Journal of the Operational Research Society (2011), 1–9

© 2011 Operational Research Society Ltd. All rights reserved. 0160-5682/11 www.palgrave-journals.com/jors/

Productivity change and innovation in Norwegian electricity distribution companies 1 1 2 2 VL Migue´is  , AS Camanho , E Bjørndal and M Bjørndal 1

2

Faculdade de Engenharia, Universidade do Porto, Portugal; and Norwegian School of Economics and Business Administration, Bergen, Norway Regulators of electricity distribution networks have typically applied Data Envelopment Analysis (DEA) to cross-section data for benchmarking purposes. However, the use of panel data to analyse the impact of regulatory policies on productivity change over time is less frequent. The main purpose of this paper is to construct a Malmquist productivity index to examine the recent productivity change experienced by Norwegian distribution companies between 2004 and 2007. The Malmquist index is decomposed in order to explore the sources of productivity change, and to identify the innovator companies that pushed the frontier forward each year. The input and output variables considered are those used by the Norwegian regulator. In order to reflect appropriately the exogenous conditions where the companies operate, the efficiency model used in this paper incorporates geography variables as outputs of the DEA model. Unlike the model used by the regulator, we included virtual weight restrictions in the DEA formulation to correct the biases in the DEA results that may be associated to a judicious choice of weights by some of the companies. Journal of the Operational Research Society advance online publication, 26 October 2011 doi:10.1057/jors.2011.82 Keywords: data envelopment analysis; regulation; electricity distribution; Malmquist index; virtual weight restrictions

1. Introduction The structure and operating environment of electricity distribution companies has changed significantly in recent years due to the global reforms in the electricity sector. The natural monopolies that characterize this industry potentially pose a cost to society by allowing excess profits and costs at the expense of customers. The regulator, representing customers, has the role of insuring the reasonableness of the price of electricity transmission and distribution. Many different approaches to incentive regulation have been implemented in different countries. The most widely adopted schemes are based on price cap, revenue cap and target-incentive models. Other incentive-based models, described in Jamasb and Pollitt (2000), include yardstick regulation, sliding scale, menu of contracts and partial cost adjustment. These regulatory frameworks are crucial for enforcing cost reductions that can benefit the customers. They are also important to promote efficiency improvements that can attract investors. From 1997, the Norwegian electricity distribution companies have been regulated according to a revenue cap 

Correspondence: VL Migue´is, Faculdade de Engenharia, Universidade do Porto, Rua Dr Roberto Frias, Porto 4200-465, Portugal. E-mail: [email protected]

model, instead of the traditional rate of return approach (see Heggset et al, 2001, for details). As noted by Agrell et al (2005), the Norwegian regulation is considered to be one of the most advanced schemes. The annual revenue caps are determined based on the comparison of actual cost with a cost norm. The cost norm for each company is estimated based on the relative efficiency score obtained from Data Envelopment Analysis (DEA). The regulatory model was enhanced in 2007, such that the efficiency scores are obtained using a super-efficiency model (Andersen and Petersen, 1993), and are subsequently calibrated such that a representative company, with the average efficiency score, is allowed to earn the normal rate of return. The DEA model used for efficiency evaluation has a single input, equal to total cost, and many outputs, that can be interpreted as cost drivers. The outputs considered are direct measures of the production activity (transported energy and customers), variables representing structural conditions (high voltage lines, network stations and interface) and geographic factors (forest, snow and coast). Despite the frequent use of DEA models as benchmarking tools for electricity distribution regulation, analysis of the impact of regulatory policies on productivity change over time are less frequent. Førsund and Kittelsen

