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Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation: The Case of Norwegian

Electricity Distribution Firms

Subal C. Kumbhakar,a,b Ørjan Mydland,b Andrew Musau,b and Gudbrand Lienb*

abstract

Numerous studies have focused on estimating technical inefficiency in electricity distribution firms. However, most of these studies did not distinguish between persistent and transient technical inefficiency. Furthermore, almost none of the studies estimated the cost of input misallocation arising from non-optimal use of inputs. One reason is that the cost function (input distance function) typically used in the literature does not allow for the separation of technical inefficiency and allocative inefficiency. In this study, we estimate both the persistent and transient components of technical inefficiency and input misallocation of Norwegian elec- tricity distribution firms, using panel data from 2000 to 2016. Our modeling and estimation strategy is to use a system approach, consisting of the production func- tion and the first-order conditions of cost minimization. Input misallocation for each pair of inputs is modeled via the first-order conditions of cost minimization. We also estimate the costs of each component of technical inefficiency and input misallocation by deriving the cost function for a multi-output separable produc- tion technology. Our modeling and estimation strategy handles endogeneity of inputs. Finally, we allow for inclusion of determinants of persistent and transient technical inefficiency. Our results show that the costs of input misallocation of Norwegian electricity distribution firms are non-negligible. Keywords: Cost and production functions, Allocative and technical inefficiency, Determinants of inefficiency, Norwegian electricity distribution firms

https://doi.org/10.5547/01956574.41.3.skum

1. INTRODUCTION

Applications of stochastic frontier analysis (SFA) to study efficiency of firms that generate and/or distribute electricity have overwhelmingly focused on technical inefficiency. The implicit assumption is that all firms are either fully allocatively efficient (i.e., there is no input misallocation (under or overutilization) that results from failure to minimize costs exactly because of some institu- tional, structural, and managerial problems) or their level of allocative inefficiency is negligible and can be ignored. There are only a handful of papers that deal with allocative inefficiency and the cost therefrom. Most studies that use the cost function tend to ignore allocative inefficiency and focus on technical inefficiency. Of these studies, only a handful have decomposed transient (short-term/

a Department of Economics, State University of New York, Binghamton, NY13902-6000, USA. b Inland School of Business and Social Sciences, Inland Norway University of Applied Sciences, Pb 952, NO-2604

mailto:[email protected]

144 / The Energy Journal

time-varying) and persistent (long-term/time-invariant) cost inefficiencies. However, none has esti- mated both technical and allocative inefficiency and costs therefrom, as well as decompose technical inefficiency and its cost into persistent and transient components. The purpose of this paper is to do this using panel data for Norwegian electricity distribution firms.

Electricity distribution firms in Norway have the characteristics of natural monopolies within their service territories. As part of a move towards greater market orientation introduced to the industry during the 1990s, the firms are regulated. The Norwegian regulator, Norwegian Water Resources and Energy Directorate (NVE), uses a benchmarking model to estimate each firm’s tech- nical efficiency score, while ignoring input misallocation. The efficiency scores, which the regulator calculates for each firm, determine sixty per cent of the firms’ revenue cap. From a regulator’s point of view, the focus is to motivate the firms to increase productivity and efficiency without intruding into micro management. However, by ignoring input misallocation in the regulation model, a firm can be found to be fully efficient in the benchmarking model of the regulator, yet in practice, the firm could reduce costs of production by changing its input allocation. This unidentified scope for cost saving could be important to society, consumers of electricity, and the owners of the electricity distribution firms. NVE’s regulation model also does not distinguish between transient and persistent technical efficiency. Again, this might not be a direct problem within the task given to the regulator, but if the goal is to minimize overall (economic) costs, one should distinguish between different sources of inefficiency. The reason is that it is likely that the sources of inefficiency might differ between firms, and disentangling these sources might influence the overall technical inefficiency score. Also ignoring persistent inefficiency, for example, might affect the estimates of the technology.

In this study, we apply panel data that make it possible to disentangle persistent and tran- sient inefficiency. We also investigate input misallocation, which is potentially more serious than technical inefficiency (see Kumbhakar and Wang, 2006a), because the estimated technology param- eters may be inconsistent.1

Previous studies that estimate both technical inefficiency and input misallocation have commonly adopted the dual approach that utilizes the duality between the cost and production func- tions. However, estimation of a cost function with both technical inefficiency and input misalloca- tion is quite complex (Kumbhakar and Tsionas, 2005; Kumbhakar and Wang, 2006b). Estimation of the production function alone cannot accommodate input misallocation. The alternative is to use a primal system that uses the production function and the first-order conditions for cost minimization. Schmidt and Lovell (1979) used this approach, which is flexible enough to incorporate both techni- cal inefficiency and input misallocation, and costs therefrom. However, they used a Cobb–Douglas (CD) production function. Subsequently, Kumbhakar and Tsionas (2005) and Kumbhakar and Wang (2006b) extended their modeling approach and used a translog production function. Although the latter studies used panel data, their model is essentially cross-sectional. Because the computation of the cost of technical and allocative inefficiency is nontrivial under a translog specification, Kumbha- kar and Wang (2006b) concluded that there is no easy solution to the estimation of both components of inefficiency. Some studies have used the production function and the first-order conditions for profit maximization or a profit function and the implied demand system using Hotelling’s lemma to

1. A related concept is relative inefficiency. For example, Dimitropoulos and Yatchew (2017) used this concept in a study of productivity growth of distributors in Ontario, Canada. The difference between a firm’s observed cost in a year and the corresponding predicted cost reflects the inefficiency of a firm relative to the model. However, the concept of relative inefficiency does not account for the potential cost effect of input misallocation. Additionally, it cannot separate the effect of random noise and input misallocation, implying that the difference can be due to several factors which are spelled out in our model.

Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation / 145

estimate the profit loss from each component (see Kumbhakar et al., 2015a and references therein). An advantage of this approach is that it accounts for endogeneity of both inputs and outputs. An- other approach is to study the observed demands to determine whether these are the cost-minimizing demands consistent with observed prices. Alternatively, one can seek to find the set of prices that would make observed demand cost minimizing. In relation to the approaches described above, sev- eral variations have been presented over the years (for more details, see Kumbhakar et al., 2015a, Ch. 8, and Greene, 1993).

To the best of our knowledge, there exists only one recent study on technical inefficiency and input misallocation within the electricity distribution industry. Nemeto and Goto (2006) used a CES cost frontier to study technical inefficiency and input misallocation in the Japanese electricity transmission and distribution industry. Using panel data of Japanese utilities for the period 1981– 1998, they reported that technical inefficiency raises costs by 1–28%, while input misallocation raises costs by 8–30%.

Our approach is an extension of that of Kumbhakar (1988). It involves estimating a pro- duction function frontier together with the first-order conditions of cost minimization. Kumbhakar (1988) introduced a production function that is more general than the Cobb-Douglas technology, which permits elasticity of output to vary across firms, and introduced input misallocation separate from random errors in optimization. In our paper, we consider some extensions of the Kumbhakar (1988) model where we disentangle persistent and transient technical inefficiency and at the same time estimate input misallocation for each pair of variable inputs.2 We also estimate the costs of each of these inefficiency components. Furthermore, our model allows for multiple inputs and outputs, handles endogeneity of inputs and includes the determinants of persistent and transient technical in- efficiency. We add panel data features to both the production function and the first-order conditions of cost minimization, which has not been done previously.

Our study has two main contributions. First, we extend the sparse literature on modeling both technical inefficiency and input misallocation in electricity distribution industries. Second, we extend the modeling and estimation approach by including additional inefficiency components decomposed into persistent and time-varying elements, including inefficiency determinants for both components, and incorporating panel data features to the modeling framework. The data set used contains infor- mation on Norwegian electricity distribution firms, observed over the years 2000 to 2016.

The remainder of the paper is organized as follows. The model specification and estimation method are described in Section 2. Section 3 describes the data, and Section 4 presents the results. Eventually, Section 5 presents a summary of the main results and offers some concluding remarks.

2. MODEL SPECIFICATION AND ESTIMATION METHOD

2.1 The model

We consider the production function used in Kumbhakar (1988) extended to accommodate a generalized error specification3

2. Studies that have examined the efficiency of Norwegian electricity distribution firms include Førsund and Kittelsen (1998), Salvanes and Tjøtta (1994), Førsund and Hjalmarsson (2004), Miguéis et al. (2011), Kumbhakar et al. (2015b), Kumbhakar and Lien. (2017), Orea et al. (2018) and Mydland et al. (2018). However, it should be noted that none of these studies considered input misallocation, the focus of our study. Additionally, except for Kumbhakar and Lien, none of the studies separated technical inefficiency into time-invariant and time-varying components.

3. The functional form used in (1) makes it possible to derive an explicit form of the cost function, and therefore separate costs of technical and allocative inefficiency. Note that the function is not only separable but the input function (the right-

146 / The Energy Journal

( ) 0 0 1

αα − − + =

  =  

  ∏ j i it it

J u u v

it jit j

F Y X e (1)

where itY is output vector for firm i and time t ( )1, , ; 1, , = = i N t T , jX are inputs ( 1, , ),= j J and 0α and jα are the parameters to be estimated.4 itv is the noise term that captures exogenous shocks

unknown to the producer, 0 iu is persistent inefficiency and itu is transient inefficiency. 5 We extend

the model to incorporate a multiple-output separable production technology. Assuming a flexible functional form of F(Yit), viz.,

( ) 1 2 2 3 1 2 1

β β= + +it it it it itlnF Y lnY lnY lnY lnY (2)

and substituting (2) into the log form of (1), we can rewrite (1) as

1 2 2 3 1 2 0 0 1

1 .

2 β β α α

+ + = + − − +∑ J

it it it it j jit i it it j

lnY lnY lnY lnY ln lnX u u v (3)

If inputs are exogenous, direct estimation of the production function parameters is possible by the maximum likelihood method using distributional assumptions on the inefficiency and noise components when there is a single output. However, for regulated industries such as the electricity distribution firms that we consider, outputs are treated as exogenous, and inputs are endogenous.6 In this case, estimating (3) will result in inconsistent parameter estimates, even if there is a single output. If outputs are exogenous (i.e., not choice variables), maximization of profit is the same as minimization of cost. Since the electricity distribution industry is a service industry and conse- quently outputs are exogenously determined, it is standard practice to estimate the technology using the dual cost function. One can then use the duality results to derive the underlying features of the production function. For the production function in (1), one can derive the cost function analytically. That is, from the parameters of the cost function, we can derive the parameters of the production function, and vice versa.

