THE ESTIMATION OF AN AVERAGE COST FRONTIER TO CALCULATE BENCHMARK TARIFFS FOR ELECTRICITY DISTRIBUTION

THE ESTIMATION OF AN AVERAGE COST FRONTIER TO CALCULATE BENCHMARK TARIFFS FOR ELECTRICITY DISTRIBUTION AEA Internatonal Conference on Modellng Energy Markets Techncal Unversty of Berln, September 10-11, 1998 by Massmo FILIPPINI Department of Economcs - Unverstà della Svzzera Italana Va Ospedale 13 6900 Lugano, Swtzerland E-mal: massmo.flppn@lu.uns.ch and Jörg WILD Socoeconomc Center - Unversty of Zurch Blumlsalpstrasse 10 8006 Zurch, Swtzerland E-mal: jwld@sozoec.unzh.ch September, 1998 1

THE ESTIMATION OF AN AVERAGE COST FRONTIER TO CALCULATE BENCHMARK TARIFFS FOR ELECTRICITY DISTRIBUTION by Massmo FILIPPINI and Jörg WILD ABSTRACT In ths paper we have examned the scale and cost neffcency of a sample of Swss electrcty dstrbuton utltes. To do so, we have consdered estmaton of a stochastc fronter average cost model usng the approach suggested by Schmdt and Sckles (1984) for panel data. A translog cost functon was estmated usng panel data for a sample of 30 muncpal utltes over the perod 199-1996. The results ndcate the exstence of economes of output and customer densty and economes of scale. Moreover, the fndngs on cost neffcency show that a majorty of the dstrbuton utltes s not producng at the mnmum level of the cost and that a possble applcaton of the fronter methodology employed n ths paper relates to the regulaton and benchmarkng of the delvery rates. Introducton The prvatzaton and the deregulaton of the electrc power sector were ntroduced n many countres, ncludng England, Norway, Chle and New Zealand. In Swtzerland, as n other European countres, several proposals exst to nsttute changes n the electrcty market and therefore move to competton. All these proposals contan as a central element of the reform the ntroducton of Thrd Party Access (TPA). Wth the ntroducton of TPA, the electrcty dstrbuton utltes are oblged to allow nondscrmnatory access to all companes that wsh to send electrcty over the utlty s transmsson and dstrbuton lnes for sale at the fnal consumer level. Ths open access must be accompaned by clear and specfc tarffs for the transmsson and dstrbuton servces, whch mples a functonal unbundlng. As a result, the dstrbuton utltes at the local level, whch are the object of our study, must separate ther dfferent functons: the delvery of electrcty and the retal sale of electrcty. Wth the ntroducton of TPA, an unbundled dstrbuton utlty should charge tself the same rate for dstrbuton that t charges other electrc utltes that want to utlze ts dstrbuton lnes. Because the electrcty dstrbuton utltes wll stll have a monopoly franchse to delver electrcty wthn ther servces terrtores, a rate regulaton by the regulatory commsson s necessary. Otherwse, the dstrbuton utltes could rase the rates above what they would be n a compettve market. Ths rases the problem of determnng proper rates for the delvery of electrcty at the local level. In Swtzerland there exsts a proposal that suggests settng the rates for the delvery of electrcty so that they equal the average dstrbuton cost measured n Swss francs per kwh. Accordng ths proposal, therefore, each dstrbuton utlty should set the delvery rate at the level of the own average cost.