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(1998) constructed a Malmquist index (MI) for the period 1983–1989 using data on Norwegian electricity distribution companies. The model specified three outputs (a distance index expressing density of customers, the number of customers and the total energy supplied) and four inputs (labour, energy loss, capital and materials). Edvardsen et al (2007) also presented a Malmquist analysis using data on Norwegian electricity distribution companies. The DEA model included the inputs and outputs used by the regulator in the second regulation period (2002–2006). The DEA model for this period corresponded to a cost efficiency assessment with five inputs and five outputs. The model used in this paper corresponds to the model used in the third regulation period (2007–2012). See also Bjørndal et al (2009) for a discussion of the different DEA models that have been used by the regulator. This paper proposes the use of MI to explore the recent productivity change experienced by electricity distribution companies in Norway, between 2004 and 2007. The MI is decomposed in order to explore the sources of productivity change. The model used in this paper includes the inputs and outputs specified by the regulatory authority. However, with this specification of variables, there seems to be a tendency for higher efficiency scores being associated to companies with high weights on geographic factors, instead of weighting outputs representing the production activity (ie, energy delivered or customers served). In order to avoid this potential bias in the analysis, the model used in this paper restricts the weights (shadow prices) associated to the geographic outputs. Compared to previous Malmquist analyses of the Norwegian electricity network industry, our DEA model should be far better suited for analysing the relative efficiency of the companies. The DEA model used is the result of a considerable development by the Norwegian regulator and others, including environmental variables and restricting their weights in order to avoid biases. Moreover, the input measure (total cost) has been improved, as direct investment contributions are now properly taken into account in the capital costs. The Malmquist analysis is also complemented with the identification of innovative companies, that is, the companies that pushed the production possibility set to more productive levels over time. The structure of the remainder of the paper is as follows. Section 2 introduces the contextual setting of the analysis and presents the DEA model used. Section 3 includes a presentation of the MI and its decomposition, corresponding to pure technical efficiency change (EC), scale efficiency change, magnitude of technological change and bias of technological change (TC). Section 4 discusses the results concerning the sources of productivity change and the identification of innovator companies. The paper finishes with a conclusion and some suggestions for future research.

2. Contextual setting 2.1 The regulatory model used in Norway From January 2007 the revenue cap (RC ) regulation in the Norwegian electricity sector is based on an annual yardstick formula. This formula implies a RC based on a combination of the actual cost c and cost norm c , according to formula 1, where rA[0, 1] is a factor that specifies the strength of the incentives. RC ¼ c þ rðc  cÞ ¼ rc þ ð1  rÞc

ð1Þ

The cost norm c is calculated based on relative efficiency scores found by DEA. The model used is a super-efficiency variant, such that the scores may be higher than 100%. This enables a company that performs better than other companies and improves over time to have a cost norm higher than the actual cost. The efficiency estimates found from the DEA analysis are calibrated such that the cost weighted average efficiency score is 100% (Bjørndal and Bjørndal, 2006; NVE, 2006a, b). This implies that a representative company, with an average efficiency score, is allowed to earn the normal rate of return, and efficient companies can earn more than the normal rate of return. This intends to promote efficiency improvements over time and the attractiveness of the industry to investors and employees.

2.2 Estimation of cost norm using DEA The choice of appropriate input and output variables is crucial when applying DEA models. In the context of electricity distribution, the most common inputs of DEA assessments are costs (operational, capital and maintenance costs), labour (number of employees and labour hours) and assets (network length and transformer capacity). The most widely used outputs are the number of customers, energy delivered and energy quality. For a literature review of efficiency measurement studies of electricity distribution utilities see Santos et al (2011). The DEA model used in this paper is identical to the model used by the Norwegian regulator until 2009. The input specified is the total cost, which includes operational costs, capital costs and quality costs (measured by the value of lost load). This last component of cost is associated to the cost of interruptions of electricity supply and consequently measures the quality of service. The selection of output variables was one of the most challenging issues when the new regulation model was developed prior to its introduction in 2007. The regulator formulated three criteria that should be met if an output variable was to be included in the model. First, the variable should have a solid ‘theoretical and practical’ foundation. Second, it should have a statistically significant effect on company costs, evaluated based on regression tests. Third,