From microeconomic theory, the firm is said to be allocatively efficient (no input misallo- cation) if it equates the marginal rate of technical substitution between each pair of inputs with the ratio of input prices. We therefore model input misallocation as

1 1

2, , η  

= =   



jit jit

X jit ji

X it

MP w k e j J

MP w (4)

where the factors of proportionality jik are firm and input specific, η jit are random errors in cost minimization,

jitX MP are the marginal products of jitX , and jitw are the input prices. Apart from input

misallocation that arises from a non-optimal mix of inputs, the equation underlines the fact that some inefficiency may also arise from uncontrolled random exogenous shocks; e.g., uncertainty

hand side of (1)) is also Cobb-Doulas (CD), which helps us to go back and forth from the production function in (1) to the cost function in (5). That is, the cost function in (5) has the exact same parameters as the production function in (1). The output function (left-hand side of (1)) can be CD or translog or some other form.

4. This is referred to as the generalized production function and was introduced by Zellner and Revankar (1969). 5. One of our models considers an extension of this by including random firm-effects. In doing so we separate persistent

inefficiency from firm-effects. 6. For example, the output of Norwegian electricity distribution companies is determined by their customers. This means

that there is no point for the companies to increase their amount of distribution services if the customers do not demand such an increase.

Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation / 147

in input and output prices, quality of inputs, etc. Solving jitX from equations (3) and (4) yields the input demand functions (see Appendix A3) that can be used to derive the cost function, which is

lnC r ln ln lnY lnY lnYit j

J j j it it it� � �� 1 1 1

2 0 1 1 2 2 3 1

� � � �

� � �

llnY it2 � � �

� � ��

1 1 1

1 2

2 �

� � � �

� � �

�

j jit j

J j

j jit iln w ln e u jit

� �

�

� � � �� [ )] 00 1�� u vit it�

� � ��1 � v Eit it

(5)

where

( ) ( )1 1 2 2 2

1 / .η ηα α α α α

γ −

= = =

   = + + − +    ∑ ∑ ∑

jit jit J

J J it j ji j ji jj j

E ln k e ln k ln e (6)

Since the derivation of the cost function uses the first-order conditions of cost minimization, the resulting cost function depends on input misallocation, and persistent and transient technical in- efficiency. More specifically, Equation 5 shows explicitly that any kind of inefficiency leads to an increase in cost because of input misallocation, as well as persistent and transient technical ineffi- ciency. The cost of technical inefficiency is given by ( )0

1 γ

+i itu u , whereas the cost of input misallo- cation is given by (6), which is equal to zero if 1=jik . The cost function also depends on the noise term in the production function itv and random errors in cost minimization η jit. The 4

th and 5th terms in the cost function (combined) exhibit the effect of η jit on cost. Once the relevant parameters are estimated, the increase in cost due to input misallocation, and to persistent and transient technical inefficiency, can be computed for each firm.

2.2 Estimation

Equation (3) can be rewritten as an input distance function (Appendix A1)

1 0 1 1 2 2 3 1 2 2 1

*δ δ µ µ µ =

  ≡ + + + + + 

  ∑

J jit

it j it it it it it j it

X lnX ln lnY lnY lnY lnY

X  (7)

where * * * = + +it io it itu u v , * * * 0 0

1 1 1 , ,

γ γ γ = = =i i it it it itu u u u v v and

1 γ

µ = . From this specification, we

can compute 1

α δ γ µ

= − ⋅ = − jj j for 1

2 21

1 2, , , 1α γ α δ

µ= =

  = … = − = + 

  ∑ ∑

J J

j j j j

j J , and 1

γ α =

= ∑ J

j j

. Es-

timation of (7) using stochastic frontier approach gives all the parameters as well as predictions of * 0iu and

* itu . To estimate cost of input misallocation the FOCs for cost minimization (equation 4) is

expressed as (see Appendix A2)

1 1 γ θ η  ⋅

≡ + +  ⋅ 

it it j ji jit

jit jit

x w ln

x w (8)

where 1 ln α

γ α

  =   

  j

for 2, ,= …j J is estimated from (7). Denote 1 1 δ  ⋅

=   ⋅ 

it it jit

jit jit

x w ln ln

x w (which is

obtained from the data) and 1

1 δ δ

= ∑ T

ji jit t

ln ln T

. The parameter lnθ =ji jik can then be calculated

148 / The Energy Journal

from ˆ ˆ θ δ γ= −ji ji jln . Since lnθ =ji jik , we can estimate jik from { }xˆ e p θ̂=ji jik . This allows us to

estimate ˆˆln η δ γ θ= − −jit jit j ji. We can therefore substitute the estimates of α j, jik and η jit into (6) to calculate the cost of input misallocation. The cost of technical inefficiency, as defined earlier, is the

sum of persistent inefficiency ( *0iu ) and transient inefficiency ( * )itu . Note that, in (8), we find that

jit it

x x

are functions of input price ratios and input misallocation. Thus, 1

= jitjit it

x x

x in (7) is exogenous if

input misallocation is independent of itu and itv . It can be seen from (8) that  jitln x depends on .η jit Thus, if η jit is independent of the error terms in (7), we can estimate (7) without any endogeneity problems so long as outputs are exogenous. However, estimation of (7) will not help us to estimate the cost of input misallocation, which also requires estimation of (8).

