International benchmarking of electricity distribution utilities

No 35/2001

International Benchmarking of Electricity Distribution Utilities

By

Finn R. Førsund and Dag Fjeld Edvardsen

ISSN: 0801-1117

Department of Economics

University of Oslo

Department of Economics Research

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O F

E

D

U

D ag Fjeld E dvardsen

The N orw egian Building Research Institute and

Finn R . Førsund

D epartm ent of Econom ics, U niversity of O slo, The Frisch Centre,

V isiting Fellow ICER

D ecem ber 12, 2001

A bstract: Benchm arking by m eans of applying the D EA m odel is appearing as an interesting alternative for regulators under the new regim es for electricity distributors.A sam ple of large electricity distribution utilities from D enm ark, Finland, N orw ay, Sw eden and the N etherlands for the year 1997 is studied by assum ing a com m on production frontier for all countries. The peers supporting the benchm ark frontier are from all countries. N ew indexes describing cross country connections betw een peers and their inefficient units are developed, as w ell as productivity m easurem ents betw een units from different countries.

K ey w ords: Electricity utility, benchm arking, efficiency, D EA , M alm quist productivity index

JEL classification: C43, C61, D 24, L94.

1 The study is done under the research project “Efficiency in N ordic Electricity D istribution” at the Frisch C entre, financed by N ordic Econom ic R esearch C ouncil. W e are indebted to a group of D anish, D utch, Finnish, N orw egian and Sw edish electricity regulators for cooperation and com m ents on earlier drafts at project m eetings in D enm ark, N orw ay, Finland and the N etherlands. W e w ill especially thank Susanne H ansen, K ari Lavaste and V ictoria Shestalova for com m ents on the last draft. The electricity regulators, headed by A rne M artin Torgersen and Eva N œ ss K arlsen from N V E, have done extensive w ork on data collection. H ow ever, notice that the responsibility for the final m odel choice and focus of study rests w ith the authors. Furtherm ore, the analysis is only addressing technical efficiency m easurem ent, and in particular not cost efficiency. The study is not intended for regulatory purposes. W e are indebted to Sverre A . C. K ittelsen for valuable com m ents on the last draft.

1. Introduction

Im provem ent of efficiency in electricity distribution utilities has com e on the agenda, as an increasing num ber of countries are m oving tow ards deregulation of the sector in the last decade. A key elem ent in assessing potentials for efficiency im provem ent is to establish benchm arks for efficient operation. A standard definition of benchm arking is a com parison of som e m easure of actual perform ance against a reference perform ance.

O ne w ay of obtaining the latter is to establish a frontier production function for a utility, and then calculate efficiency scores relative to the frontier.

In this study a piecew ise linear frontier is used, and technical efficiency m easures (Farrell, 1957) and M alm quist productivity m easures (Caves et al., 1982a) are calculated by em ploying the D EA m odel (Charnes et al., 1978). The D EA m odel has been used in several studies of the utilities sector recently (see a review in Jam asb and Pollitt, 2001). A special feature of this study is that the data is based on a sam ple of utilities from five different countries: D enm ark, Finland, The N etherlands, N orw ay, and Sw eden. M ost of the efficiency studies of utilities are focussing on utilities w ithin a single country, but som e studies have also com pared utilities from different countries (see Jam asb and Pollitt, 2001). In som e cases an international basis for benchm arking is a necessity due to the lim ited num ber of sim ilar firm s, like benchm arking for the single N orw egian national grid transm ission com pany w here the sim ilar com pany for Sw eden is used. W hen the num ber of units is not the key m otivation for international sam ple for benchm arking, the m otivation m ay be to ensure that the national best practice utilities are also benchm arked².

There are som e extra problem s w ith using an international data set for benchm arking.

The m ain problem is that of com parability of data. O ne is forced to use the strategy of the least com m on denom inator. A special issue is the correct handling of currency exchange rates. There are really only tw o practical alternatives; the average rates of

2 A n alternative is to use hypothetical units based on engineering inform ation, as m entioned already in Farrell (1957). In Chile and Spain hypothetical m odel best practice units are used for benchm arking, see Jam asb and Pollitt, 2001.

exchange and the Purchasing Pow er Parity (PPP) as m easured by O ECD . The latter approach is chosen here. Relative differences in input prices like w age rates and rates of return on capital m ay also create problem s as to distinguish betw een substitution effects and inefficiency.

A ccording to the findings in Jam asb and Pollitt (2001) international com parisons are often restricted to com parison of operating costs because of the heterogeneity of capital.

They form ulate as a precondition for international com parisons to focus on im proving the quality of the data collection process, auditing, and standardisation w ithin and across countries. Cross section data for the present study has been collected uniquely for the effort by national regulating agencies, and special attention has been paid to standardise the capital input as a replacem ent cost concept.

Regarding the extent of international studies Jam asb and Pollitt (2001) found that 10 of the countries covered in the survey (O ECD- and som e non-O ECD countries) have used som e form of benchm arking and about half of these use the frontier-oriented m ethods D EA , Corrected Least Squares (CO LS) and Stochastic Frontier A pproach (SFA ). They predict that benchm arking is likely to becom e m ore com m on as m ore countries im plem ent pow er sector reform s.

The paper is organised in the follow ing w ay: In Section 2 a brief discussion of the m ethods of D EA and M alm quist productivity index calculations is offered. Som e new indices are developed to capture the cross-country pattern of the nationality of peers and the nationality of units in their inefficient unit sets. In Section 3 the theory of distribution of electricity as production is review ed as to the choice of variable specification. The data is presented in the form of partial diagram s developed to reveal the structure of the data and the occurrence of outliers. A trial run is perform ed in Section 4 to check any outlier problem . The results on efficiency distributions and inter- country productivity differences using M alm quist indexes are presented in Section 5. Conclusions and further research options are offered in Section 6.

