y ki y k0, k = 1,, r (A2) λ i = 1 λ i 0, i = 1,, Stadard DEA assumes that the compared uits are homogeeous, ad that they operate i similar eviromets. If ot, factors characterisig the operatig eviromet ca be icorporated i the aalysis. The most straightforward way to do this is to iclude evirometal factors i the model as so-called o-discretioary iputs or outputs. Baker ad Morey [1986] itroduced this kid of a model with o-discretioary iputs. The otatio is modified so that x ji refers to the cotrollable i.e. discretioary iput j of uit i, ad z mi to the o-cotrollable i.e. o-discretioary iput m of uit i. Otherwise the otatio is as above. Usig this otatio the model ca be formulated as follows. mi s.t. θ θ x j0 λ i x ji 0, j = 1,, p i=1 z m0 λ i z mi 0, m = 1,, s (A3) i=1 i=1 i=1 λ i y ki y k0, k = 1,, r λ i = 1 λ i 0, i = 1,, The costat returs to scale versio of this model is elicited by excludig the covexity costrait i=1 λ i = 1 from the model. Model (A3) ad its costat returs to scale variat are the models used i the aalysis described i this paper.

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