In our study, we define the composite error term εit in (7) across four different model spec- ifications. The numeraire input ( )1X in all the models is capital. Model 1 has no persistent ineffi- ciency and does not include any panel data features. We assume a normal distribution for the noise term ( )itv and half-normal distribution for the efficiency term ( )itu . In Model 2 we assume ib are fixed firm-effects and not a part of inefficiency. The only inefficiency is itu which can have some de- terminants (“true fixed-effects” (TFE) model with determinants for inefficiency). Model 3 assumes

ib are random firm-effects and is known as “true random-effects” (TRE) model with determinants for inefficiency (Greene, 2006a, 2006b). Model 4 has random firm-effects ( )ib , persistent technical inefficiency ( 0 )iu and is a generalization of the TRE (GTRE) model. We allow determinants of in- efficiency in both the persistent and time-varying components (Badunenko and Kumbhakar, 2017; Lai and Kumbhakar, 2018; Lien et al., 2018). The model specifications are summarized in Table 1.

Table 1: Econometric specification of stochastic frontier models Model 1 Model 2 Model 3 Model 4

εit εit = uit + vit εit = bi + uit + vit εit = bi + uit + vit εit = bi + ui0 + uit + vit Firm effect bi ~ fixed parameter bi ~ iidN(0,σ 2b ) bi ~ iidN(0,σ 2b )

Noise vit ~ iidN(0,σ 2v ) vit ~ iidN(0,σ 2v ) vit ~ iidN(0,σ 2v ) vit ~ iidN(0,σ 2v )

Transient inefficiency

uit ~ iidN +(0,σ 2u ) uit ~ iidN +(0,σ 2u (zit)) = N +(0,exp(θu0 + θ ′uit zit))

uit ~ iidN +(0,σ 2u (zit)) = N +(0,exp(θu0 + θ ′uit zit))

Persistent inefficiency

ui0 ~ iidN +(0,σ 2u (zi)) = N +(0,exp(ϑu0 + ϑ ′ui zi))

Main reference(s) Kumbhakar (1988) Greene (2006a, b) Greene (2006a, b) Badunenko and Kumbhakar (2017), Lai and Kumbhakar (2018), Lien et al. (2018)

Details on the estimation issues can be found in the relevant papers (main references) cited in Table 1. Model 1 corresponds to the specification in Kumbhakar (1988), and we include this as a benchmark in our study. This model is the most restrictive and it does not account for the panel structure of the data. Models 2 and 3 are panel data models that separate firm heterogeneity from transient inefficiency but do not include persistent inefficiency. In the former model, firm heteroge- neity is treated as a fixed effect whereas in the latter, it is treated as a random effect. Model 4 is a gen- eralized version of the TRE (Model 3). It decomposes the error term into four components, where the first captures random firm heterogeneity; the second, persistent inefficiency; the third, transient inefficiency; and the final term random shocks. Models 2 and 3 allow for determinants of transient inefficiency, whereas Model 4, in addition, allows for determinants of persistent inefficiency.

Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation / 149

Models 1 and 2 are estimated by standard one-step maximum likelihood techniques. Model 3 is estimated using a simulation-based one-step maximum likelihood method (Filippini and Greene, 2016). Estimation of Model 4 can be done in several ways. One is the single-step full maximum likelihood procedure, first proposed in Colombi et al. (2014), and extended in Badunenko and Kumbhakar (2017) and Lai and Kumbhakar (2018) to allow for heteroscedasticity in the error components. The main drawback with the single-step procedure is that it is quite complex because distribution assumptions are needed for all the error components. In this study, we estimated Model 4 using a multi-step procedure introduced by Lien et al. (2018), which is a modified version of the procedure of Kumbhakar et al. (2014) where the inefficiency components are not necessarily inde- pendently and identically distributed (iid), but their means/variances are functions of exogenous determinants. The advantage of the multi-step procedure is that the coefficients of the production function in the first-step are not affected by distributional assumptions about the error components. This implication simplifies matters if the aim is to obtain consistent estimates of the technology parameters, as is the case in our modeling framework. Distributional assumptions are, however, necessary to predict absolute measures of persistent and transient inefficiency. All four models are estimated using the statistical package Stata.

While we use a parametric approach to estimate equation (7) in this study, it should be noted that, at least in principle, both nonparametric and semiparametric approaches can be used, especially if there are no technical and allocative inefficiency (as in Yatchew (2003) and Henderson and Parmeter (2015)). However, our model is more complicated and we need to estimate not only the input distance function (which is dual to the cost function) but also the FOCs of cost minimi- zation which are intimately linked to the cost function. This link can be easily established with parametric functions.7 Even without input misallocation, a single step nonparametric estimation procedure cannot separate persistent and transient technical inefficiency and accommodate deter- minants for these components. Kumbhakar et al. (2019) is the only study that estimates persistent and transient technical inefficiency with determinants (Model 4) using a semiparametric approach.8

3. DATA

The data used in this study are an unbalanced panel of 146 Norwegian electricity distri- bution firms for the years 2000 to 2016, compiled by the Norwegian Water Resources and Energy Directorate (NVE). The data include economic and technical information on the firms. We used 2143 firm-years in total.

