Measurement of productive efficiency with frontier methods: A case study for wind farms

This agrees with what was pointed out in the pooled DEA application, where we did not observe time trends in the efﬁciency indexes of each farm... higher t -ratio of the unitary surface.[r]

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Measurement of productive efﬁciency with frontier methods: A case study for wind farms

Guillermo Iglesias⁎, Pablo Castellanos, Amparo Seijas

Facultad de Ciencias Económicas y Empresariales, Departamento de Economía Aplicada I, Universidad de A Cora, Campus de Elviña s/n, 15071 A Coruña, Spain

a b s t r a c t a r t i c l e i n f o

Article history: Received May 2009

Received in revised form March 2010 Accepted 10 March 2010

Available online 16 March 2010 JEL classiﬁcation:

Q4 D241 Keywords: Efﬁciency Wind farm DEA SFA

In this paper, we measure the productive efficiency of a group of wind farms during the period 2001–2004 using the frontier methods Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) Taking an extensive definition of the productive process of wind electricity as our starting point, we obtain results which allow us to identify, on the one hand, an essentiallyex anteefficiency measure and, on the other hand, aspects of relevance for wind farm development companies (developers), technology suppliers and operators in terms of their economic impact These results may also be of interest for regulators and other stakeholders in the sector Furthermore, we discuss the implications of the simultaneous use of DEA and SFA methodologies

1 Introduction

Renewable energies are playing an increasingly relevant role in the electricity sector This is attributable to a number of causes, but particularly the quest for sustainable development and the political desire to achieve this through the promotion of these energy sources (Najam and Cleveland, 2003) Spain is a country that clearly reﬂects this situation, being especially noteworthy the advance of wind energy in the electricity sector Indeed, by the end of 2007, the installed capacity stood at 15,145 MW, ranking it third in the world, only behind Germany and U.S.A (EurObserv'ER, 2008) In terms of its growing importance for the electricity supply, it can be pointed out that in 2007 10% of Spain's total electricity demand was covered by wind power, compared with just 3% in 2001 (CNE, 2008).1

In this context, our research reﬂects the interest that the study of productive efﬁciency has raised from the seminal contribution of

Farrell (1957), transferring it to an evaluation of the productive efﬁciency of wind electricity generation units.2Using data obtained

from a group of Spanish wind farms located in the region of Galicia3 over the period 2001–2004, we have applied DEA and SFA frontier methodologies in order to obtain efﬁciency scores which can provide information of use to those agents involved in the development of this sector A further objective is the appraisal of both methodologies, taking into account the similarities and differences detected from the results obtained

This paper begins with a section dedicated to a general review of DEA and SFA methodologies, and a summary of their principal advantages and inconveniences regarding the possibility of their combined use We then carry out a brief survey of DEA and SFA studies in theﬁeld of electricity generation that provides an outline for the concept of technical efﬁciency in this sector, through the relationship among output obtained—electricity —and inputs used—capital, labour and fuel

In the empirical section of the paper, we begin by identifying the relevant decisions and factors that affect the productive results of the wind farms, both those prior to start-up (ex ante) and those linked to the operating phase (ex post) Taking this into account, we adapt the theoretical framework to the case of wind energy for electricity generation, establishing the output and inputs, together with the data used to deﬁne them Next, we apply the DEA and SFA models, showing

⁎Corresponding author

E-mail addresses:gwig@udc.es(G Iglesias),pcg@udc.es(P Castellanos), asdeai@udc.es(A Seijas)

1

Spanish National Energy Commission

We could adopt other approaches of considerable interest in this sector For example,Forsund et al (2008) and Zubi et al (2009) study the effects of the incorporation of wind energy into the electric system as a whole

3

Galicia is one of the pioneering autonomous communities in wind energy development, which, with nearly 2900 MW, represented 19.15% of the total Spanish installed capacity as of December 31 2007 It is estimated that thisﬁgure will rise to more than 6000 MW by the end of 2012

Contents lists available atScienceDirect

Energy Economics

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the main results of their application to our group of wind farms In the discussion and interpretation section, in addition to making a comparative analysis of the methodologies used, we identify factors that can explain the results of efﬁciency obtained and discuss their implications, outlining their possible practical uses, mainly for wind farm development companies (developers), technology suppliers, operators4and regulators in the sector The analysis of the results

would be of use in assessing the learning process The process of deploying more wind farms would result in cost reductions, in accordance with the logic of the experience curves, including all wind energy learning systems (Junginger et al., 2005; Neij, 2008)

We end by summarising the main conclusions and pointing out several considerations that may be useful in future studies

2 DEA and SFA methodologies

Establishing an efficient production frontier that defines produc-tive possibilities in terms of maximum output given some inputs, or minimum inputs given an output level, is the key to the methods applied in this paper In this way, if a productive unit operates on the frontier it is defined as efficient; in contrast, if it operates beneath this frontier it would be classified as inefficient The degree of inefficiency will depend on the distance in relation to the frontier This general method of defining the concept of efficiency is rooted in Farrell (1957).5