2.The m ethodological approach

The D EA m odel

A s a basis for benchm arking w e w ill em ploy a piecew ise linear frontier production function exhibiting the transform ations betw een a set of outputs, ym (m =1,..,M ) and the substitutions betw een a set of inputs, xs (s=1,..,S). W e w ill assum e constant returns to scale. O ne reason for this choice is that w e are going to study productivity, and this specification is in accordance w ith a total factor productivity interpretation. A nother reason is specific to our dataset: the units are all am ong the larger units w ithin each country, and thusthe basis for specifying a variable returns technology is not there³. The frontier is enveloping the data as tight as possible and the observed best practice utilities w ill span the benchm arking technology. The Farrell technical efficiency m easures are calculated sim ultaneously w ith determ ining the nature of the envelopm ent subject to basic properties of the general transform ation of inputs into outputs (see e.g. Färe and Prim ont, 1995). The efficiency scores for the input- and output oriented D EA m odels, E1i and E2i respectively for utility no i (i = 1,..,n), are found by solving the follow ing tw o linear program m es:

(1)

3 H ow ever, it could be argued that a non-increasing (N IRS) scale specification w ould be relevant.

n j

S s x

x

M m

y y t s

M in E

ij n

j sj ij si

i n

j

m i m j ij

i i

,.., 1 , 0

,.., 1 , 0

,.., 1 , 0 .

.

1 1 1

=

≥

=

≥

−

=

≥

−

=

∑

∑

=

=

l

l q

l q

J j

S s x

x

M m y

y t s

E M ax

ij n

j sj ij si n

j

m i i m j ij

i i

,.., 1 , 0

,.., 1 , 0

,.., 1 , 0 .

. 1

1 1 2

=

≥

=

≥

−

=

≥

−

=

∑

∑

=

=

l l

f l

f

(2)

(For notational ease w e use the sam e sym bol, λ, for the w eights in both m odels.) In the general case the m easures E1i and E2i are identical since w e have specified constant returns to scale. H ow ever, w e m ay need to keep som e variables fixed w hen calculating the efficiency scores. In the case of e.g. one output as fixed, the input-oriented m odel w ill be the sam e as (1), but the output-oriented m odel w ill be different since the constraint in (2) involving this variable w ill be reform ulated to hold w ithout the efficiency correction of this output variable. The num erical results for efficiency scores m ay then be different.

The Peers

The efficient units identified by solving the problem s (1) or (2) above are the basis for studying possible causes for inefficiency. Each inefficient unit w ill have one or m ore benchm ark or peer units. W e w ant to m easure the influence of the peers. LetP be the set of peers and I the set of inefficient units; P ∪I = N (N=set of all units). The im portance of the fully efficient units as peers can be show n by an index term ed the Peer index⁴. In the case of input orientation the index for each peer is based on the relative saving potential of the inefficient units that have the peer in their reference sets.

The reference set is defined as:

{

}

P_i= :l_ip>0∀ ∈ , ∈ (3) Each inefficient unit, i, has a positive w eight, lip, associated w ith each of its peers, p, from the solution of the D EA m odel (1). The w eights, lip, are zero for inefficient units not having unit p as a peer. The absolute saving potential (based on the radial Farrell m easure, i.e. disregarding slacks) for each inefficient unit is expressed by the difference

4See Torgersen et al. (1996) for the introduction and dem onstration of the concept of Peer index for both the radial efficiency m easure and efficiency m easures including slacks.

betw een the observed input quantity and the am ount on the frontier sufficient to support the observed output levels for each type of input, s:

S s I r E x x

E

x _{r p}

I r

rs I

r

rs r rs

p p

,.., 1 , ,

) 1 ( )

( − ₁ =

∑

∑

(4) w here Ip is the inefficient unit set referenced by the peer, p:

{

}

I_p= :l_ip>0∀ ∈ , ∈ (5) O ne m easure of the im portance of a peer w ould be the ratio of potential savings of an input of inefficient units in the peer’s inefficient unit set, I_p, to total savings of all inefficient units. H ow ever, an inefficient unit m ay have several peers, in the CRS case up to the num ber of input- plus output dim ensions m inus one (since all facets go through the origin), in our case m axim al five peers. To discrim inate betw een peers the w eights,lip, can be utilized. To m easure the im portance of a peer w e w ill calculate the savings potential for each type of input of all inefficient units in the peer’s inefficient unit set w eighted w ith the w eight, lip, for the peer w hen form ing the reference point for uniti on the frontier, relative to the total potential saving of the input in question for all inefficient units (the set I). The saving potential calculated above in (4) is therefore corrected by w eighing each inefficient unit’s potential w ith this w eight (see the appendix for the w eights). The (input oriented) Peer index,rps

, for each peer and each type,s, of input, is the ratio of the total w eighted saving potential of the inefficient units in the reference set of the peer and the total saving potential in the com plete dataset⁵:

S s

P p E

x

E x

I

i is i

i is

I i

P

p ip

ip

s p

p

,.., 1 , )

1 (

) 1 (

1 1

=

∈

− ∀

−

= ∑

∑ ∑

∈

∈ ∈ l l

r (6) In the V RS case the sum of w eights, lip, over peers, p, is equal to one, but in the CRS case there is no restriction on the sum (but each lip is restricted to be non-negative).

Therefore, the w eight lip has to be norm alized by division w ith the total sum of w eight for each inefficient unit. Sum m ing also over all the peers (index p) in the num erator, w e get the index value of one for each type of input.

5 A n output-oriented peer index can be constructed in an analogous w ay, see Torgersen et al. (1996).

A nother m easure of the im portance of peers is provided by calculating the super efficiency score (SE) (A ndersen and Petersen, 1993). This score is obtained by rem oving the peer in question from the full data set used w hen calculating the efficiency scores according to the program (1), and then calculating the efficiency score of the peer against this new frontier. The efficiency score m ust necessarily be greater than (or equal to) one. A third m easure of the im portance of a peer that has been used in the literature is a pure count of the num ber of tim es a peer is a referencing unit for inefficient units, i.e. the num ber of sets P_i defined in (3) w here the peer appears. The m easures give us different inform ation. The Peer index show s the im portance of a peer as role m odel for best practice in term s of potential im provem ent of perform ance, the pure count show s num ber of appearances, but w ithout discrim inating betw een differing peer influence on the reference point of the inefficient units, w hile the Super efficiency score tells us about the influence on the shape of the production frontier.