We used three inputs and two outputs. The inputs are capital, labor and operational costs, and the outputs are the total number of customers and the size of the network, defined as the length of the high-voltage power lines in kilometers. We defined capital as the aggregate book value of all assets owned by the firm, labor as number of man-years, and operational costs as total cost minus capital cost, labor cost and value of lost load.9 We used the regulatory rate of return as the input price of capital. This rate is calculated annually by NVE using the weighted average cost of capital method (Amundsveen and Kvile, 2016). Averch and Johnson (1962), however, criticized the use of

7. To our knowledge, there are no nonparametric papers that structurally link the cost function with the cost share equa- tions.

8. For more details and discussions about estimation of nonparametric/semiparametric cost/production functions, refer to Yatchew (2003), Henderson and Parmeter (2015) and Sickles and Zelenyuk (2019).

9. We subtract labor cost from operational cost because this is included as an input variable in our analysis. Similarly, the value of lost load is subtracted from operational cost because we include this as a determinant of transient inefficiency.

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the regulatory rate of return as the input price of capital, noting that it may substantially deviate from the true opportunity cost of capital in the market. This critique is of a lesser concern in our study because the regulatory rate in Norway (NVE-rent) is annually determined by an expert committee, specifically tasked to identify a rate that reflects the true opportunity cost of capital. The price of labor is a year- and county-specific variable calculated by the regulatory agency as the annual aver- age cost per man-year (yearly and county average for the firms in the survey). The price of labor is measured in 2015 Norwegian kroner (NOK).10 Finally, we used the consumer price index compiled by Statistics Norway as the price index for operational costs.

We include two environmental variables in the analysis, one as a determinant of transient inefficiency and the other as a determinant of persistent inefficiency. NVE uses several environmen- tal variables in its regulation model, and these are intended to account for heterogeneity in the firms’ production environments. In this study, we used the proportion of underground cables as a determi- nant of persistent inefficiency, and the value of lost load per kilometer of network as a determinant of transient inefficiency. The value of lost load (or electricity not supplied) is the amount in Norwegian kroner (NOK) the electricity distribution companies must pay for disruptions in the service.11 As the value of lost load also varies with firm size, we divided it by the firms’ kilometers of network to get a standardized measure.

Firms with fewer than two consecutive years of observations are dropped from the analysis because this is a requirement for panel data models that exploit the within variation in the data. Ta- ble 2 presents descriptive statistics of the inputs, input prices, outputs and environmental variables. Region-specific descriptive statistics are in Appendix, Table A1.

Table 2: Descriptive statistics (N=2143, Year 2000–2016) Variable Name Mean SD Min Max

Input Capital (book-value, 1000 NOK) X1 265,290 570,248 1,605 6,873,112 Man-years (numbers) X2 31.1 48.9 0.6 396.3 Operational costs (1000 NOK) X3 24,957 65,173 168 901,652

Price of input Price of capital W1 0.072 0.016 0.042 0.100 Price of labor (per man-year, 1000 NOK) W2 600 107 341 939 Price of operational costs (CPI) W3 1.145 0.103 0.965 1.325

Output Number of customers Y1 20,176 54,751 4 696,540 Network (Km) Y2 727 1,252 5 11,866

Environmental (Z) transient variable Value of lost load per km of network (1000 NOK) Z1 2.70 2.92 0.000 31.32 Environmental (Z) persistent variable Proportion of underground cables Z2 0.318 0.204 0.000 1.000

4. RESULTS

Table 3 presents estimates of the input elasticities. Although the estimates exhibit some variation depending on the model, we observe that, across all models, the elasticity of capital is the largest of the three, ranging from 0.67 to 0.85. This is followed by the elasticity of labor (man-

10. 1 USD = 8.14 NOK, 1 EUR = 9.50 NOK as at 25 June 2018. 11. The value of lost load is calculated as lost load times a unit price, with different unit prices for various customer

groups (Bjørndal et al., 2010).

Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation / 151

years), and finally the elasticity of operational costs, ranging from 0.56 to 0.64, and 0.43 to 0.53, respectively.

Table 3: Input elasticities Input elasticities Model 1 Model 2 Model 3 Model 4

Capital 0.847 0.672 0.676 0.788 Man-years 0.563 0.638 0.642 0.636 Operational costs 0.533 0.442 0.428 0.460

Table 4 presents the estimates of transient, persistent and overall technical efficiency across all four models outlined in Table 1. The mean transient (same as overall) technical efficiency for Model 1 is 0.76. Because this model does not account for unobserved firm heterogeneity, we expect it to overestimate the level of inefficiency relative to the other models, and this is what we observe. The mean transient technical efficiency for Model 3 is 0.93, a value slightly higher than that found by Kumbhakar and Lien (2017) in their study of Norwegian electricity distribution firms using the same model but over a shorter time frame (2000–2013). However, transient efficiency in Model 4 is 0.92, which is higher compared with that found by Kumbhakar and Lien, who also use the same model but did not include determinants of inefficiency. Persistent inefficiency, on the other hand, is virtually the same in both studies. The mean transient efficiency in the TFE model (Model 2) is 0.85, which is within the range of values found by Kumbhakar et al. (2015b), who used Norwegian data for the period 1998 to 2010 and used the same estimator. In that study, technical efficiency scores range from 0.82 to 0.87. Filippini et al. (2018), using data for electricity distribution firms in New Zealand for the years 2000 to 2011, found mean transient efficiency varying between 0.70 to 0.88, depending on the model, whereas persistent efficiency varied from 0.88 to 0.94.