The DEA non-parametric technique, starting from some general assumptions on the technology, allows us to use linear programming to establish an efﬁcient frontier of best practice that “envelopes”

the observations of the decision-making units (DMU) evaluated The mathematical resolution implies maximising the ratio between the outputs and inputs of each unit with weights that not break the principle whereby, with the same those weights, no other unit overcomes the maximum reachable value of efﬁciency, which is equal to Theﬁrst DEA model to be formulated is attributed toCharnes et al (1978) A number of extensions to this model later gave rise to an ample variety of new models (Ray, 2004)

In turn, SFA methodology is of a parametric nature It requires establishing a functional form for the production frontier, which must be estimated econometrically, obtaining two error term components: one that refers to the statistical noise, with a normal distribution, and another error linked to technical inefﬁciency, with an alternative form of distribution (semi-normal, truncated, gamma) Seminal research in thisﬁeld was developed byAigner et al (1977), Battese and Corra (1977) and Meeusen and van den Broeck (1977) As with the DEA technique, the models linked to stochastic frontiers have evolved in multiple directions, increasing the possibilities for analysis ( Kumbha-kar and Lovell, 2003)

As for the advantages and inconveniences of the use of both methodologies6, on the one hand, DEA methodology is moreﬂexible,

does not require restrictive assumptions on the technology, and facilitates individualized and combined information of the evaluated observations However, its limitations include its deterministic character, its sensitivity to output and input speciﬁcations and its limited possibilities for contrasting hypotheses On the other hand, the key advantage of SFA methodology is its stochastic nature, whereby frontier deviations include both technical inefﬁciency and external effects that are not within the company's control In addition, it incorporates the possibility of overcoming measurement errors in

variables, allows for statistical inference, reduces the influence of extreme observations and can be easily adapted to work with panel data As for its disadvantages, apart from requiring a functional form for the production function, it needs to establish prior to the esti-mation a statistical distribution for the error term that shows the technical inefficiency and it does not provide additional individual-ized information of the units evaluated apart from the efficiency scores

Due to the aforementioned factors, literature on efﬁciency evaluation has repeatedly discussed the possible combined use of DEA and SFA.7Insofar as both methods start from different theoretical

conceptions and present differentiated information, the fact that they produce similar results in terms of efﬁciency reinforces the validity of the studies carried out, allowing us to reach more deﬁnite conclusions, and providing more detailed information regarding both the general productive process and the individual behaviour of the units In the case of discrepancies, this can compel us to reconsider the initial assumptions, and reformulate the models If these discrepancies persist, this kind of analysis forces us to keep in mind the limitations of the results obtained with either methodology, leaving its use to the researcher's consideration.8

3 DEA and SFA applications in the electricity generation sector

Early research into efﬁciency evaluation in the electricity sector targeted fossil fuel power plants, using parametric deterministic methods (Nerlove, 1963; Barzel, 1964) They established the basic conceptual framework for the electricity generation process, which involves one output—electric power—and three inputs—capital, labour and fuel DEA or SFA were not used in applications in the sector until the late seventies and early eighties; nevertheless, this does not mean that no contributions were made to the development of both methodologies.9

Thefirst DEA application in the electricity generation sector was the work ofFäre et al (1983), who measured the efficiency of electric plants in Illinois (USA) between 1975 and 1979, in order to relate the scores obtained to the regulation of the sector In the case of SFA methodology, thefirst studies were carried out bySchmidt and Lovell (1979, 1980), who used a sample of 150 privately-owned steam-electric plants constructed in the USA between 1947 and 1965 to support the application possibilities of this stochastic methodology

Advances in both methodologies have led to numerous studies related to the sector They include modiﬁcations to the basic techniques, as well as changes in the output and input variables to include, context indicators and applications to different phases of the sector.10 Particularly, the analysis made by Pollitt (1996) on the

productive efficiency of nuclear power stations using DEA is of relevance in understanding our approach, as it shows a variety of plant specific efficiency scores, relying on the distinction betweenex anteandex postefficiency

As for speciﬁc references, linked to the efﬁciency in the renewable electricity sector, we must highlight the SFA and DEA applications of

4

On occasions, a singleﬁrm assumes the role of all three agents, installing its technology, promoting the wind farm (design and construction phase) and operating it once production has commenced

5For an overview of the concepts related to efﬁciency, and the main methods used in its evaluation, seeCoelli et al (2005)

6

This paper does not aim to provide an exhaustive analysis of the basic concepts, advantages and limitations of the different methods and the theoretical developments in order to overcome the said inconveniences For these issues, seeMurillo (2004)

7

SeeGong and Sickles (1992) and Ruggiero (2007), from a theoretical perspective, and as a practical application the comparison of methods made byHjalmarson et al (1996)

8

SeeMortimer (2002), that incorporates a survey of the literature that used both methods at the same time and discusses the interest that the application of deterministic parametric models can have as nexus between DEA and SFA models