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VL Migue´is et al—Productivity change and innovation in Norwegian electricity distribution companies

the variable should be statistically significant in the so-called ‘Banker test’, (see Banker, 1993), such that the efficiency estimates obtained using models with or without the variable had to be significantly different. Hence, although a large number of candidate variables were considered initially, the final set of variables shown in Table 1 was determined mainly based on statistical tests. The variables energy delivered and the number of customers measure direct outputs from the production activity of the distribution companies. Customers were separated in cottage customers and regular customers because they are structurally different, as cottage customers typically consume less energy than ordinary customers. The model also contains output variables that represent structural and environmental conditions that may influence the cost of the companies. Three of the variables (HV-lines, network stations and interface) are in fact input variables. Their role in the DEA model is to represent demographical and topological conditions, as well as transmission functions, that influence the costs of particular companies, and for which a better representation could not be found. The last three variables (forest, snow and coast/wind) describe environmental conditions that may influence the costs of the companies, and are the only variables that are not based on data reported by the companies. The linear programming model for determining the cost norm of company j , producing the outputs yrj , (r ¼ 1, . . . , 9) with input xj , corresponding to total cost, is shown in (2): min

X

lj xj

jaj 

s:t:

X

lj yrj Xyrj

r ¼ 1; . . . ; 9

jaj 

lj X0

j ¼ 1; . . . ; n

ð2Þ

The interpretation of the linear program is that in the performance evaluation of company j , obtained by comparison to other companies in the sample, we construct a reference company that produces at least as much of each output as the evaluated company, while minimizing cost. The reference company corresponds to a linear combination of other companies in the sample, aggregated using the multipliers lj, which are the decision variables of model (2). This model assumes constant returns to scale, and is based on a super-efficiency evaluation, as the unit under assessment is removed from the comparator set. Note that the objective function minimizes the cost norm, and not the efficiency scores, as in Dyson and Thanassoulis (1988). The regulator uses a constant returns to scale model since the assumption of variable returns to scale would lead to weak regulation for some companies. Indeed, for variable returns to scale models, the largest and smallest company with respect to each output would be automatically

Table 1 Output variables of the DEA model Variables

Measurement unit

1. Energy delivered 2. Customers (except cottages) 3. Cottage customers 4. High voltage lines 5. Network stations (transformers) 6. Interface

MWh No. of customers No. of customers Kilometers No. of stations Cost weighted sum of equipment in the interface between the distribution network and the regional transmission network Proportion (0–100) of area with high-growth forest  HV-lines through air (kilometers) Average precipitation as snow (mm)  HV-lines through air (kilometers) [Average wind speed (m/s)/ Average distance to coast (meters)]  HV-lines through air (kilometers)

7. Forest 8. Snow 9. Coast

considered efficient, regardless of their cost level, what seems unreasonable in a regulation context. Furthermore, the evaluation of scale efficiency for the companies under assessment revealed the existence of very high scale efficiency estimates in all years, whose average was higher than 95%. Therefore, we concluded that there was no strong evidence of the existence of variable returns to scale in the activity of Norwegian electricity distribution companies. The dual problem of (2) can be formulated as shown in (3). The model used for regulatory purposes is a modified super-efficiency procedure, which also takes into account the performance of the companies in previous years. However, for the purpose of this paper we used a simplified version of the regulator model, as our main purpose is to assess the productivity change over time in the electricity distribution sector. max

X

yrj prj

r

s:t:

X

yrj prj pxj

jaj 

r

prj X0

8r

ð3Þ

The dual model can be interpreted so as to find prices for each output of company j that maximize revenue, and at the same time assure that none of the other companies exceeds its total cost at these prices (they are within a budget limit). The prices prj in problem (3) are the shadow prices of the output constraints in (2), and