Cross group influence of peers

Since w e have countries as sub-groups it is of interest to so investigate the cross-country relationships by focussing on the im portance for inefficient units in a country of peers from each of the other countries. Such a cross-country index of peer im portance has been used in Schaffnit et al. (1997). U nits m ust now be identified by country. U sing the notation in (3) w e first form the set, Iⁱ, of inefficient units, ki, of a country, i, appearing in the peer referencing sets, P^j, of another country, j:

{

}

N_{ij i kl i} ⁱ _j ^j

j

i 0 , , ,

: > ∈ ∈ ∀

= l (7) Let us denote the num ber of inefficient units in a country, i, for nⁱ (i=1,..,n). D ividing the num bers of inefficient units in country i having peers from country j w ith the total num ber of inefficient units in each country w e get a relative m easure, r_ij, for cross country peer im portance⁶:

j i n N

i ij ij= ,∀,

r (8) The index r_ij is based on w hether the l -coefficients are zero or positive. A m ore instructive representation of im portance as peers m ay be obtained by developing the peer index (6) to serve a study of links betw een countries. A Cross country peer pattern

6 Schaffnit et al. (1997) also include the num ber of peers in the set in the denom inator.

index,r_ij^s,can be established by w eighing the saving potential of an input, s, for a country,i, w ith the

j il

lk – w eights, and then looking at the potential associated w ith the peers from another country, j:

j i S s E

x

E x

i i

i i

j j

i i

i i

j i j i

I

k ks k

P

l k I

k s k P p kl

l k

s

ij , 1,.., , ,

) 1 (

) 1 (

1 1

∀

− =

−

= ∑

∑ ∑ ∑

∈

∈ ∈

∈ l l

r (9)

This index w ill be variable specific, as is the case for the peer index (6).

The M alm quist productivity index

The M alm quist productivity index, introduced in Caves et al. (1982a), is a binary com parison of the productivity of tw o entities, usually the sam e unit at different points in tim e, but w e m ay also com pare different units at the sam e point in tim e. Let the set of units in country j be Nj, and consider tw o utilities, ki and lj, from country i and j, respectively. The output- and input vectors of a unit are w ritten yki,xki, etc. The M alm quist productivity index, M , for these tw o units is then:

j j i i k k i

l l i l l k k i

l

k k N l N

x y E

x y E x y x y M

i i

j j j

j i i j

i = , ∈ , ∈

) , (

) , ( ) , , ,

, ( (10) The M alm quist index is the ratio of the Farrell technical efficiency m easures for the tw o units, as calculated by solving the program m es (1) or (2)⁷. The superscript on the indexes show s the reference technology base (i.e. i m eans that the efficiency m easures are calculated w ith respect to the frontier for country i). W e follow the convention of having the first unit in the subscript in the denom inator and the second in the num erator, thus unit l_j is m ore productive than unit k_i if _kⁱ_l

j i

M _, > 1, and vice versa. If it is relevant to operate w ith different reference technologies for the units, follow ing Färe et al. (1994), the M alm quist index can be decom posed m ultiplicatively into a term reflecting each

7 W e have used Farrell (1957) efficiency m easures, E, instead of distance functions as in Caves et al.

(1982a) because the definition (3) is then sym m etrical w hether w e assum e an input- or output oriented m easure. H ow ever, w e adopt the assum ption of constant returns to scale. The input- and output oriented m easures are then identical. W e still stick to the efficiency m easure notation.

unit catching up w ith its reference technology, and a term reflecting the distance betw een the tw o reference technologies.

It m ay be of interest to involve a com parison of several units. A ccording to Caves et al.

(1982b) m ulti-country com parisons are the problem s to w hich m ultilateral com parative techniques m ost often have been applied. W e m ay w ant to both com pare productivity levels betw een countries, and to com pare utility productivity levels. The crucial point concerning the choice of com parisons is the assum ption about production technologies.

There are tw o basic possibilities:

i) A com m on frontier technology m ay be assum ed, allow ing utilities from different countries to support the D EA envelope.

ii) The technologies are national, i.e. only ow n country firm s m ay be best practice firm s.

Caves et al. (1982b) operated w ith country-specific technologies and countries as units, and developed a m ultilateral country productivity index for a com parison of tw o countries. The calculation involved the geom etric m ean of the bilateral productivity com parison betw een each of the tw o countries and all other countries in order to obtain transitivity. A nother w ay to obtain transitivity proposed in Caves et al. (1982b) w as to introduce a representative country to be com pared w ith the tw o countries involved in the bilateral com parison. The approach in Berg et al. (1993) of using a fixed base technology can be interpreted as use of a representative country (see Førsund, 2002). In a setting sim ilar to ours N ordic banks are studied by assum ing separate technologies for each country, and then by using the frontier for one country as a com m on reference, productivity betw een countries are com pared by com paring the efficiency scores of the largest banks in each country, as w ell as the average banks. A com m on N ordic technology w as also tried. W e w ill in our study assum e a com m on frontier technology.

Com m on inter country technology

A s pointed out in in Caves et al. (1982) it is an advantage to use a transitive index w hen com paring productivities of tw o countries (units). Berg et al. (1992), (1993), and Førsund (1993) (see also the general discussion in Førsund, 2002) dem onstrate that the

M alm quist index (10) is not transitive. H ow ever, in the case of the sam e frontier technology being valid for all countries, corresponding to assum ption i) above, the M alm quist productivity index is greatly sim plified, since the benchm ark technology w ill be com m on for all productivity calculations. The index is then transitive.