9

For example, we can highlightSeitz (1971), who makes an explicit allusion to the concept of efﬁciency and the necessity of a reference frontier to compare generation plants His analysis procedure consisted of estimating a convex frontier function by means of lineal programming techniques that produce multidimensional efﬁciency scores for electricity generation plants

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Barros and Peypoch (2007) and Barros (2008), respectively, to Portuguese hydroelectric generation units, in which they make a meticulous analysis of the determinants of the efficiency scores obtained A more common line of research is the analysis of the impact on efficiency of the participation of renewable energy technologies in the energy mix For example, and within the context of the Spanish electric system,Arocena (2008)uses DEA to analyse, among other things, the impact on efficiency that results from diversifying the sources of power generation, in the light of companies' use of hydroelectric power

In the electricity generation sector we have also found studies of interest for our research due to their joint use of DEA and SFA, such as

Meibodi (1998), Park and Lesourd (2000) and Murillo and Vega (2001) In order to compare both methodologies, they all applied Pearson's and Spearman's statistical tests of correlation to the efﬁciency scores and unit rankings derived from both methods The limited number of studies prevents us from reaching categorical conclusions, although, at least in terms of unit ordination, it seems that both methodologies can be complementary,11generally

produc-ing DEA scores that are lower than those obtained by means of econometric techniques

4 Empirical analysis

4.1 Wind power generation framework and data

Since our empirical application is focused on the wind power sector, we are going to provide now a brief explanation of the production process The standard unit (DMU) of electricity generation with wind energy is formed by a group of wind turbines connected to a distribution or transmission grid, in what is called a wind farm This way it is possible to make optimum use of the productive potential, exploiting economies of scale both in the automatism control and the labour factor It is important to emphasize that the productive results depend on a complex sequence of decisions.12We can therefore speak of an extensive production process concept consisting of the following phases:

• The evaluation of the productive possibilities of a site, taking into account wind speed, general weather conditions, topography over the site and surrounding area, grid capacity andﬁnancial risks

• The project design, an engineering phase during which decisions regarding the type of machine (turbine), the installed capacity and other technical characteristics are taken This stage also includes the selection of the turbine layout on the wind farm site (micro-siting)

• The operating phase, when the wind farms commence production It is at this phase that the farm performance can be assessed This performance is closely linked to the previous two phases At all events, this phase is important for the productive results throughout the useful life, because the objective is to maintain the highest availability factors of the wind farms, optimising the downtimes according to planned operation protocols

Within this context, and according toKrokoszinski (2003), we can distinguish two general levels of decisions that are differentiated by the stage at which they are taken13: anex antelevel, including theﬁrst

and second phases, that is closely linked to farm investment and is the responsibility of the developers and engineers; and, once the farm has become operational, anex postlevel, linked to the third phase and the results of which depend on the operator This implies that the

efﬁciency results obtained following the aforementioned basic conceptual framework for the electricity generation process ( Sec-tion 3) will have two components that are evaluated together

By adapting the wind power variables to this general framework, the output would be the quantity ofelectrical energy deliveredto the grid, while the inputs would be thecapital, which basically includes the wind turbines, thelabour, and thefuel, which is supplied by the wind when it is captured by means of the surface swept by the wind turbine rotors A production relationship can therefore be established which is similar to any traditional electricity generation technology and we could deﬁne a micro-economic production function, given by the general formula:

E=f Kð ; L; FÞ ð1Þ

whereEis the electrical energy,Kthe capital,Lthe labour andFthe fuel

For the purpose of our study, the productive units are a group of 57 Spanish wind farms located in the region of Galicia that operated between 2001 and 2004, and that commenced production from 1997 onwards In principle they are homogeneous units, because they use similar productive foundations and can therefore be compared in terms of their efﬁciency by means of some non-frontier or frontier method The information to determine the output and input variables was provided by the operators, distribution companies, sector regulators and ofﬁcial meteorological centres

The output of each farm is the component of active energy delivered to the distribution or transmission grid measured in MWh Regarding the inputs, the capital factor is associated with the installed capacity in MW of the farms, which is obtained as the product of the number of wind turbines multiplied by the nominal power of each one As for the labour factor, we have considered the number of full-time man-years employed in the tasks of operation, maintenance and control of the farms

Finally, the input fuel that feeds the facilities depends on the wind and is given exogenously by the nature Developers and operators try to take advantage of the location of their wind turbines by orientating them towards the wind direction in order to transform their kinetic energy in electricity Following the principles of the wind power generation, the fuel per unit of time would be calculated in the following way:

F=1

2 ììSìv

3

2ị

whereis the air density,Sthe interposed surface andvthe wind speed

The fuel is measured in MWh and to determine it, the wind turbines number multiplied by their unit surface is used as the interposed surface and, given the information available, we also used the annual average wind speed at each site.14Table 1summarizes the

main productive characteristics of the farms in the years studied, in what constitutes a non-balanced panel of 152 observations.15