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consequently prj gives the increase in minimum cost due to an increase in yrj , and is a local per unit cost of output r. Except for the budget constraint and the non-negativity constraints in (3), there is complete freedom in choosing the prices in the dual problem (3). This may result in prices that are in contradiction to prior views or additional information. It may for instance be that the prices of different outputs turn out to be illogical. With slack in the inequality constraints in (2), the corresponding prices in (3) will be equal to zero, and as a consequence, the minimum cost can be determined more or less completely by the weights or prices of only a few outputs. Analysing the composition of the cost norm for all companies in the industry in 2006, it was found that energy and customer variables together constitute 54% of the total cost norm for the industry, as shown in Figure 1(a). The geography variables, on the other hand, account for only 14% of the norm, which seems reasonable. However, some companies have a very high proportion of their cost norm attributed to geographic factors. In fact, some small companies, which represent a relatively small share of the total industry cost, present very high virtual weights for geography variables (ie, the product of the output variable and its corresponding price), and low virtual weights for production activity variables, which seems unreasonable. Consequently, in order to make a fair analysis of companies’ efficiency and productivity change, the model specified in this paper restricts the virtual weights of the geography variables. This intends to enforce that the prices of geography variables are not inflated to unreasonably high levels for any company. Several types of weight restrictions have been proposed in the DEA literature. In Allen et al (1997), the weight restrictions are categorized into different types, including direct weight restrictions, such as assurance regions and absolute weight restrictions, and restrictions to the virtual weights. Absolute weight restrictions are upper or lower bounds on the prices for each output in model (3). Relative weight restrictions limit the relationship between the prices of different outputs. Virtual weight restrictions are upper or lower bounds on the virtual input or output levels. A literature review on the use of weight restrictions in DEA can be found in Thanassoulis et al (2004). Biased DEA results can arise if we make the wrong choices in the weight restrictions imposed, for example, by omitting relevant restrictions or by making false assumptions with respect to the bounds. Direct weight restrictions would require choices to be made at a fairly detailed level concerning output prices. Therefore, the approach followed in this paper implements virtual weight restrictions, since this type of restrictions can be used on a more aggregate level, reducing the need for detailed assumptions. In particular, the DEA model used in the empirical analysis of this paper was specified such that no more than 30% of the cost norm for each company

Figure 1 Distribution of the virtual weights for the companies in year 2006. (a) Distribution of virtual weights without weight restrictions; (b) Distribution of virtual weights considering geographic virtual weights restriction.

can be accounted for by geography variables, as shown in (4). A discussion concerning the identification of appropriate values for the bounds of virtual weight restrictions can be found in Bjørndal et al (2008, 2009). max

X

yrj prj

r

s:t:

X

yrj prj pxj

8j

r

pforestj yforestj þ psnowj ysnowj X þ pcoastj ycoastj p0:3 yrj prj r

prj X0

8r

ð4Þ

Since we intend to assess the productivity change over time, it is important to specify the location of the efficient frontier in a given period. Thus, we need not to discriminate between efficient companies, and consequently we do not use the super efficiency formulation used by the regulator. The impact of imposing virtual weight restrictions on geography variables is illustrated in Figure 1. There

VL Migue´is et al—Productivity change and innovation in Norwegian electricity distribution companies

are many companies with large virtual weights on the geography variables, but these companies tend to be small, as shown in Figure 1(a). To reflect appropriately the contribution of these variables to the industry cost norm, the bars corresponding to each company in Figure 1 are weighted by cost. Figure 1(b) shows the results from model (4), with the weight restrictions. It can be observed that in this case the cost norm is more balanced between the three types of factors, that is, production activity, structural conditions and geographic factors.

3. Methodology for the assessment of productivity change and innovation This section presents the MI and its decomposition, which enables allocating productivity change to different sources. The MI is currently the standard approach to productivity measurement within the non-parametric literature. The MI was introduced by Caves et al (1982) and enhanced by Fa¨re et al (1994). This index, calculated for measuring productivity change between period t and t þ 1 can be expressed as: M tþ1

 t tþ1 tþ1 1 E ðX ; Y Þ E tþ1 ðX tþ1 ; Y tþ1 Þ 2  ¼ E t ðX t ; Y t Þ E tþ1 ðX t ; Y t Þ