Models 2 through 4 in Table 4 show that the value of lost load per kilometer of network in- creases the variance of transient inefficiency (illustrated by the positive θ coefficient), which implies increased inefficiency (or decreased efficiency). Similarly, in terms of persistent inefficiency, we observe that higher proportions of underground cables increase inefficiency from Model 4. Figure 1 graphically exhibits the marginal effects of value of lost load per kilometer of network on transient inefficiency, as well as the marginal effects of the proportion of underground cables on persistent inefficiency, showing a positive association that is increasing in both cases. The value of lost load represents a cost to the distribution companies resulting from disruption in the service. High rates of disruption, more likely due to lack of maintenance, represent higher costs to the companies and thus will have a negative impact on the efficiency scores.

Generally, we would expect that firms that invest in newer network infrastructure will also have higher efficiency. However, it is possible that firms with a high proportion of underground cables operate in an environment that makes this type of network necessary. If so, it is not the underground cables that increase persistent inefficiency but rather the environment. A more direct explanation of the positive marginal effect of the proportion of underground cables on persistent inefficiency is that it is more difficult and more costly to do maintenance and repairs on these cables compared to other distribution infrastructure. Kuosmanen (2012), for example, replicates this result for Finnish electricity distribution firms, observing that the proportion of underground cables has a positive and highly significant effect on the total cost.

The estimates of input misallocation, where capital is used as the numeraire, are shown in Table 5. k2 and k3 respectively indicate whether the capital/labor and capital/operational costs ratios deviate from unity (or the optimal proportion). Our findings show that the capital/labor ratio is on average less than one, indicating excessive use of labor relative to capital. Figure A1 in the Appen-

152 / The Energy Journal

dix exhibits the distribution of labor costs across regions in Norway, showing that inter-regional differences exist. For example, a comparison between the Northern region and Oslo reveals that the price of labor is higher in the latter. This could partly explain the excessive use of labor relative to capital. However, since we regard input prices as exogenous, the observed differences are not surprising and stem from differences in both living costs and taxes on labor across the regions. The estimation results show large variations both between and within the specified models. For example, in Model 4, we observe that more than 15% of the firms have a k2 value greater than 1, indicating over-capitalization for these firms. The capital/operational costs ratios, however, show excessive use of operational costs relative to capital. This ratio is less than unity for firms at the 95th percentile across all models, illustrating the robustness of the mean values.

Table 4: Estimates of technical efficiency and determinants of technical inefficiency Statistics Model 1 Model 2 Model 3 Model 4

Transient technical efficiency Mean 0.757 0.850 0.933 0.921 SD 0.121 0.082 0.083 0.027 P5 0.563 0.687 0.760 0.872 P95 0.913 0.943 0.982 0.953

Persistent technical efficiency Mean 0.949 SD 0.065 P5 0.868 P95 0.981

Overall technical efficiency Mean 0.757 0.850 0.933 0.874 SD 0.121 0.082 0.083 0.065 P5 0.563 0.687 0.760 0.768 P95 0.913 0.943 0.982 0.928

Determinants of transient technical inefficiency Value of lost load per km network 0.073*** 0.090*** 0.126***

Determinants of persistent technical inefficiency Proportion of underground cables 7.177*

* Significant at p > 0.10, ** Significant at p > 0.05, *** Significant at p > 0.01.

Figure 1: Scatterplot of marginal effects of value of lost load and proportion of underground cables on expected value of inefficiency, based on Model 4.

The left plot shows marginal effects of value of lost load per km network on transient inefficiency. The right plot shows marginal effects of proportion of underground cables on persistent inefficiency

Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation / 153

Our finding that increased capital investments are required in the electricity distribution industry is not surprising. In an evaluation report commissioned by the Norwegian Ministry of Energy and Oil, Reiten et al. (2014) clearly stressed the need for such investments in the electricity distribution sector in the next few decades.

Table 5: Estimates of input misallocation of labor and operational costs Misallocation in labor (k2) Misallocation in operational costs (k3)

Statistics Model 1 Model 2 Model 3 Model 4 Model 1 Model 2 Model 3 Model 4

Mean 0.644 0.921 0.922 0.783 0.484 0.506 0.487 0.449 SD 0.417 0.597 0.597 0.507 0.206 0.216 0.208 0.191 P5 0.304 0.436 0.436 0.370 0.227 0.237 0.228 0.210 P95 1.730 2.480 2.480 2.110 0.811 0.848 0.817 0.752