Taking as our starting point the fact that the wind farms included in our sample are of recent installation and that their operation availability factors are around 98%, in the empirical section we deal with below, the analysis focuses on the assessment of the ex ante efﬁciency

11

In this sense the research of Park and Lesourd (2000) reﬂects the worst correlations, compared to the higher correlation levels of other works, thereby reinforcing this fact

12

For the technical and economic aspects of the wind electricity generation, see Sathyajith (2006) and EWEA (2009)

13

This distinction is similar to that made byPollitt (1996)

14A more precise calculation would require taking into consideration the wind speed distribution, which is usually a Weibull distribution In our case this was impossible to obtain, due to the lack of data

15

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4.2 DEA application

The use of DEA methodology involves deciding the type of production possibility set where the productive units are included.16

In this sense, it is necessary to assess the different options of returns to scale, the presence or non-presence of weak disposability in the inputs, or if the assumption of convexity for the frontier is acceptable Later on it must be determined whether the models are input-oriented, output-input-oriented, or instead not have any type of orientation

In our case we have opted to check the two pioneering radial character options in DEA models On the one hand the so-called CCR (Charnes et al., 1978), that deals with constant returns to scale, and on the other, BCC (Banker et al., 1984), that allows for the presence of variable returns to scale in the frontier.17The other characterizations

of the production possibility set are common In our application, and with regard to weak disposability, we not believe that there is any inconvenience in adopting the option of strong disposability both in the inputs and output Nor did we ﬁnd any problems with the assumption of convexity, since any input combination inside the production possibility set determined by the wind farms is feasible

Consequently, the respective production possibility sets would be as follows:

EPC ðx;yÞ:x≥ ∑n j=

xjλj;y≤ ∑ n

j=

yjλj;λj≥0;j= 1; 2; :::;n

( )

with the CCR model

EPV ðx;yÞ:x≥ ∑n j=

xjλj;y≤ ∑ n j=

yjλj;λj≥0;∑ n j= λj

= 1; j= 1; 2; :::;n

( )

with the BCC model

wherexis the inputs vector,yis the outputs vector andλis a weight coefﬁcients vector

The difference between both models resides in the restriction ofλ, which in the BCC model forces the sum of the weights of the inputs and outputs vector to be equal to This restriction is that which identifies the presence of returns to scale, so each unit is compared with the part of the frontier built with units of similar dimension Due to this specification, the BCC efficiency scores are always higher or equal to the CCR ones

We have opted for oriented models, speciﬁcally output-oriented ones (CCR-O and BCC-O), because during the period under analysis the objective of the farm operators was to produce maximum energy without any kind of restrictions Unlike other models, productive behaviour is not motivated by exogenous factors In this sense, the electricity supply is not conditioned by demand or the decisions of

systems managers, or by competition with other operators in the generation market orﬁrms that use alternative technologies.18

Literature fails to provide a common stance on the treatment of panel data with the DEA methodology, a fact which becomes even clearer when comparing the results with parametric methodologies (Tulkens and van den Eeckaut, 1995) In our study we posed three options in this respect, thereby enabling us to carry out a sensitivity analysis and obtain a greater insight into the implications of each option:

• The four year period allows us to consider the option of a DEA analysis for each year, thereby providing fourcross-section applica-tions, and later, if the efﬁciency is seen not to vary over time for each farm, to average out the efﬁciency scores obtained This was the choice made byGong and Sickles (1992)

• An alternative option is to assume that all the observations are comparable units, regardless of the year, so we would have apooled data analysis, which logically gives rise to efﬁciency scores that are equal or smaller than the former ones This option was adopted by

Färe et al (1983) and Meibodi (1998)

The two options outlined above respond to the extremes of what is known as a window analysis19 The advantages and inconveniences of each depend on the number of periods and observations available, and also the researcher's intentions In this sense, the cross-section option compares units of the same year, so it eliminates stochastic effects that could affect all the observations for a one-year period, while the pooled option allows for the identification of the most efficient observations in the group and, where appropriate, to detect if there are any rules of temporary behaviour of the farms' efficiency (Hjalmarson et al., 1996)

• The third option used in our research corresponds to the proposal of

Ruggiero (2004) This author points out that in order to avoid biases in the estimation of efficiency scores for measurement errors of inputs and outputs, it is advisable with panel data to useaveraged data before applying DEA models One of the downsides to this approach is that it considers efficiency of the units as time-invariant The average efficiency results obtained, both with the CCR-O model and the BCC-O, in accordance with the aforementioned anal-ysis options (cross-section, pooled or averaged) are shown in

Tables and

Generally speaking, farm efficiency levels are high In the CCR-O model, the average efficiency of the group is 0.8208 in the cross-section option, 0.7846 for pooled data and 0.8045 for averaged data, with a standard deviation around 0.10 in all the cases Logically, in the actual definition of the models, the BCC-O efficiency is higher than the