A useful characterisation of the productivity of a unit, ki , in a country, i, m ay be obtained by com paring the efficiency score for this unit w ith the geom etric m ean of all the other scores, follow ing up Caves et al. (1982b), (p. 81, Eq. (34)), m easuring the productivity of one country against the geom etric m ean of the productivities of all countries:

[

]

) , ( )

,

( 1/ k N l N

x y E

x y E x

y

M _{i i}

n l l C N l

k k C k

k C k

i i i

i

i ∈ ∈

= Π

∈

C = com m on technology (11) w here n is the total num ber of all utilities and N represents the set. To focus on bilateral productivity com parisons betw een countries as units one w ay of form ulating a bilateral country com parison is to com pare the geom etric m eans of efficiencies over units for each country, i and j:

[ ]

[

]

) , , ,

( 1/

/ 1

, n i i j j

l l C N l

n k k C N k k

k l l C

k

l k N l N

x y E

x y E x

y x y M

j j j j j

i i i i i i

i j j i

j ∈ ∈

Π

= Π

∈

∈ (12)

w here niand nj are the total num ber of utilities w ithin each country i and j. This index m ay be term ed the bilateral country productivity index, and is also transitive, in the sense that the index is invariant w ith respect to w hich third country efficiency score average w e m ay w ish to com pare w ith countries iand j.

If w e w ant to express how the units w ithin a country, i, are doing com pared w ith the average over all units, the country j specific index in the denom inator of (12) can be substituted w ith the geom etric average of the efficiency scores of all the utilities like the denom inator in (11).

W e could also study structural differences by calculating relative productivities for the average units for each country. Farrell (1957) introduced the notion of how the average unit kept up w ith the best practice units as a m easure of structural efficiency w ithin an industry. In Førsund and H jalm arsson (1979) structural efficiency is m easured as the

average unit’s efficiency score. If w e denote variables w ith bars on top for arithm etic averages, the follow ing M alm quist productivity index m ay serve as a m easure of overall productivity:

, ,.., 1 , , ) , (

) , ( ) , , ,

( ij n

x y E

x y E x y x y M

i i C

j j C j j i i C

ij = = C = com m on technology (13)

3. M odel specification and data

D istribution as production

In the review of transm ission and distribution efficiency studies Jam asb and Pollitt (2001) point to the variety of variables that have been used as an indication that there is no firm consensus on how the basic functions of electric utilities are to be m odelled as production activities. H ow ever, they m ention that the variety of the variables used m ay, to som e extent, be explained by the lack of data.

M odelling the production activity of transportation of electricity has old traditions w ithin engineering econom ics (see e.g. Førsund (1999) for a review ). A ccording to Sm ith (1961) the problem of the m ost econom ical w ay of setting up transm ission of electricity betw een a point of production and a point of consum ption w as first analysed by Lord K elvin in 1881. Before a pow er line is constructed there are substitution possibilities betw een the w eight of the conductor and energy generated at the point of production due to a larger conductor (in m ass) im plying less loss of pow er, all other aspects being held constant. A pplying the various law s of electricity, like O hm 's law , a production function can be derived w ith electricity delivered as output and w eight of conductor and energy generated as inputs. A s param eters w e have length of conductor, specific resistance, specific w eight of conductor, and voltage at consum er point. A s to scale properties this function exhibits constant returns to scale.

M oving from the stylised transm ission problem of Lord K elvin to m odelling a distribution utility w e m ay start by noting som e basic activities of distribution, follow ing N euberg (1977). D istribution w as there divided into four related but

distinguishable activities. D istribution proper consists of load dispatching, custom er installations, and equipm ent m aintenance. Custom ers account activity includes m eter reading and billing. Sales activity encom passes dem onstrating, selling, and advertising.

Lastly there is general adm inistration, including office supplying and renting. O n the input side these activities w ill be captured by properly specified labour, capital and m aterials inputs. H ow ever, deregulation usually unbundled supply of electricity and distribution by the local utility, thus sales of electricity, custom er accounts, etc. are then not included in distribution.

A s to the physical production activity electricity is delivered through a netw ork to a num ber of custom ers. The basic picture is the sam e as in Lord K elvin’s transm ission problem above. In addition to lines (consisting of overhead-, under ground-, and under w ater cables) transform ers are im portant to physical distribution. H ow ever, w e w ill not m odel the optim al configurations of lines and transform ers. W e assum e that the utilities take the existing lines, transform er capacity and num ber and geographical distribution of custom ers as given. But, at pointed out in N euberg (1977), this is not the sam e as saying that these variables m ust be regarded as constants in our analysis. Past decisions reflected in configurations of lines and transformers m ay give rise to current differences in efficiency. These variables that are exogenous for the firm , m ay be seen as endogenous from the point of view of society. Even distribution jurisdictions can be rearranged, m aking num ber of custom ers endogenous.

O n a general abstract level the outputs of distribution utilities are energy delivered to each node (custom er), and inputs are the energy received by the utility and real capital in the form of lines and transform ers, in addition to inputs used for the distribution activity m entioned above. D ue to the high num ber of custom ers for a standard utility it is im possible to im plem ent the conceptualisation of a m ulti-output production function to the full extent. The usual approxim ation is to operate w ith total energy delivered and num ber of custom ers separately as outputs (see e.g. Salvanes and Tjøtta, 1994). The latter variable is also often used in engineering studies as the key dim ensioning output variable, and taken as the absolute size of a utility (W eiss, 1975). The role of lines varies. It can be regarded as a capital input, but it is also used as a proxy for the

geographical extent of the service area. For fixed geographical distribution of custom ers the m iles of distribution line w ould be approxim ately set (but note the possibilities of inefficient configurations), thus line length m ay serve as a proxy for service area. D ue to probability of w ire-outage and cost of servicing the extent of custom er area w ill influence distribution costs. N on-traditional variables such as size of service area m ay be used to specify differences in the production system or technology from firm to firm .

The energy received by a utility is usually not represented as an input, but the loss in the netw ork system can be used as an input, although it is conceptually a by-product of the transportation activity.