The purpose of ths paper s to make a contrbuton to the debate on transmsson and dstrbuton prcng through the econometrc estmaton of a translog average cost fronter for a sample of Swss electrcty dstrbuton utltes. The estmated average cost fronter could be employed by the regulatory commsson to benchmark rates at the dstrbuton level. Ths artcle s organzed as follows. Secton presents the fronter average cost model for the electrc dstrbuton utltes. In secton 3, the data for 30 Swss publc electrcty dstrbutors from our sample are presented. Parameter estmates of the average fronter cost functon are presented n secton 4. In secton 5 we present the results n term of economes of densty and scale and n term of cost neffcency. Secton 6 reports the conclusons. Specfcaton of the Fronter Average Cost Functon Cost functons n the electrcty dstrbuton ndustry are well documented n emprcal research 1. All these studes estmated a cost functon whch also ncludes the expendture on purchasng electrcty n the total costs. Thus, these studes do not separate the sale functon of a utlty from the delvery functon and, therefore, are not deal for benchmarkng delvery rates. The costs of operatng a dstrbuton system are the costs of buldng and mantanng the system of servce lnes, mans and transformers. These costs may depend upon: - the total number of customers served; - the maxmum demand on the system, whch determnes the capacty of the system; - the sze of the dstrbuton area; - the capacty of the transformers; - the length of dstrbuton lne; - the total kwh sold, whch affects wear and tear on the transformers; - the prce of labor; and - the prce of captal. The maxmum demand on the system and the total kwh sold can be nterpreted as output ndcators, whereas the total number of customers, the sze of the dstrbuton area, the length of dstrbuton lne and the capacty of the transformers can be classfed as network characterstc varables. Therefore, gven that the electrcty dstrbuton utltes provdes servces va a network, the network characterstcs should be ncorporated n the cost model. Followng Salvanes and Tjφtta (1994), Burns and Weymann-Jones (1996) and Flppn (1996, 1997, 1998), n the average cost model specfcaton we take nto account a number of network characterstc varables, whch should capture the heterogenety dmenson of the dstrbuton system. For the purpose of our analyss we specfy two models. In the frst model the output s measured by the total number of klowatt hours (kwh) delvered, whereas n the second model the output s measured by the maxmum demand. These two model specfcatons allow us to estmate the two types of average costs relevant for the actual dscusson about 1 See Wess (1975), Henderson (1985), Roberts (1986), Nelson and Prmaux (1988), Callan (1991), Salvanes and Tjφtta (1994), Flppn (1996, 1997,1998) and Thompson (1997) for emprcal evdence of the exstence of scale economes n the transmsson and dstrbuton of electrcty. 3

tarff regulaton at the dstrbuton level: the average dstrbuton costs per kwh and the average dstrbuton costs per klowatt (kw). Inputs to the operatng of the dstrbuton system consst prmarly of labor and captal. Assumng that output and nput prces are exogenous, and that (for a gven technology) frms adjust nput levels so as to mnmze costs of dstrbuton, the frm's total average cost of operatng the electrcty dstrbuton system can be represented by the average cost functon AC = C y = AC ( y, w, w, CU AS) l c, (1) where C represents total cost, AC represents total average cost per kwh or, alternatvely, total average cost per kw, and y s the output represented by the total number of kwh delvered or, alternatvely, by the maxmum demand n kw. w c, and w l are the prces of captal and labor, respectvely. AS s the sze of the servce terrtory of the dstrbuton utlty measured n squares klometres and CU the number of customers. These varables are ntroduced n the model as output characterstcs. Intally, we consdered others output characterstc varables such as the klometres of mans lnes and the transformer capacty. However, these varables were dscarded because of a very hgh correlaton between these varables and y, CU and AS, leadng to nsgnfcant parameter estmates because of multcollnearty. Usng a translog functon, (1) can be approxmated by the followng average cost functon: 3 AC ln P K + + = o 1 ll CUl + lny + y PL ln P K K CU 1 + PL lncu ln + P lncu + ASAS AS CUAS PL l ln + P + ycu K lncu ln AS + AS ASl ln AS + lny lncu + yl 1 K yy PL ln AS ln P lny PL lny ln + P + ϖ K t 1 + yas CUCU lny ln AS lncu () Snce lnear homogenety n factor prces s mposed, the prce of captal wll act as a numerare. A fronter average cost functon defnes mnmum average costs gven output level, nput prces, output characterstcs and the exstng producton technology. It s unlkely that all frms wll operate at the fronter. Falure to attan the average cost fronter mples the exstence of techncal and allocatve neffcency. Dfferent approaches can be used to estmate a fronter cost functon wth panel data. A good overvew s gven by Bauer (1990), Battese (199) and Smar (199). See Neuberg (1977) for the estmaton of an average cost functon for electrc dstrbuton utltes and Hubbard and Dawson (1987) for a general dscusson on the estmaton of average cost functons. 3 A translog functon requres the approxmaton of the underlyng cost functon to be made at a local pont, whch n our case, s taken at the medan pont of all varables. Thus, all ndependent varables are normalzed at ther medan ponts. 4