As described in the model description, input misallocation increases cost. Therefore, it is interesting to examine by how much. Table 6 presents estimates of the overall cost of inefficiency, which is decomposed into technical and input misallocation costs. Apart from highlighting that there are substantial costs arising from technical inefficiency, the findings show that input misallocation also poses a significant challenge to the industry. Eliminating technical inefficiency can reduce costs by between 6.8% (Model 3) and 24.3% (Model 1), while for input misallocation, the correspond- ing cost reductions are between 9.4% (Model 2) and 10.9% (Model 4). From Model 4, we observe that the cost of input misallocation is larger than the cost of technical inefficiency for 28% of the observations in the sample, implying that for more than a quarter of all firms, input misallocation is the main cost challenge. Nemeto and Goto (2006) found that, for Japanese electricity transmission and distribution firms observed over the period 1981 to1998, technical inefficiency increased cost by between 1% and 20%, whereas for input misallocation, the increase was between 8% and 30%.12 As is evident from the lower part of Table 6, when input misallocation is taken into account, the overall cost of inefficiency is significant for the sample of firms, ranging from 16.6% (Model 3) to 34.9% (Model 1).

Table 6: Estimates of cost inefficiency Model 1 Model 2 Model 3 Model 4

Estimates of cost of technical inefficiency Mean 0.243 0.150 0.068 0.142 SD 0.121 0.082 0.083 0.103 P5 0.087 0.057 0.018 0.076 P95 0.437 0.313 0.240 0.272

Estimates of cost of input misallocation Mean 0.106 0.094 0.099 0.109 SD 0.090 0.105 0.108 0.103 P5 0.007 0.000 0.001 0.009 P95 0.290 0.316 0.328 0.327

Estimates of overall cost of inefficiency Mean 0.349 0.244 0.167 0.251 SD 0.149 0.130 0.155 0.156 P5 0.168 0.088 0.032 0.110 P95 0.558 0.490 0.495 0.501

12. Our findings that both technical inefficiency and input misallocation contribute to the overall cost inefficiency is con- sistent with a similar study (using a different framework) by Brissimis et al. (2010) examining the European banking industry.

154 / The Energy Journal

5. SUMMARY AND CONCLUDING REMARKS

In this study, we have estimated persistent and transient technical inefficiency and input misallocation using a panel of Norwegian electricity distribution firms for the years 2000 to 2016. Our modeling and empirical strategy was to formulate a primal system consisting of the production function and the first-order conditions of cost minimization. We estimated the costs of technical inefficiency and input misallocation by deriving the cost function for a multi-output separable pro- duction technology, extending the model in Kumbhakar (1988).

The results show that there exist non-negligible costs of input misallocation for Norwegian electricity distribution firms and call into question a commonly imposed modeling assumption that all firms are fully allocatively efficient. Even if we assumed that all firms are technically efficient, the costs to the industry arising from input misallocation would be high, ranging on average from 9.4% to 10.9% in our analysis.13 The robustness of these estimates across the different model spec- ifications emphasize the importance of estimating input misallocation in general, and for electricity production and distribution firms in particular, where the practice has been to focus on technical efficiency.

Beyond the modeling aspects, our results may also have important implications for regu- lators of electricity generation and distribution firms across the world. The priority so far has been to identify the best method for estimating technical efficiency for benchmarking; see, e.g., Bogetoft and Otto (2011). The question that this study poses is: given that the goal of regulation is cost mini- mization, isn’t it imperative that allocative efficiency should also be included in the benchmarking? Here, we argue that the cost of input misallocation needs to be explicitly considered.

The results from the generalized true random effects model show evidence of persistent inefficiency. Filippini et al. (2018) argued that regulators may fail to set optimal efficiency targets if they are unable to identify systematic shortfalls in managerial capabilities that generate persistent inefficiency and to distinguish these from non-systematic management problems in the short run. For firms, however, investment decisions could be delayed and incentives for innovation weakened. Therefore, in line with Kumbhakar and Lien (2017), our findings further emphasize that future effi- ciency studies need to disentangle persistent and transient technical inefficiency.

ACKNOWLEDGEMENTS

The project is funded by Norwegian Water Resources and Energy Directorate, Energy Nor- way and six electric utilities in Norway (BKK Nett, Eidsiva Nett, Hafslund Nett, Helgeland Kraft, Lyse Elnett and Skagerak Nett). The authors are grateful to three anonymous referees who provided extensive and thoughtful comments.

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APPENDIX

A1. Derivation of Equation 7

By taking the log of equation 1, we have

( ) 0 0 1

ln .α α =

= + − − +∑ J

it j jit i it it j

F Y ln lnX u u v (A11)

Inserting equation 2 into the left-hand side of equation A11 yields

1 2 2 3 1 2 0 0 1

2 β β α α

+ + ⋅ = + − − +∑ J

it it it it j jit i it it j

lnY lnY lnY lnY ln lnX u u v

which can be rewritten as

0 1 1 1 2 2 2

α α α β =

+ = − + +∑ J

it j jit it it j

ln lnX lnX lnY lnY

3 1 2 0 1

. 2 β+ ⋅ + + −it it i it itlnY lnY u u v (A12)

By adding and subtracting 1 2

α = ∑

j it j

lnX to the right-hand side of Equation A12, we can restate the equation as

https://econpapers.repec.org/article/ouprestud/

Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation / 157

0 1 1 1 2 2 3 1 2 2

2 α α α β β

+ = − + + + ⋅∑ J

it j jit it it it it j

ln lnX lnX lnY lnY lnY lnY

0 1 1 2 2

.α α = =

  + + − + − 

  ∑ ∑

J J

i it it j it j it j j

u u v lnX lnX

Taking 1 2

α =

−∑ J

j it j

lnX to the left-hand side and simplifying, noting that ( )ln ln /− =lnx y x y , we have

0 1 1 1 2 1

α α α = =

    + = − +   

   ∑ ∑

J J jit

it j j it j j it

lnX ln lnX lnY

lnX

2 2 3 1 2 0 1

. 2

β β+ + ⋅ + + −it it it i it itlnY lnY lnY u u v (A13)

Finally, expressing equation A13 in terms of 1itlnX yields equation 7.