In engineering studies the load density m ay be a characterisation of capital. Load density is the product of custom er density and coincident peak load per custom er (kW h per square m ile). The m axim um peak load m ay also describe capital, or also be used as an output indicator as a quality attribute.

A ccording to the extensive review in Jam asb and Pollitt (2001) the m ost frequently used inputs are operating costs, num ber of em ployees, transform er capacity, and netw ork length. The m ost w idely used outputs are units of energy delivered, num ber of custom ers, and size of service area.

Choice of m odel specification

Considerations of costs, tim e and feasibility of establishing variables w ith com m on definitions by the national regulators have restricted the choice of variables for this study. A s regards input variables it has not been possible to use a volum e m easure of labour due to the lack of this inform ation for one country (D enm ark). Instead a cost m easure has been adapted. Labour cost and m aintenance have been added to total operating expenses (TO M ). W e then face the problem m entioned in the introduction about national differences in w ages for labour. It has been chosen to m easure total operating and m aintenance costs in Sw edish prices.

A m easure for real capital volum e has been established for 1997 by the involved regulators by first creating for the sam ple utilities a physical inventory of existing real capital in the form of length of types of lines (air, underground and sea) distributed on three classes according to voltage, categories of transform ers according to type (distribution, m ain) and capacity in kV , transform er kiosks for distribution, and transform er stations for m ain transform ers. The num ber of capital item s has been in the range of 60-100. A s a m easure of real capital the replacem ent value (RV ) is the theoretical correct m easure (see Johansen and Sørsveen, 1967). To obtain such a m easure aggregation over the categories has been necessary due to the high num ber of item s. It is then necessary to use the sam e w eights, i.e. national prices w ill not yield a correct picture if prices differ. It has been chosen to use N orw egian prices for all countries. A m ore preferred set of w eights m ay be average prices for all countries, but it has not been feasible to establish such a database so far. A lthough lines and transform ers have been used separately as inputs in the literature (see e.g. H jalm arsson and V eiderpass (1992a), (1992b) and Jam asb and Pollitt, 2001), the groups have been aggregated into a single aggregated capital volum e m easure in this study.

The energy fed into the distribution system is the physical input, and electricity taken out and losses in lines and transform ers are the physical outputs. W e w ill m easure as input the loss in M W h in the system . This variable w ill capture a quality com ponent of the distribution system . A problem is that data are usually m ore unreliable than for energy delivered due to m easuring routines not coinciding w ith the calendar year. In som e countries an average loss for the last three years is used, w hile loss for the last year or its estim ate is used for other countries.

O n the output side energy delivered and num ber of custom ers are used as outputs. The countries have inform ation on low and high voltage, but since the classification of high and low voltage differs w e have used the aggregate figures. Som e m easure of geographical configuration of the distribution netw orks should also be included for a relevant analysis of efficiency. The service area can be m easured in different w ays (see e.g. K ittelsen (1993) and Langset og K ittelsen, 1997). O ur option in this study is to use the total length of lines.

Table 1a. Sum m ary statistics 1997

Table 1b. Sum m ary statistics, average country values 1997

The data structure

A n overview of key characteristics of the data is presented in Tables 1a,b. The difference in size betw een utilities is large, as revealed by the last tw o colum ns in Table 1a. A sum m ary of the structure of the data of the individual countries show n in Table 1b is also show n in the radar diagram in Figure 1, w here country averages relative to the total sam ple averages are portrayed. The absolute size of the N etherlands is obvious in all dim ensions except for energy delivered. It is evident that the N etherlands is especially large in num ber of custom ers, but also in replacem ent value. It is relatively sm all in length of lines. N orw ay is largest w ith respect to energy delivered and also correspondingly large in energy loss, although w ith a sm aller value than the N etherlands. Sw eden stands out w ith relatively high operating and m aintenance costs (TO M ), w hile Finland stands out w ith a high num ber for length of lines. D enm ark has the sm allest num ber for length of lines and energy loss, and have a relatively high num ber of custom ers.

A verage M edian Standard

D eviation M inim um M axim um

TO M (kSEK ) 152388 97026 182923 11274 981538

LossM W h 91449 52318 104777 7020 615281

R V (kSEK ) 2826609 1907286 3288382 211789 22035846

N um C ust 109260 55980 163422 20035 1052096

TotLines _{7640 4948 8824 450 54166}

M W hD elivered _{2110064 1003472 2815025 166015 178054730}

C ountries N o.

of units

TO M Loss

M W h

R V N o. of C ust

Total Lines

M W h D elivered

D enm ark 24 101285 43537 2397853 98459 4943 1039806

Finland 25 89942 91663 2564553 82242 9390 1274032

N etherlands 15 283806 164080 6003522 299139 11923 4054312

N orw ay _{18 153533 149430 3099260 72871 6923 4510329}

Sw eden _{42 164933 63921 1852481 75170 6608 26848}

0 % 100 % 200 % 300 %

TO M

LossM W h

RV

N um C ust TotLines

M W hD elivered

D enm ark Finland N etherlands N orw ay Sw eden

Figure 1. The average structure of the countries

In order to see m ore details of the structure of the data w e w ill use diagram s to portray ratios of variables. There are three types of com binations of the variables that shed light on different structures. Form ing ratios of output variables w ill show the distribution of output m ixes, form ing ratios of inputs w ill show the distribution of input m ixes, and form ing ratios of output on input (or inverse) w ill show us partial productivity ratios.

W ith three outputs and three inputs the num ber of output m ix ratios is three, and the sam e for input m ix ratios, w hile the num ber of partial productivity ratios is nine. D ue to space considerations w e w ill only show som e of these. U sing a bar diagram w ith the w idth of the bars proportional to a m easure of size (e.g. one of the inputs or outputs), total operating and m aintenance cost (TO M ) is used here, and sorting the units according to ascending values, w e have w hat has been term ed Salter diagram s. To see the structure w ithin each country, and to com pare country data w e have sorted w ithin each country in the sam e diagram s. Such a data study is also a w ay to detect outliers that seem extrem e. W e can then proceed to investigate in particular the data quality of such observations.