Table

Average variables of the wind farms.a,b,c

Year Installed capacity Labour Interposed surface Wind speed Fuel Availability factor Active energy Number of farms 2001 24.39 (8.00) 3.87 (1.76) 5.99 (2.12) 8.77 (0.28) 215,195 (70,401) 98.45 (0.29) 71,561 (23,500) 24

2002 25.07 (9.40) 3.82 (1.66) 6.15 (2.57) 8.03 (0.24) 169,199 (64,651) 98.16 (0.48) 68,126 (28,782) 32 2003 26.63 (11.22) 3.84 (1.63) 6.62 (2.96) 7.27 (0.28) 135,250 (55,947) 98.27 (0.35) 64,273 (29,181) 40 2004 27.80 (11.46) 3.86 (1.48) 6.90 (3.04) 7.52 (0.32) 155,270 (63,639) 98.12 (0.46) 70,385 (30,371) 56 a

Between parentheses, standard deviations b

The installed capacity is measured in MW, the labour factor is approximated by the number of full-time employees, the interposed surface is measured in hectares, the wind speed is expressed in m/s, the availability factor is expressed in % and the fuel and the active energy are measured in MWh

c

We have supposedρ= 1.22 kg/m3, taking into account that the group of wind farms face analogous general weather conditions and have a similar altitude (500–800 m).

16That is to say, feasible combinations of inputs (X) and outputs (Y). 17

Meibodi (1998), Park and Lesourd (2000) and Murillo and Vega (2001)also use these methods, due to the discriminant capacity of CCR methodology, and on the other hand, in the BCC case, to incorporate a more general productive behaviour

18

At least in the period under consideration in which the Royal Decree 2818/1998 to support renewable energies was in force Since March 2004, with Royal Decree 436/ 2004 wind farms have been joining the generation market, although they still beneﬁt from the Special Regime, and their aim is to reach the maximum generation levels possible

19

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CCR-O, with an average value of 0.8700 for the cross-section option, 0.8386 with pooled data and 0.8584 for the averaged data alternative, with a standard deviation slightly over 0.10 in all the cases As can be observed, the alternative of averaged data is placed between the option that reports higher efﬁciency scores, i.e the cross-section, and that with the lowest average, the pooled one

A more detailed comparison between the various options allows us to conﬁrm a high level of correspondence Consequently, in efﬁciency terms, all the Pearson's correlations for the DEA models show values higher than 0.9 Regarding ranking comparisons, Spearman's correlations also revealed high values that exceed the correlation of 0.9, except for the BCC model, when the cross-section and averaged are compared, with a value of 0.8874, still a high correspondence

As for the units, with the CCR-O model there are ten farms that in any of the specifications exceed at least 90% of the efficiency rate; and in the BCC-O case, at least nineteen farms were able to exceed that efficiency level As for more inefficient farms, with the CCR-O model, there are seven farms that not exceed 70% of efficiency with any option, afigure which drops tofive in the case of the BCC-O

Therefore, the DEA methodology allows us to differentiate between the farms, proving that there are major differences in the results obtained among farms with the three inputs and the output established The DEA methodology also provides information on returns to scale, weights, slacks and peer groups Without going into detail, it simply can be pointed out that the scale efﬁciency (ratio of the CCR-O and BCC-O scores) is high, and that the inefﬁcient units are placed in decreasing returns to scale; in other words, their size is higher than the most productive unit This result responds to the productive logic of the wind generation of electricity, since the higher the dimension of a farm, the higher the incidence of the wake effect between wind turbines.20

Inputs weights and slacks show, both with the CCR-O model and with the BCC-O, that the inputs capital and fuel explain to a large extent the efﬁciency results achieved On the other hand, the input labour presents the highest slacks and, therefore, participates less in efﬁciency levels

As for the peer groups, in the case of the pooled CCR-O model, four farms are the reference against which the others evaluate their efﬁciency, with observations for 2001, 2003 and 2004 With the pooled BCC-O model the reference farms rise to eleven, with observations for

every year This fact explains the high correspondence, both in places and in efficiency scores, with the analysis variant that supposes the use of four cross-sections; in this sense, only 2002 shows a significant incidence in efficiency results regarding the data pooled for the analysis method For the averaged option, the comparison units are also four for CCR-O, rising to nine in the case of BCC-O, most of them coinciding with the reference units of the other options

Even considering the limitations of DEA methodology with non-balanced panels, it can be observed that the pooled results not show a behaviour rule in relation to time that allows us to claim, for example, that there is greater efﬁciency of the observations for the same farm for 2004 with regard to 2001

The most efficient units reveal a prevalence of observations of farms that became operational between 2003 and 2004 This fact implies that there might be some technological superiority with relation to the farms installed previously, including local learning from strategic deployment To measure this impact, as a sensitivity analysis, we applied the DEA pooled models on a balanced panel formed by the twenty-two farms present in each of the four years analysed and we compared their rank and efficiencies with regard to the pooled general analysis (non-balanced panel) Without detailing individual information, it was seen that the presence of the recent installation units in the general analysis does not alter the relative rank of the oldest farms in relation to the balanced panel As for their average efficiency, the effect discussed above was clearly observed, since the average efficiency of the oldest farms drops by just over 5% when comparing them in a balanced panel and in a non-balanced panel with the units installed at a later date