In ths paper we consder the estmaton of a stochastc fronter average cost functon usng the approach suggested by Schmdt and Sckles (1984) for panel data. In ths approach the overall resdual ϖt s composed of two terms (ωt = α + εt): a symmetrc component of the dsturbance ( εt) that allows for nose, dstrbuted N (0,sv ) and a one-sded component (α) that represents cost neffcency. 4 There are N frms and T observatons for each frm. The attractveness of ths approach s that no assumptons need be made about the dstrbutons of α. There s, however, a lmtaton, namely that one has to be prepared to assume that neffcency remans constant over tme. The fact that the average cost functon (1) ncludes a varable, the sze of the servce terrtory, that remans constant over tme excludes the possblty to treat neffcency as a fxed effect. Therefore, neffcency has to be treated as a random effect and the coeffcents of equaton () estmated by GLS. 5 The Data Ths study s based on a combned tme seres and cross-sectonal data set for 30 Swss electrcty dstrbuton utltes over the perod 199-1996. 6 The model s estmated for crosssectonal samples of publcly-owned electrcty dstrbuton utltes operatng n Swss ctes. 7 In Swtzerland, there are approxmately 130 companes that could be ncluded n a study of cty electrcty dstrbuton utltes. The Swss Federal Energy Offce collects fnancal data only for a sample of about 100 utltes servng ctes. Part of the companes lsted n ths sample, however, are not approprate for the purpose of our analyss because the amount of self-generated electrcty s hgh. Snce the am of ths study s to analyze the cost structure of dstrbuton, companes whch had an amount of self-generated electrcty hgher than 0% of the total sales were excluded. 8 For estmaton, panel data for fve years, 199,1993,1994, 1995 and 1996, has been used. The prmary sources were the Swss Federal Offce of Energy's Fnanzstatstk; addtonal data were collected usng a mal questonnare sent to the utltes. The restrctons on data descrbed above and completed questonnares result n a sample of 30 electrcty dstrbuton utltes for whch approprate data are avalable. The necessary data nclude the total dstrbuton cost, the prces of captal and labor, the quantty of kwh 4 For a presentaton of ths method see Schmdt and Sckles (1984) and Smar (199). 5 See Hsao (1986) for a presentaton of ths econometrc approach. 6 Flppn (1996, 1997, 1998) estmated a total cost functon for the Swss electrcty dstrbuton utltes usng a dfferent dataset (39 Swss electrcty dstrbuton utltes over the perod 1988-1991). 7 The Swss electrc power ndustry s composed of about 100 frms, publc and prvate, that are engaged n the generaton, transmsson and/or dstrbuton of electrc power. There s a great dvergence both n terms of sze and actvtes of these companes. In partcular, approxmately 900 utltes, or 74% of the total, are merely dstrbutors of electrc power. The majorty of these companes are muncpal and provde power servce exclusvely for ther communty. In addton they are surrounded by 300 electrc utltes whch operate wthn an urban or regonal area. Ths group of frms operates n all three stages of provson lsted above, but generally the amount of generated power s small. The muncpals and the regonal electrc utltes purchase most of ther power from 10 utltes whch form the backbone of the ndustry. 8 Ths group of frms s nvolved n generaton, transmsson and dstrbuton, but the amount of generated power s small and s determned by the ablty to explot favorable hydroelectrc power generaton possbltes. 5