In Figure 2 distributions of output m ixes are show n. Panel a show s the energy delivered per custom er. N orw ay is here in a special position w ith about three tim es as high ratio as the other countries. The distributions for the other countries are sim ilar as to range.

There is no clear size pattern. A s to outlier detection tw o N orw egian units have quite high values for energy per custom er. This m ay be due to deliveries to energy intensive industries.

0 20 40 60 80 100 120

0 2 000 000 4 000 000 6 000 000 8 000 000 10 000 000 12 000 000 14 000 000 16 000 000 18 000 000

Size in TO M

MWhDelivered / NumCust

3009

D enm ark Finland N etherlands N orw ay Sw eden

Panel a. Energy delivered per custom er

0.00 0.05 0.10 0.15 0.20 0.25

0 2 000 000 4 000 000 6 000 000 8 000 000 10 000 000 12 000 000 14 000 000 16 000 000 18 000 000

Size in TO M

TotLines / NumCust

3009

D enm ark Finland N etherlands N orw ay Sw eden

Panel b. Lines per custom er Figure 2. O utput m ix distributions

0.00 0.05 0.10 0.15 0.20 0.25

0 2 000 000 4 000 000 6 000 000 8 000 000 10 000 000 12 000 000 14 000 000 16 000 000 18 000 000

Size in TO M

Opex / RV

3009

Denm ark Finland N etherlands Norway Sweden

Panel a. Total operating costs on replacem ent value of capital

0.00 0.02 0.04 0.06 0.08 0.10

0 2 000 000 4 000 000 6 000 000 8 000 000 10 000 000 12 000 000 14 000 000 16 000 000 18 000 000 Size in TO M

LossMWH / RV

3009

D enm ark Finland N etherlands N orw ay Sweden

Panel b. Loss in M W h on replacem ent value of capital Figure 3. Input m ix distributions

Total length of lines on num ber of custom ers is show n in Panel b. The distributions w ithin each country are very skew for all countries except the N etherlands, w ith large units having the sm allest ratios for D enm ark, Finland and N orw ay, and som e large units having sm all ratios also in Sw eden, but then som e large units also having high ratios.

The N etherlands is a special case w ith the units in tw o distinct size classes and the distribution of lines on num ber of custom ers being quite m ore even than for the other

countries. The distributions of Finland and Sw eden have the sam e m axim al ranges, w hile N orw ay, D enm ark and the N etherlands then follow . A s to outlier detection there are no extrem e ones.

D istribution of input m ix is show n in Figure 3. Com parison of total operating and m aintenance cost on replacem ent value of capital in Panel a reveals that Sw eden has a special distribution com pared w ith the other countries, having about tw ice as high costs per volum e of capital. The range of the distributions for the other countries is about the sam e. For D enm ark, Finland, and N orw ay large units have high ratios, w hile for the N etherlands it is tw o sm all units w ith the highest ratios, and for Sw eden large units are located at both ends of the distribution. A s to outlier detection one sm all D anish unit and tw o sm all D utch units have exceptional high values w ithin their national distributions and m ay deserve a closer inspection.

Energy loss on replacem ent value of capital is show n in panel b. D enm ark and the N etherlands have about the sam e range and considerably narrow er than the other three countries. For D enm ark sm all units have the low est value of this input m ix, w hile large units have high m ix values. For Finland, the N etherlands and N orw ay there are no clear size pattern, w hile Sw eden has large and sm all units at both ends of the input m ix. A s to outlier detection there are one unit from each of the countries D enm ark, Finland and Sw eden that stand out w ith high m ix, and one from Finland and tw o from the N etherlands that stand out w ith low m ix value w ithin national distributions.

Som e productivity ratios are show n in Figure 4. H igh productivity outliers m ay be im portant for the solution of the D EA m odel, so special attention should be paid to them . In Panel a num ber of custom ers on operating and m aintenance costs are show n.

The distribution for the countries varies both w ith regards to range and m inim um – m axim um values. D enm ark has the m ost extrem e range, and then Finland and the N etherlands. For these three countries there are sm all units w ith the highest productivities. The distributions for N orw ay and Sw eden are sim ilar and the range m uch m ore lim ited. The m axim um values are considerably low er than for the other countries.

There is no distinct size pattern as for the other countries. A s to outlier detection one

D anish unit is quite extrem e, as w ell as tw o Finnish ones and tw o D utch ones. W e w ill expectthese to show up as best practice units, and their data should be investigated carefully.

0.0 0.5 1.0 1.5 2.0

0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000 14,000,000 16,000,000 18,000,000

Size in TO M

NumCust/TOM ³⁰⁰⁹

D enm ark Finland N etherlands N orw ay S w eden

Panel a. Num ber of custom ers on total operating costs

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040 0.0045

0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000 14,000,000 16,000,000 18,000,000

Size in TO M

TotLines/RV

3009

D enm ark Finland N etherland N orw ay Sw eden

Panel b. Lines on replacem ent value of capital

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

0 2 000 000 4 000 000 6 000 000 8 000 000 10 000 000 12 000 000 14 000 000 16 000 000 18 000 000

Size in TO M

LossMWh / MWhDelivered

3009

D enm ark Finland N etherlands N orw ay Sweden

Panel c. Loss in M W h on M W h delivered Figure 4. Partial productivities

Panel b portrays length of line on replacem ent value. The distributions are different for each country. D enm ark and N orw ay are m ost sim ilar, w ith about the sam e range and no extrem e observations. Finland’s distribution is shifted alm ost com pletely to a higher level than the D anish, w ith the low values in the range of the D anish high values. The Sw edish distribution is m ore sim ilar to the Finnish one. Large units dom inate the low er tail of the D anish, Finnish and N orw egian distribution. The D utch distribution is m ost extrem e w ith a few sm all units having extrem ely high productivities. These units are candidates for closer scrutiny as outliers.