4.3 SFA application

Although the original SFA specification referred to a production function for cross-section data, panel data present important advantages Thus, the estimate of a model with cross-section data does not allow the researcher to assure that the estimated coefficients only reflect the impact of the explanatory variables on the dependent variable, because the supposed relationship can hide unobservable behaviour differences between the individuals, which are correlated with the variables However, panel data allow for the control of this unobservable heterogeneity between crossed sections, if it remains relatively constant throughout time On the other hand, panel analysis avoids the rather restrictive supposition of a pooled data model whereby the impacts of the explanatory variables are identical for all individuals

Table

CCR-O efﬁciency scores

Farm Cross-section Pooled Averaged Farm Cross-section Pooled Averaged Farm Cross-section Pooled Averaged

1 0.7138 0.6946 0.7302 20 0.7939 0.7069 0.6814 39 0.7058 0.7003 0.7080

2 0.8195 0.8038 0.8365 21 0.7410 0.7136 0.7362 40 0.6930 0.6592 0.6930

3 0.9207 0.9031 0.9397 22 0.8725 0.8551 0.8758 41 0.9150 0.8842 0.9153

4 0.8959 0.8492 0.8451 23 0.7454 0.7307 0.7473 42 0.7793 0.7558 0.7956

5 0.9050 0.8580 0.8540 24 0.6067 0.5999 0.6224 43 0.5607 0.5583 0.5609

6 0.8140 0.7949 0.8162 25 0.8545 0.8338 0.8398 44 0.6144 0.6059 0.6188

7 0.9074 0.9022 0.9334 26 0.9664 0.9349 0.9663 45 0.8448 0.8264 0.8297

8 0.7716 0.7642 0.7936 27 0.9750 0.9691 1.0000 46 0.8303 0.8203 0.8247

9 0.9514 0.9423 0.9796 28 0.8378 0.8156 0.8205 47 0.8158 0.8094 0.8217

10 0.9729 0.9687 1.0000 29 0.7300 0.7123 0.7190 48 0.9422 0.8803 0.9551

11 0.7326 0.7295 0.7551 30 0.8408 0.7594 0.7866 49 0.9633 0.9030 0.9656

12 0.7630 0.7431 0.7613 31 0.8829 0.7238 0.7326 50 0.8354 0.7862 0.8149

13 0.8239 0.7457 0.7072 32 0.9005 0.7745 0.8034 51 0.7954 0.7173 0.7566

14 0.7785 0.7460 0.7513 33 0.9391 0.9199 0.9372 52 0.9515 0.8581 0.9052

15 0.9356 0.8136 0.8003 34 0.8330 0.8075 0.8488 53 0.7031 0.7031 0.7081

16 0.6100 0.5909 0.6009 35 0.7996 0.7552 0.8004 54 0.6895 0.6895 0.6944

17 0.7067 0.6950 0.7184 36 0.9449 0.9403 1.0000 55 0.6833 0.6162 0.6500

18 0.9634 0.8984 0.8742 37 1.0000 1.0000 1.0000 56 0.7187 0.6481 0.6837

19 0.9099 0.8127 0.7798 38 0.7491 0.7359 0.7650 57 0.8381 0.7558 0.7973

20

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In our case, the version of the SFA model corresponding to panel data would be as shown below:

yit=f xðit;βÞ+εit=f xðit;βÞ+vit−uit ð3Þ

whereyis the output,xis the inputs vector,βis a vector of unknown production parameters andεis a random disturbance which includes statistical noise (v) and technical inefﬁciency (−u) As for the subindexes,idenotes each one of the wind farms (i= 1, 2, , 57) andtthe considered years (t= 2001, 2002, 2003, and 2004)

In order to estimate the model given by Eq (3), it is necessary to impose some type of structure on the inefﬁciency effects, in the sense of whether or not they are variable with regard to time In theﬁrst case,uit=f (t) · ui, wheref (t)is a function that determines how the

technical inefficiency varies throughout time In the second case uit=ui, where ui is considered either as afixed parameter (fixed

effects model) or as a random variable (random effects model) One of the drawbacks to time-invariant models–in comparison with time-varying ones–is that they are slightly restrictive: it is to be expected that the managers will learn from their experience and that efﬁciency levels will change systematically over time Nevertheless, as

Schmidt and Sickles (1984), Schmidt (1985) and Kalirajan and Shand (1989)point out, technical inefﬁciency and its relative ranking are unlikely to vary substantially throughout short periods of time and therefore in these circumstances the time-invariant assumption seems reasonable If the number of units is high but the number of time periods is small, the time-invariant assumption is more appropriate for the application of SFA techniques for panel data