ð5Þ

Productivity growth corresponds to an MI greater than one and productivity decline corresponds to an index smaller than one. The MI requires the estimation of singleperiod efficiency scores assuming constant returns to scale, Et(Xt, Yt) and Et þ 1(Xt þ 1, Yt þ 1), and mixed-period efficiency scores, Et(Xt þ 1, Yt þ 1) and Et þ 1(Xt, Yt), using DEA models. Et(Xt, Yt) is a factor used to scale back the inputs, holding output constant, in order to make a decision making unit (DMU) in period t efficient in relation to the technology at the same period, while Et þ 1(Xt, Yt) is the factor used to adjust the inputs, so as to make a DMU in period t efficient in relation to the reference technology in period t þ 1. A similar interpretation applies to Et þ 1(Xt þ 1, Yt þ 1) and Et(Xt þ 1, Yt þ 1). The single period efficiency estimates are always less than or equal to one. They can be obtained by dividing the optimal solution of model (4) by the observed cost in the period considered. In the mixed-period assessments, the efficiency value may be smaller or greater than unity. This is because the input– output combination observed in one period may not be part of the feasible set in another period, and may result in an efficiency score greater than one. The single-period and mixed-period DEA models required for the estimation of an MI can be found in Coelli et al (1998). For a review of the literature on the theoretical developments and applications on the MI see Fa¨re et al (1998). Fa¨re et al (1994) showed how to decompose the MI (5) into the product of EC and TC components, as

5

shown in (6). M tþ1 ¼

E tþ1 ðX tþ1 ; Y tþ1 Þ E t ðX t ; Y t Þ  t tþ1 tþ1 1 E ðX ; Y Þ E t ðX t ; Y t Þ 2  tþ1 tþ1 tþ1  tþ1 t t E ðX ; Y Þ E ðX ; Y Þ

ð6Þ

The ratio outside the brackets measures the EC between periods t and t þ 1. The square root of the term inside the brackets measures the TC, or shift in the frontier, between the same periods. Fa¨re et al (1997) demonstrated that the technological change component of the MI can be decomposed into a magnitude term and a bias term (BTC). Thus, technological change can be rewritten as follows: TC ¼

E t ðX t ; Y t Þ E tþ1 ðX t ; Y t Þ  t tþ1 tþ1 1 E ðX ; Y Þ E t ðX t ; Y t Þ 2  tþ1 tþ1 tþ1 = tþ1 t t E ðX ; Y Þ E ðX ; Y Þ

ð7Þ

The first term of the expression measures the magnitude of technological change along a ray using data from period t and the second term captures the bias. If technological change is biased, the production possibility set shifts out (or in) by a different magnitude, along a ray through period t þ 1 data than it does along a ray through period t data (Grifell-Tatje´ and Lovell, 1997). If the two magnitudes are equal, biased technological change equals 1 and the magnitude term equals the technological change component. In this case, technological change is said to be Hicks neutral. If the two magnitudes are different, there is a positive (BTC41) or negative (BTCo1) contribution to productivity change, indicating weather the DMU adjusts production in the right or wrong direction when confronted with a non-neutral change in production possibilities. Concerning the identification of the distribution companies that shifted the frontier to more productive levels over time, it is not enough to analyse the technological change component of the MI (ie, second term of expression (6)). This measure merely indicates, for a particular company, whether at its input–output combination, the frontier shifted outwards or inwards, but not whether that company was located on the frontier and contributed to that technological progress. According to Fa¨re et al (1994), in order to find the companies that innovated it is also necessary to see if the companies are located on the frontier. Therefore, a company i can be considered an innovator, between period t and t þ 1, if the conditions in expression (8) are satisfied. The term Et(Xt þ 1, Yt þ l) can be used as an innovative score. E tþ1 ðX tþ1 ; Y tþ1 Þ ¼ 1

and

E t ðX tþ1 ; Y tþ1 Þ41

ð8Þ

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4. Discussion of results 4.1 Characterization of industry performance The efficiency scores calculated for 127 electricity distribution companies using model (4), including virtual weight restrictions on geography variables, are summarized in Table 2. The tendency of change observed in the efficiency scores cannot be interpreted directly as a productivity change tendency, since the comparison set changes from year to year. However, it is possible to conclude that the average efficiency score remained stable over the years, with only a small decrease in 2007. While some companies came closer to best practices, others did not manage to follow the best performers, as can be seen by the decrease in the minimum efficiency score over the years. Concerning a tentative exploration of factors that may influence efficiency levels, we examined the relation between efficiency scores and some contextual variables, such as: company remaining life span (represented by book value divided by depreciation), size (represented by total cost) and environmental conditions (forest, coast and snow indices, corresponding to the DEA output variable divided by HV-lines). A Tobit regression was used to explore the degree of association between these factors. The results of the regressions are reported in Table 3. The values in parenthesis represent the level of significance of the parameter (p-value).