Panel c show s the energy loss on energy delivered. This is the inverse of productivity, but is the standard form of presenting such inform ation. The Finnish distribution stands out w ith the m axim al range. A large unit has a sm all loss ratio, w hile tw o m edium sized units have m axim al loss ratio. For D enm ark the sm all units have sm allest loss ratios, i.e.

they are m ost productive in this partial dim ension. The distributions for the N etherlands, N orw ay and Sw eden are som ew hat m ore even and no clear pattern as to location of units according to size. Regarding outliers Finland has an outlier w ith a low ratio internally, but not com pared w ith other countries.

Looking at the tails of the Salter distributions show n above som e potential outliers m ay

be identified ⁸. The output-m ix not show n, energy delivered on lines, is dom inated at the high end-range by Finnish utilities, w hile the input-m ix not show n, energy loss on operating costs, is not dom inated by utilities from a particular country. The six partial productivities not show n confirm N orw egian dom inance of ratios w ith energy delivered in the num erator, and Finnish dom inance as to lines on operating costs. The participating regulators have all investigated these units (including the ones not show n in the figures) and controlled the data for faulty reporting on prelim inary analyses. The dataset described above is to the best know ledge of the parties the m ost reliable data that can be obtained at this stage. Som e uncertainties exist, especially w ith respect to data for energy losses.

4. Trial runs

Technical perform ance of the m odel

The choice of variables to be used has also been based on the results of the step-w ise testing procedure for inclusion of relevant variables perform ed in K ittelsen (1993), starting w ith the m ost aggregate m odel regarded as relevant, and then disaggregating the variables. But it m ay be of interest to check the significance of the variables by looking at significant differences in the efficiency scores by excluding variables. This can be done by testing H_o: that all variables should be included against H₁: that each variable in turn is taken out. The results of such a test is show n in Table 2. The difference in

Table 2. Test of significance of variables by change in efficiency scores,E

H0 H1 D iff. E H0- H1 D + T

C ritical level 0.9 0.14 1.29

C ritical level 0.95 0.16 1.65

C ritical level 0.99 0.19 2.34

Loss A ll- Loss -0.03 0.11 1.74

R V A ll- R V -0.32 0.73 16.35

T O M A ll- TO M -0.05 0.19 3.25

Totlines A ll-Totlines -0.21 0.57 9.68

N um C ust A ll- N um C ust -0.08 0.25 4.63

M w h A ll- M w h -0.05 0.19 3.15

8O ne unit, no. 3009, is pointed out in the figures for use in Section 4 below .

average values of the E-scores is highest for RV , then Totlines, w hile both N um Cust and M w h have m ore m odest differences. The sm allest difference is for the input variable Loss. W e have used the K olgom orov- Sm irnov one-sided test (D⁺ ) for the equality of tw o distributions, and a T-test for com parison of m eans. H₁ is rejected for all variables on a 10% -level. The variable Loss has the w eakest perform ance, failing the D⁺ test on the levels 5% and 1% , and the T -test on level 1% . For all the other variables H1 is rejected on a 1% -level. O n the basis of these results w e find it reasonable to proceed w ith our m odel specification.

U nduly outlier influence

In order to detect unduly influence from the outliers that by definition w ill form the set of best practice units w e w ill first conduct a trial run. W e w ill base our analysis on the three m easures for the influence of peers introduced in Section 2. The m easures are set out in Table 3. The peers split into three groups. O ne peer, unit 3009, stands out w ith especially high Peer index values, w ith an average of 44% that is over four tim es higher values on average than the next group of four units w ith average values in the range 10- 8% . The third group of nine units has index values in the range 4-0% , w ith one self- evaluator. W e note that the index values m ay vary considerably according to type of inputs for som e of the peers, like unit 1023 w ith high value for Replacem ent V alue, and unit 4192 w ith high value for loss in M W h. U nit 3009 has the highest count value alm ost double of the next tw o units that belong to the second group as to the value of the Peer index. Thus the tw o w ays of m easuring peer im portance coincide.

The super-efficiency index varies from 1.01 for the self-evaluator to 1.88. The m axim al num ber m eans that the reference point on the frontier established w ithout the peer in question in the data set on w hich the frontier is based, im plies a use of inputs that is 88%

higher than for the peer. But w e see that this unit has quite low Peer index values, indicating that if the input data for this unit is increased it w ill not m atter m uch for the overall results. It also has a m oderate count value. The Super-efficiency index is 1.21 for the m ost influential peer, im plying that the “over consum ption” of inputs at the frontier excluding this peer is 21% . G iven that the units supporting the full frontier by definition are outliers this figure in itself dos not give rise to too m uch concern. W e conclude that it

Table 3. The Peer index in % , Super efficiency score and count

is one unit, 3009, the one w ith the outstanding high value of the peer- and the count index that should be investigated further w ith respect to the overall results.

O ne consideration is how the peers influence inefficient units in other countries. O f the 14 peers w e observe four truly m ultinational peers in the sense that they are referencing inefficient units from all five countries. The units are 1009, 1023, 2014, and 3009. The tw o units 2014 and 3009 stand out as referencing considerably m ore inefficient units than the other tw o m ultinational peers. The D utch peer 3009 is especially im portant for Sw eden in the sense that all but tw o of the Sw edish inefficient units have this unit as their peer.

D ue to the special influence of unit 3009 and its special character as a sm all utility in an urban area w e have chosen to rem ove it from the data set. H ow ever, in the figures 2-4 w e see that except for a very high m axim al ratio of lines to replacem ent values the unit is not extrem e. O ne reason for the high peer index value is its central location on the

U nits Total operating + m aintenance

costs

L oss in M W h

R V R eplacem ent

value

A verage Peer index

Super- Efficiency

C ount

1009 10.1 10 8.1 9.4 1.33 23

1023 6.4 6.2 19.3 10.6 1.83 37

2014 7.6 9.4 7 8 1.05 49

2016 0.8 1.4 2.4 1.5 1.88 15

2026 3 5.8 3.7 4.2 1.16 21

2124 2.9 0.9 2.2 2 1.29 25

3005 2.5 2.5 3 2.7 1.17 15

3009 47.9 44.5 38.6 43.6 1.21 88

3010 4.8 1.2 1.3 2.4 1.07 12

3017 2.4 0.8 1.7 1.6 1.1 9

4192 5.9 15.1 11.5 10.8 1.69 49

4462 0 0 0 0 1.01 0

5022 0.8 0.8 0.4 0.7 1.02 7

5047 4.9 1.3 0.8 2.3 1.41 18

frontier.