Given the characteristics of the sample used in this research (a time horizon of just four years), we considered that the technical change of each farm is imperceptible in such a short period of time.21 Additionally, the time-invariant hypothesis is the most

appropriate within the framework of theex anteefﬁciency analysis, which forms the core of this research Moreover, we took into account that the comparison between the DEA and SFA methods is made considerably easier by this invariance hypothesis (Gong and Sickles, 1992) Bearing in mind all these factors, we opted to use time-invariant models.22

Although theﬁxed effects models have the advantage of being able to be estimated in a standard regression framework, one of

their drawbacks is that they can only be used to measure relative efficiency with regard to the most efficient company in the sample This means that if the number of companies is small, as in the case of our study, the reliability of the estimates may be questioned On the other hand, the random effects models not suffer from this disadvantage, and they can be estimated by means of LS techniques (more specifically, Estimated Generalised Least Squares, EGLS) or ML The latter involve stronger assumptions about the distribution of the inefficiencies (variableu): semi-normal distribution, trun-cated normal distribution… Taking into consideration what has been pointed out formerly by authors such asMeibodi (1998), we opted to use a random effects model, in accordance with the guidelines explained below

To sum up, and based on the reflections discussed above, one of the objectives of this study was to analyse the situation of Galician wind farms from the point of view of their technical efficiency, by means of the methodology of stochastic frontiers, using a time-invariant with random effects specification The data used, all in logarithms, refer to the output active energy (y) and the inputs installed capacity (x1), workers' number (x2) and fuel (x3) Their

main descriptive statistics are shown inTable

Using those data, we deﬁned a time-invariant random effects model with truncated normal distribution for the inefﬁciency term, starting from a translog production function In the case of our study, this function would be expressed by the following:

y=β0+β1x1+β2x2+β3x3+β4x 1+β5x

2 2+β6x

2

+β7x1x2+β8x1x3+β9x2x3+ε ð4Þ

The truncated normal option was used because it allows for a more

ﬂexible representation of the efﬁciency pattern in the data ( Kumbha-kar and Lovell, 2003); on the other hand, the use of the translog production function obeyed both to its technical virtues (Coelli et al., 2005) and to its long-standing tradition in literature

This model estimate revealed that the coefﬁcients ofx1andx3were

significant at the 1% level Labour input had a negative coefficient, but this was not significant even at 10%.23This reinforces the nature of the

ex anteefﬁciency measure under study, because this productive factor plays the key role during the operating and maintenance phase Thex1

square was signiﬁcant at 10%, and the interaction term betweenx1

andx2was signiﬁcant at 5%

Table

BCC-O efﬁciency scores

Farm Cross-section Pooled Averaged Farm Cross-section Pooled Averaged Farm Cross-section Pooled Averaged

1 0.7535 0.7172 0.7766 20 0.8136 0.7590 0.7380 39 0.8296 0.8029 0.8107

2 0.8685 0.8407 0.8901 21 0.8236 0.7599 0.8113 40 0.7124 0.6920 0.7185

3 0.9759 0.9446 1.0000 22 0.9672 0.8675 0.8964 41 0.9963 0.9963 1.0000

4 0.9522 0.9235 0.9375 23 0.7850 0.7624 0.8043 42 0.8289 0.8217 0.8409

5 0.9737 0.9422 0.9597 24 0.6527 0.6227 0.6521 43 0.6173 0.5994 0.6151

6 0.8665 0.8456 0.8801 25 0.9346 0.9192 0.9389 44 0.6679 0.6372 0.6561

7 0.9315 0.9152 0.9536 26 1.0000 1.0000 1.0000 45 0.9328 0.9169 0.9463

8 0.8048 0.7885 0.8101 27 0.9828 0.9716 1.0000 46 0.9189 0.9035 0.9317

9 0.9913 0.9718 1.0000 28 0.9144 0.8858 0.9137 47 0.9142 0.8762 0.9130

10 0.9827 0.9798 1.0000 29 0.7965 0.7511 0.7725 48 0.9631 0.9492 0.9685

11 0.7397 0.7375 0.7551 30 0.8707 0.8278 0.8422 49 0.9815 0.9744 0.9921

12 0.8330 0.8040 0.8410 31 1.0000 0.7519 0.7648 50 0.8914 0.8826 0.9007

13 0.8696 0.8183 0.8017 32 0.9340 0.8360 0.8534 51 0.8300 0.8205 0.8312

14 0.8586 0.8285 0.8561 33 0.9984 0.9765 1.0000 52 0.9722 0.9349 0.9611

15 0.9785 0.8699 0.8485 34 0.8778 0.8778 0.9020 53 0.7929 0.7746 0.7995

16 0.6485 0.6339 0.6505 35 0.8083 0.7749 0.8129 54 0.7480 0.7334 0.7519

17 0.7483 0.7239 0.7569 36 1.0000 1.0000 1.0000 55 0.6959 0.6634 0.6807

18 0.9882 0.9613 0.9567 37 1.0000 1.0000 1.0000 56 0.7334 0.7012 0.7185

19 0.9345 0.8683 0.8397 38 0.8273 0.8007 0.8080 57 0.8743 0.8594 0.8706

21In this sense, the DEA analysis of the previous section reinforces this choice. 22On the other hand, note that, asKumbhakar and Lovell (2003)point out, the inclusion of the time variable between the regressors as proxy for the technological change would have the inconvenience that it would be difﬁcult to distinguish the separated effects of the technological change and the change of technical efﬁciency 23