delvered, the maxmum demand, as well as the number of customers and the sze of the servce terrtory. All nput prces, total cost and varable cost were deflated to 1996 constant Swss francs usng the Consumer Prce Index. For smplcty, total dstrbuton cost s equated to total expendture as reported by the companes excluded the expendture for purchased electrcty. Average yearly wage rates are estmated as the labor expendture dvded by the number of employees. Followng Fredlander and Wang Chang (1983) and Flppn and Magg (1993), the captal prce s calculated from the resdual captal costs dvded by the captal stock. Resdual cost s total dstrbuton cost mnus labor cost. Accordng to Callan (199), the captal stock s approxmated by the total nstalled transformer capacty, measured n kva. 9 Some detals of these varables are presented n Table 1. Varables Unt of measurement 1. Quartle Medan 3. Quartle Total average dstrbuton cost SwF. / kw 66.8 375.8 486.10 Total average dstrbuton cost SwF. / kwh 0.05 0.07 0.10 Maxmum demand kw 16,50 1,90 36,785 Dstrbuted electrcty mllon kwh 84.95 108.30 159.50 Number of customers 7,76 10,538 17,17 Sze of the servce terrtory hectares 1,130,90 5,995 Labor prce SwF. per worker 77,109 96,304 114,680 Captal prce SwF. per unt of captal 66.3 90.4 1 Table 1 - Descrptve statstcs Estmaton Results Table presents the GLS estmates of the translog fronter average cost functon () under two cases. In Model 1 the dependent varable s average cost per kwh and the output s measured n kwh, whereas n Model the dependent varable s average cost per kw and the output s measured n kw. The GLS estmates n Table can be used to recover estmates of neffcency for each dstrbuton utlty. The estmated functons are well behaved. Most of the parameter estmates are statstcally sgnfcant and carry the expected sgn. Moreover, the coeffcents of both models are smlar. Ths results s not surprsng because the two output varables, kwh and kw, have a correlaton coeffcent of 0.95. Snce average total cost as well as the dependent varables are n natural logarthms and have been normalzed, the frst order coeffcents are nterpretable as average cost elastctes evaluated at the sample medan. 9 Unfortunately no data are avalable whch would allow the calculaton of the captal stock usng the perpetual nventory method. 6

Coeffcent Model 1 average cost per kwh 0 -.58 *** (0.067) y -1.016 *** (0.075) l 0.30 *** (0.015) CU 0.45 *** (0.086) AS 0.6 *** (0.044) yy 0.657 * (0.356) ll 0.081 ** (0.031) CUCU 0.975 ** (0.415) ASAS -0.059 (0.048) yl -0.063 (0.050) ycu -0.61 * (0.35) yas 0.011 (0.069) CUl 0.105 ** (0.048) ASl -0.019 (0.01) CUAS -0.08 (0.067) Model average cost per kw 5.96 *** (0.068) -0.913 *** (0.063) 0.301 *** (0.015) 0.396 *** (0.077) 0.08 *** (0.046) 0.997 *** (0.41) 0.067 ** (0.030) 1.144 *** (0.75) -0.039 (0.04) -0.013 (0.046) -0.850 ** (0.34) -0.017 (0.047) 0.045 (0.046) -0.017 (0.01) -0.053 (0.053) *, **, ***: sgnfcantly dfferent from zero at the 90%, 95%, 99% confdence level. Table - Total-cost parameter estmates (standard errors n parentheses) The output elastcty s negatve and mples that an ncrease n the producton of output wll decrease average total cost. A 1% ncrease n the delvery of power wll decrease the average total cost by approxmately 1% n model 1 and by approxmately 1.10% n model. The average cost elastcty wth respect to area sze s postve n all versons of the average cost model, ndcatng that a 1% ncrease n area sze wll ncrease average cost by approxmately 0.% n model 1 and by approxmately 0.39% n model. The average cost elastctes wth respect to the number of customers are postve and mply that an ncrease n the number of customers wll ncrease average total cost. 7