Table 2 Efficiency scores for Norwegian electricity distribution companies (2004–2007) Year

TE

SD

No. of efficient companies

Minimum

2004 2005 2006 2007

0.866 0.866 0.869 0.838

0.108 0.111 0.114 0.120

22 26 26 20

0.641 0.608 0.588 0.552

Analysing the results, it can be concluded that none of the factors considered has a significant effect on efficiency levels. Concerning the remaining life span, due to linear depreciations there was a suspicion that the DEA model could be biased by company age, such that more recent companies could be penalized in the efficiency evaluation (for further details see the controlled simulation experiment in Bjørndal et al (2010)). However, the results obtained in the regression do not confirm this hypothesis, although remaining life span may be a poor age indicator. Regarding the environmental conditions, since there is no significant relationship between efficiency scores and environmental indices, the geographic conditions seem to be well accounted for in the model. This point can be illustrated further by analysing the relationship between geography variables and the efficiency scores obtained using a model without geography variables. In this case it was observed that there is a significant and negative effect of coast and snow on efficiency levels. Adding weight restrictions further reduces model bias, as unrestricted weights on geography variables seem to overcompensate the companies with high values on the geography factors. Next, we examined productivity change using the MI to see if the companies are improving or deteriorating performance over time. The results of the MI for the period between 2004 and 2007 are summarized in Table 4. It should be noted that the results reported in Table 4 are arithmetic means of the results for the electricity distribution companies. Results for individual companies exhibit considerable variation around these means. These results reveal that, on average, distribution companies’ productivity increased between 2004 and 2005, did not change significantly from 2005 to 2006 and decreased slightly from 2006 to 2007. Over the years, there is no strong evidence of bias in technological change. Considering the EC component, we recall that Table 2 showed an increase in the variation of efficiency scores and a reduction in the minimum efficiency scores over the

Table 3 Results of Tobit regressions 2004

Remaining life span Size Forest Coast Snow

2005

2006

2007

Constant

Slope

Constant

Slope

Constant

Slope

Constant

Slope

0.9144 (0.0000) 0.8716 (0.0000) 0.8878 (0.0000) 0.8772 (0.0000) 0.8856 (0.0000)

0.0022 (0.6009) 0.0000 (0.2162) 0.0835 (0.4948) 0.0062 (0.9424) 0.1132 (0.2644)

0.8930 (0.0000) 0.8726 (0.0000) 0.8715 (0.0000) 0.9092 (0.0000) 0.8891 (0.0000)

0.0008 (0.8668) 0.0000 (0.1875) 0.0852 (0.5190) 0.1259 (0.1685) 0.1355 (0.2206)

0.8768 (0.0000) 0.8765 (0.0000) 0.8773 (0.0000) 0.8793 (0.0000) 0.8902 (0.0000)

0.0005 (0.9160) 0.0000 (0.2090) 0.0652 (0.6335) 0.0225 (0.8128) 0.0965 (0.4029)

0.8460 (0.0000) 0.8423 (0.0000) 0.8581 (0.0000) 0.8558 (0.0000) 0.8520 (0.0000)

0.0002 (0.9709) 0.0000 (0.2875) 0.0875 (0.5247) 0.0318 (0.7397) 0.0518 (0.6583)