5. The results

Efficiency scores

The distribution of efficiency scores for the CRS m odel (1) is show n in Figure 5. The distribution is sorted from the m ost inefficient unit to fully efficient ones. Each bar represents a unit; an electric utility com pany. The size of each unit, m easured as total operating and m aintenance costs (TO M ) (including labour costs), is proportional to the w idth of each bar. The efficiency score is m easured on the vertical axis and the TO M values m easured in SEK are accum ulated on the horizontal axis. Since an input is used as size m easure, the share of the area betw een the step contour of the efficiency distribution and the upper lim iting line at the ordinate value of 1 of the total area of the rectangle is approxim ately (the exact potential is input specific) equal to the total input saving potential (given the observed output structure). A rough visual estim ation gives a total potential of about 20% . The exact num bers are 18% for total operating –and m aintenance costs, 18% for energy loss and 19% for replacem ent value of capital. The

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 2 000 000 4 000 000 6 000 000 8 000 000 10 000 000 12 000 000 14 000 000 16 000 000 18 000 000 Size in ToM

E3

Figure 5. Efficiency distribution with com m on frontier

units are distributed in the interval from 0.44 to 1, and the share of TO M of fully efficient units is rather sm all, representing about 5% of accum ulated TO M costs. There are 13 fully efficient units (one is a self evaluator) of the total num ber of 122 units. A s to the size of the efficient units they are sm all and under m edium , except for one large unit, but this is a self-evaluator. The largest units are all inefficient and located tow ards either end of the distribution.

Structural features of best- and worst practice units

From the efficiency distribution show n in Figure 5 w e have calculated the average input- and output values of the 12 active peers (excluding the self-evaluator) and for the12 w orst practice units. Since w e have 122 units this num ber represents the upper and low er deciles of the distribution. The com parison is show n in Figure 6. It is the relative position in the radar diagram that reveals the structure. W e see that best practice units (BP) on the average have higher values for all outputs, and relatively less in front regarding num ber of custom ers com pared w ith w orst practice units (W P). Concerning inputs the W P units have a significant over-use of capital (m easured by the replacem ent value) leading to a m uch higher use of this input than for BP units, and also higher for

0 % 100 % 200 %

TO M

LossM W h

R V

N um C ust TotLines

M W hD elivered

Average 12 best Average 12 w orst

Figure 6. Structural com parison of best- and worst practice units

total operating and m aintenance costs (TO M ), w hile energy loss is actually a little low er than for BP units.

Country results

Since one com m on technology is assum ed an inspection of w here each country’s units are located w ill be of interest. In Figure 7 the units for each country are put together and sorted according to ascending value of the efficiency score. It is rem arkable that all countries have fully efficient units. This supports the use of a com m on technology, in the sense that no country is com pletely dom inated by another. There are tw o aspects that the figure sheds light on: the size of the efficient units and how the efficient units stand out in the country specific distributions. For the three countries D enm ark, the N etherlands and Sw eden, the efficient units are quite sm all com pared to average size w ithin each country. This is especially striking for the N etherlands w ith the m ost pronounced dichotom y in size w ith one group of large units and the other w ith considerably sm aller ones. The units w ithin the group of large units have about equal efficiency levels, w hile the group w ith sm all units has units both at the least efficient part and the m ost efficient part of the distribution. The least efficient units have only half the value of the efficiency score than the average. For Finland and N orw ay the efficient units are closer to the m edium size (disregarding the large N orw egian self

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 2 000 000 4 000 000 6 000 000 8 000 000 10 000 000 12 000 000 14 000 000 16 000 000 18 000 000 Size in ToM

E3

D enm ark Finland N etherlands N orw ay Sw eden

Figure 7. Country distribution of efficiency scores

evaluator).The inefficient units w ith the highest efficiency scores are quite below 1 for D enm ark,the N etherlands and N orw ay, w hile they are m uch closer to the fully efficient ones in Finland and Sw eden. This m ay indicate that w e should pay attention to the influence of these form er units w hen perform ing sensitivity tests. W e w ill return to w ays of m easuring influence of efficient units below . The Sw edish distribution is characterised by the large units being at the upper end of the inefficiency distribution, w hile m edium - and sm all sized units are evenly located over the entire distribution. The N orw egian distribution has no m arked size pattern, but has a m uch m ore narrow range of the efficiency scores for the inefficient units than Sw eden. The range of the distribution for Finland is the m ost narrow w ithout one or tw o extrem ely inefficient units like the case for the N etherlands, N orw ay and Sw eden. Both for Finland and D enm ark the largest units are located centrally in the distributions.

A sum m ary expression for the different shapes of the efficiency distributions and different absolute size betw een units and location of size classes w ithin country distributions the country share of the savings potential for the three inputs are set out in Table 4. D ue to the large inefficient D utch units that w e see in Figure 7 the N etherlands has a higher savings potential than the other countries, especially for replacem ent value of capital. Sw eden has a high potential for total operating- and m aintenance costs, and N orw ay for energy loss. D enm ark com es second to the N etherlands as regards saving potential for replacem ent value of capital, and has the sm allest share for energy loss on the level w ith Finland. Finland has significantly low er savings potential for total operating- and m aintenance costs and replacem ent value of capital than the other countries.

Table 4. Country distribution of savings potential shares TO M Loss R V

D enm ark 0.19 0.14 0.22 Finland 0.08 0.14 0.10 N etherlands 0.29 0.28 0.33 N orw ay 0.16 0.25 0.18 Sw eden 0.28 0.19 0.17