To test whether ndvdual effects are present we ran a Lagrange Multpler test for the random effects model. The result of ths test favors the random effects model over the OLS model. Scale and Cost Effcency Economes of Scale and Densty The ncluson n the average cost functon of the number of customers and the sze of the servce terrtory allows for the dstncton of economes of output densty, economes of customer densty and economes of scale. We defne economes of output densty (EOD) as the proportonal decrease n total average cost brought about by a proportonal ncrease n output, holdng all nput prces, the number of customers and the sze of the servce terrtory fxed. Ths s equvalent to the elastcty of total average cost wth respect to output, EOD = d ln AC d ln y (3) We wll talk of economes of output densty f EOD s negatve, and accordngly, we wll talk of dseconomes of output densty f EOD s postve. In the case of EOD = 0 no economes or dseconomes of output densty exst. Economes of output densty exst f the average costs of an electrcty dstrbuton utlty decrease as the volume of electrcty sold to a fxed number of customers n a servce terrtory of a gven sze ncreases. Economes of customer densty (ECD) are defned as the proportonal decrease n total average cost brought about by a proportonal ncrease n output and the number of customers, holdng all nput prces and the sze of the servce terrtory fxed. Economes of customer densty (ECD) can thus be defned as ECD = d ln AC + d ln y d ln AC d ln CU (4) We wll talk of economes of customer densty f ECD s negatve, and accordngly, we wll talk of dseconomes of customer densty f ECD s greater than 0. Ths measure s relevant for analyzng the cost of dstrbutng more electrcty to a fxed servce terrtory as t becomes more densely populated. Economes of scale (ES) are defned as the proportonal decrease n total average cost brought about by a proportonal ncrease n output, the number of customers and the sze of the servce terrtory, holdng all nput prces fxed. ES can thus be defned as ES d ln AC d ln AC d ln AC = + + (5) d ln y d ln CU d ln AS We wll talk of economes of scale f ES s smaller than 0, and accordngly, we wll talk of dseconomes of scale f ES s greater than 0. In the case of ES = 0 no economes or dseconomes of scale exst. Ths measure s relevant for analyzng the mpact on cost of mergng two adjacent electrcty dstrbuton utltes. 8

Table 3 presents the estmates of economes of output densty, customer densty and economes of scale evaluated usng the estmaton results from Schmdt-Sckles fronter models. 10 Model 1 (kwh) Model (kw) Economes of output densty -1.01-0.91 Economes of customer densty -0.79-0.5 Economes of scale -0.34-0.3 Table 3 - Economes of scale and densty We note that all ndcators for economes of scale and economes of output and customer densty are greater than 1, whch means that the majorty of the Swss electrcty dstrbuton utltes operate at an napproprately low scale and densty level. 11 The average cost (AC) curves mpled by our estmated translog models appear n Fgure 1 and, evaluated wth all varables other than output (measured n kwh or kw alternatvely) set to ther sample medan. These curves are L shaped and ndcate the presence of economes of densty. 0. Average cost (Swf. /kwh) 0.15 0.1 0.05 0 0 100'000'000 00'000'000 Energy delvered (kwh) Fgure 1 - Estmated AC curve usng kwh as output ndcator (Model 1) 10 Equatons (3), (4) and (5) have been evaluated at the nput prces of the medan company. 11 These results confrm the results obtaned by Flppn (1997, 1998) estmatng a translog total cost functon for another sample of Swss electrcty dstrbuton utltes. 9