VL Migue´is et al—Productivity change and innovation in Norwegian electricity distribution companies

period analysed. This may follow from a more heterogeneous industry, where some companies are working hard in order to improve, some are able to follow, while others fall behind, not succeeding in improving efficiency. This may be consistent with the EC numbers of Table 4, which show that the average efficiency levels are more or less constant for the two first periods, and then fall from 2006 until 2007. 2007 was the starting year of a new regulation period, changing from a 5-year period (2002–2006) where revenues were determined by a combination of average historical cost (1996–1999), efficiency requirements based on DEA, and annual updates of prices and new activities, to a system with annual updates based on a yardstick formula, as described in Section 2.1. With 5-year regulation periods it has been argued that incentives for cost reductions are weakened when approaching a new regulation period, since actual costs are used as the starting point for the revenue caps for the next period (often called ‘the ratchet effect’). With a weight on actual cost of only 50% for the first years of the new regulation period, the ratchet effect should be less than in previous regulation periods, however, it may still partly explain the regression of the frontier between 2005 and 2006. Table 5 reports the number of companies that improved, declined or kept unchanged productivity levels between 2004 and 2007. Most companies (106 companies) were located in areas of the production possibility set where the frontier shifted to more productive levels. Possibly due to this movement of the frontier, a considerable number of companies (76 companies) experienced a decline in their efficiency level. Overall, the number of companies with a MI greater than one, representing a productivity improvement, is smaller than the number of companies with a MI

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smaller than one, representing productivity decline (59 versus 68). Figures 2, 3 and 4 illustrate the distribution of the values of the MI, EC component and technological change component for all companies, obtained by comparing year 2004 with 2007. Each dot represents one electricity distribution company. The distribution of the MI is approximately symmetric but includes three companies whose level of productivity improvement is very high. The company with the largest MI value, represented by the highlighted dot, has also a very high value of the EC and TC components. This company (Lyse Nett AS) may be considered a benchmark, whose practices should be studied to try to spread them to the other companies. The distribution of the EC and TC are approximately symmetric, but the spread of the EC component is larger than the spread of TC.

Figure 2 Illustrative representation of the Malmquist index distribution between 2004 and 2007.

Table 4 Productivity change of Norwegian electricity distribution companies (2004–2007) Year

Malmquist index

EC

TC

MTC

BTC

2004–2005 2005–2006 2006–2007

1.026 0.992 0.988

1.002 1.005 0.965

1.026 0.988 1.024

1.023 0.985 1.022

1.005 1.006 1.004

2004–2007

1.003

0.969

1.035

1.030

1.009

Figure 3 Illustrative representation of the efficiency change term distribution between 2004 and 2007.

Table 5 Distribution of Malmquist index and sub indexes for efficiency change and technological change Index

o1 =1 41

2004–2007 MI

EC

TC

68

76 13 38

21

59

106

Figure 4 Illustrative representation of the technological change term distribution between 2004 and 2007.

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Table 6 Companies that innovated 2004–2005 Company

2005–2006 Innovation

Askøy Energi AS Drangedal Everk KF Eidefoss AS Energi 1 Follo-Røyken as

1.029 1.066 1.041 1.067

Fortum Distribution AS Fredrikstad Energi Nett AS Fusa Kraftlag Hafslund Nett AS Hallingdal Kraftnett AS Klepp Energi AS

1.065 1.110 1.084 1.140 1.016 1.006

Kvikne-Rennebu Kraftlag AL Lier Everk AS Luster Energiverk AS Lyse Nett AS Meløy Energi AS Nord-Østerdal Kraftlag AL Nord-Salten Kraftlag AL

1.090 1.043 1.026 1.037 1.032 1.015 1.090

Nordvest Nett AS Ørskog Energi AS

1.025 1.003

Røros Elektrisitetsverk AS Sunnfjord Energi AS Trøgstad Elverk AS

1.060 1.014 1.126

Company

2006–2007 Innovation

Company

Innovation

Andøy Energi AS

1.063

1.057 1.007 1.002 1.018

Energi 1 Follo-Røyken as

1.003

Hallingdal Kraftnett AS Klepp Energi AS Krødsherad Everk KF

1.026 1.032 1.153

Hallingdal Kraftnett AS Klepp Energi AS Krødsherad Everk KF

1.034 1.075 1.050

Lyse Nett AS

1.092

Lyse Nett AS

1.113

Nord-Trønd. Elektrisitetsverk

1.023

Røros Elektrisitetsverk AS

1.031

Nord-Salten Kraftlag AL Nord-Trøn. Elektrisitetsverk Nordvest Nett AS Ørskog Energi AS Rauland Kraftforsyningslag Røros Elektrisitetsverk AS