A2. Derivation of Equation 8

The marginal product of input 1 itX is given by

( ) ( ) 0 1

0 1

1 1

αα +− − =

 ∂∂   = = ∂ ∂

∏ i it vj it it

J u u jitjit

X it it

X eF Y MP

X X

1 01

0 1 21

. α

αα α +− − =

  =  

  ∏ i it vj it

J u uit

jit jit

X X e

X (A21)

The marginal product of jitX is similarly defined by changing the subscripts 1 in the ex- pression in equation A21 to j and amending the product within the parenthesis to include all terms except the thj . Inserting these marginal products into equation 4 and cancelling out the common terms yields

1 1

2, , η α α

  = = = 

  

jit jit

X j it jit ji

X jit it

MP X w k e j J

MP X w

which can be rearranged to

1 1 1 .η α α

  =   

 

jitit it ji

jit jit j

X w k e

X w (A22)

Taking the log of equation A22 results in the expression in equation 8.

A3. Derivation of the input demand functions

Equation A22 equates the marginal rate of technical substitution between inputs jitX and 1itX to the slope of the isocost line, which is the ratio of the input prices; that is ( )1/jit itw w . We can

solve for 1itX in the equation to obtain the expansion path, which represents all combinations of inputs that are cost minimizing.

1 1

ηα α

  =   

 

jitjit jit it ji

j it

X w X k e

w (A31)

158 / The Energy Journal

Substituting equation A31 into the input distance function in equation 7 (i.e., substituting the expression for 1itX ) and solving for jitX yields the following log efficient input demand functions

δ γ=

  = + − 

  ∑

J j

jit j ij jit j

lnX a lnk 1 2 2 3 1 2 1 1

β β γ  

+ + + ⋅   

it it it itlnY lnY lnY lnY

1 1

α γ=

   +   

    ∑

J j jit

j it

w ln

w ( ) ( )0

1 /α γ δ η

γ= + − + + −∑

j ij jit i it it j

u u v (A32)

where

0 1 1

1 , , andα α α α γ α

γ = =

  = − + = 

  ∑ ∑

J J

j j j j j j j

a ln ln ln

1, 2, , which are intimately linked to the cost function . 0 ,

δ =

= = 

ij

if j i j J

otherwise

Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation / 159

Table A1: Descriptive statistics for regions Variable Mean SD Mean SD

Capital (book-value, 1000 NOK) 263152 486443 4846125 995613 Man-years (numbers) 30.9 50.6 128.0 58.2 Operational costs (1000 NOK) 20587 40278 688281 125375 Price of capital 0.07 0.02 0.07 0.01 Price of labor (per man-year, 1000 NOK) 599 93 804 57 Price of operational costs (CPI) 1.14 0.10 1.10 0.08 Number of customers 18115 34816 574522 67363 Network (km) 693 1143 9178 1451 Proportion of underground cables 0.34 0.19 0.74 0.02 Value of lost load per km of network (1000 NOK) 2.45 2.57 5.44 1.10

Capital (book-value, 1000 NOK) 197109 352988 2301409 650762 Man-years (numbers) 26.0 36.5 94.8 24.6 Operational costs (1000 NOK) 17833 36498 204621 32371 Price of capital 0.07 0.02 0.07 0.02 Price of labor (per man-year, 1000 NOK) 578 103 732 100 Price of operational costs (CPI) 1.15 0.10 1.13 0.10 Number of customers 13761 27848 171167 15307 Network (km) 700 1220 5511 183 Proportion of underground cables 0.21 0.11 0.24 0.03 Value of lost load per km of network (1000 NOK) 2.04 2.01 5.73 3.50

Capital (book-value, 1000 NOK) 180349 242003 182824 360976 Man-years (numbers) 30.4 36.6 30.1 55.5 Operational costs (1000 NOK) 18034 23727 15193 29207 Price of capital 0.07 0.02 0.07 0.02 Price of labor (per man-year, 1000 NOK) 544 92 615 98 Price of operational costs (CPI) 1.14 0.10 1.14 0.10 Number of customers 11438 15438 12505 28059 Network (km) 744 887 478 778 Proportion of underground cables 0.19 0.11 0.35 0.18 Value of lost load per km of network (1000 NOK) 2.96 3.01 2.91 3.20

Eastern-Norway (N = 621) Oslo (N = 13)

Mid-Norway (N = 202) Southern-Norway (N = 16)

Northern-Norway (N = 390) Western Norway (N = 718)

160 / The Energy Journal

Figure A1: Histogram of labor price by region

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