100 1000 Average cost (Swf./kW) 800 600 400 00 0 10'000 0'000 30'000 40'000 50'000 60'000 Maxmum demand (kw) Fgure - Estmated AC curve usng kw as output ndcator (Model ) Cost neffcency The estmaton results reported n Table can be used to recover estmates of the level of cost neffcency of each dstrbuton utltes along the lne suggested by Schmdt and Sckles (1984). Ths amounts to countng the most effcent dstrbuton utlty n the sample as 100% effcent and measurng the degree of cost neffcency of the other utltes relatve to the most effcent dstrbuton utlty. The level of cost effcency ranges from 10 to 100%. Complete summary statstcs of the varous effcency measures for both models appear n Fgure 3. These relatvely low scores ndcate a hgh dsperson of cost neffcences across dstrbuton utltes, and could be due to the relatve nhomogenety of the actvtes of the frms consdered n the sample. 15 kw kwh 10 5 0 1 >0.9-<1.0 >0.8-0.9 >0.7-0.8 >0.6-0.7 >0.5-0.6 >0.4-0.5 >0.3-0.4 >0.-0.3 >0.1-0. Fgure 3 - Dstrbuton of cost effcency 10

Conclusons In ths paper we have examned the scale and cost neffcency of a sample of Swss electrcty dstrbuton utltes. For ths purpose, we have we have estmated a of a stochastc fronter cost model functon usng the approach suggested by Schmdt and Sckles (1984) for panel data. A translog cost functon was estmated usng panel data for a sample of 30 muncpal utltes over the perod 199-1996. The results ndcate the exstence of economes of output and customer densty and economes of scale. Moreover, the fndngs on cost neffcency show that a majorty of the dstrbuton utltes s not producng at the mnmum level of the cost. A possble applcaton of the fronter methodology employed n ths paper relates to the regulaton of the delvery rates. Dstrbuton utltes have a monopoly franchse to dstrbute electrcty wthn ther servce terrtores and, therefore, are to be subject to rate regulaton by the regulatory commsson. Otherwse, the dstrbuton utltes could rase the rates above what they would be n a compettve market. The dstrbuton rates should be set at levels reasonable and adequate to meet costs whch must be ncurred by effcently operated facltes. As presented n the ntroducton, n Swtzerland there exsts a proposal that suggests settng the rates for the delvery of electrcty so that they equal the average dstrbuton cost measured n Swss francs per kwh. We beleve that the regulators could use the estmated average cost fronter model to control the level of the rates proposed and appled by the sngle dstrbuton utltes. In ths case the average cost fronter model would become an nstrument to benchmark dstrbuton rates. Bblography Battese, G.E, 199, Fronter Producton Functons and Techncal Effcency: a Survey of Emprcal Applcatons n Agrcultural Economcs, Agrcultural Economcs, 7, 185-08. Bauer, P.W., 1990, Decomposng TFP Growth n the Presence of Cost Ineffcency, Nonconstant Returns to Scale, and Technologcal Progress, Journal of Productvty Analyss, 1, 87-300. Burns, P. and Weymann-Jones T.G., 1996, Cost Functons and Cost Effcency n the Electrcty Dstrbuton: a Stochastc Fronter Approach, Bulletn of Economc Research, 48, 4-64. Callan, S.J., 1991, The Senstvty of Productvty Growth Measures to Alternatve Structural and Behavoral Assumptons: An Applcaton to Electrc Utltes 1951-1984, Journal of Busness & Economcs Statstcs, 9, 07-13. Flppn, M. and Magg, R., 1993, Effcency and Regulaton n the case of the Swss Prvate Ralways, Journal of Regulatory Economcs, 5, 199-16. Flppn, M., 1996, Economes of Scale and Utlzaton n the Swss Electrc Power Dstrbuton Industry, Appled Economcs, 8, 543-550. Flppn, M., 1997, Elements of the Swss Market for Electrcty, Physca-Verlag. Berln. Flppn, M., 1998, Are Muncpal Electrcty Dstrbuton Utltes Natural Monopoles?. Annals of Publc and Cooperatve Economcs, (forthcomng). Fredlaender, A.F.and Shaw-Er Wang Chang, J., 1983, Productvty Growth n the Regulated Truckng Industry, Research n Transportaton and Economcs, 1, 149-184. 11

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