1.055 1.057 1.052 1.047 1.072 1.004

Trøgstad Elverk AS

1.098

Tydal Kommu. Energiverk KF

1.043

Trøgstad Elverk AS Trollfjord Kraft AS Trondheim Energi Nett AS Tydal Kommu. Energiverk KF

1.021 1.044 1.109 1.029

Askøy Energi AS

1.078

Energi 1 Follo-Røyken as Evenes Kraftforsyning AS Fortum Distribution AS Fredrikstad Energi Nett AS

To explore if the companies that increased most their productivity between 2004 and 2007 (ie, the 20 companies with the highest MI for the period 2004–2007) were able to keep a consistent path of improvement over time, we looked at the extreme of the MI distribution for each pair of consecutive years (2004/2005, 2005/2006 and 2006/ 2007). We observed that only one company was consistently in the best performing group in the three consecutive periods. This company is the one highlighted in the Figures 2, 3 and 4, that is, Lyse Nett AS. Similarly, we explored the consistency in the group of the worst performing companies in the period 2004–2007 (ie, the 20 companies with the lowest MI). It was found that none of the companies remained in the worst performing group in all pairs of consecutive years. This suggests that companies are able to change considerably their performance profile over the years, since both the set of best and worst performing companies is different over the years.

4.2 Identification of innovative companies It is interesting to examine that distribution companies are innovating, that is, pushing the production frontier towards more productive areas. In the period considered, a reasonable number of distribution companies

were innovators. These companies are listed in Table 6. The number of innovator companies was 22 between 2004 and 2005, 13 between 2005 and 2006 and 16 between 2006 and 2007. Only six of these companies were part of the innovative group in all years considered. The average innovation score was high between 2004 and 2005 (1.057), decreased between 2005 and 2006 (1.045) and increased between 2006 and 2007 (1.053). In order to promote the diffusion of best practices between the electricity distribution companies, these companies could be monitored and used as benchmarks by other companies to promote continuous improvement in the sector. Next, it was explored if the companies with the largest productivity improvements between consecutive years in each period were the innovators. Between 2004 and 2005 only six of the 20 companies with the highest MI were innovators. In the next periods the number of innovators in the top 20 group was seven. It can be concluded that not all companies with the largest productivity improvements are innovators. Despite improving significantly its productivity, a company may not bring innovation to the industry, as it may originally be located inside the production possibility set, far from the frontier. The company previously emphasized as the most productive in consecutive years is also an innovator in all periods.

VL Migue´is et al—Productivity change and innovation in Norwegian electricity distribution companies

5. Conclusions This paper analyses the productivity change of Norwegian distribution companies using a MI. The analysis involves the estimation of the MI and its components (EC, and magnitude and bias of technological change). The sample studied consists of 127 distribution companies for the years 2004–2007. The model computed incorporates virtual weight restrictions for geography variables, to ensure a reasonable performance evaluation, which limits the importance of the impact of the geography conditions on the estimation of the cost norm. In general, the MI is a tool for assessing productivity change over time, and it can thus be useful for regulators in order to evaluate effects of changes in policy and regulation over time. However, in order to achieve this, the regulator has to collect consistent data on inputs and outputs to be able to make the comparisons needed to calculate the Malmquist indices. In the Norwegian regulation, the model specification and data on inputs and outputs have changed considerably over the years. An interesting question is then how to make comparisons over time when this happens. Should the regulator keep collecting data for the ‘old’ models, or if not, how to compare results for different years if different models are used? In addition to the Malmquist indices and their decomposition, it is interesting to see from the present data set that the variation in the efficiency results increases over time, that is, companies become more different under the same DEA model specification over time. Thus, it is of particular interest both for the regulator and the industry to identify the innovative companies, and to learn from them how to improve. Acknowledgements —The funding of this research through the scholarship SFRH/BD/60970/2009 from the Portuguese Foundation of Science and Technology (FCT) is gratefully acknowledged by the first author.

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Received June 2010; accepted April 2011 after one revision