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We contrasted the null hypothesis thatx2, the quadratic terms and

the interaction terms could be supposed jointly equal to zero, producing ap-value of 0.0425; that is to say, at the 5% level it could be claimed that the Cobb–Douglas speciﬁcation with two inputs (x1

andx3) would be adequate This Cobb–Douglas function24would be

expressed by:

y=β0+β1x1+β3x3+ε ð5Þ

The main results of this estimate are shown inTable The Wald andzstatistics show that the explanatory capacity of the model is good, and all the regressors are highly signiﬁcant

The coefﬁcients of the inputs are inferior to 1, and their sum (0.9599) implies that there are slightly decreasing returns to scale On the other hand, the gamma value25is signiﬁcantly different from zero,

and we can therefore not reject (at a conﬁdence level of 95%) the null hypothesis that there are technical inefﬁciency effects that here are of considerable importance

Once the estimates shown inTable 5were obtained, we calculated the predictions of the technical efficiencies of each of the 57 farms that appear inTable The values range between 0.6139 and 0.9807, with an average of 0.8192 and a standard deviation of 0.0954 Fourteen wind farms exceed at least 90% of the efficiency rate, and there are seven wind farms that not exceed 70% of efficiency As in the case of the DEA scores (Tables and 3), the fact that very few units reach the top of the efficiency frontier signifies that our methodology is robust for the purpose of analysing the wind farm data

5 Discussion and interpretation of results

5.1 Comparison of methodologies

The efﬁciency scores obtained allow us to compare methodologies However, we should stress that since the SFA estimate does not grant enough signiﬁcance to labour, in order to make appropriate compar-isons between both methods, it was necessary to recalculate the DEA models excluding the labour factor of the production relationship between output and inputs.26

As for the comparisons between DEA and SFA models, the average SFA efﬁciency of 0.8192 is higher than the CCR averages and inferior to the BCC averages, with any of the three outlined options of DEA analysis for panel data (cross-section, pooled and averaged) Regarding the individual efﬁciency scores and the ranking by positions, the highest correlations between the results of the SFA method and the DEA variants are found in the pooled BCC-O model, with Pearson's and Spearman's indexes of 0.9750 and 0.9777

respectively The worst results, albeit within a narrow margin of differences, are found when we compare SFA with cross-section CCR-O, with Pearson's and Spearman's indexes of 0.8735 and 0.8539

In the light of the correlation results we can claim that there is a pretty strong correlation between the methods The conceptual distinction between non-parametric deterministic technique that characterizes the DEA, and parametric stochastic technique of the SFA, does not lead empirically to different results, which would initially endorse the joint complementary use of the information provided by both techniques The explanation may lie in the high gamma value obtained in the econometric estimate, which reveals a strong presence of the inefficiency component in relation to the component of statistical noise, which means that the stochastic effect is minimal The SFA information, apart from questioning the inclusion of the labour factor and reinforcing the validity of the DEA scores and rankings, allows us to derive additional conclusions with regard to those provided by the DEA methodology In this sense, given the coefficients obtained with the Cobb–Douglas production function, we can calculate production elasticities, and complement the conclusions on decreasing returns to scale that this methodology indicates 5.2 Explanation of the efficiency scores

Finding variables that explain the efﬁciency scores achieved by the evaluated units is one of the regular concerns in literature on efﬁciency This is also true of the electricity sector, and the use of variables that consider the age of the facilities, technological or other factors that differentiate a group of units from others, such as property type (public or private), is common.27

In our case, given the information available, we proved three variables that can provide an explanation for the farms' scores Speciﬁcally, we included a time trend (equivalent to considering the year that corresponds to each observation), the year of installation of the farms (age) and, lastly, the unitary size of the standard wind turbine of each farm in terms of unitary swept surface expressed in square metres, as a technological character variable

Considerable controversy surrounds the application of two-stage methods of analysis; as a result, we have leaned to apply the effects model ofBattese and Coelli (1995), who incorporate these explan-atory variables into the calculation of the error term attributed to the inefﬁciency of the SFA method itself

Before carrying out the calculations we found an important correlation of (−0.6064) between the variables age and surface, which could adversely affect the estimate This result is absolutely logical: age and unitary surface (per turbine) are related by the very nature of the technological progress in the wind energyﬁeld, which is showing a trend towards larger blades Age and unitary surface can be interpreted as two alternative indicators of a wind farm's‘vintage’ Taking these considerations into account, we opted to initially carry out two estimates, one with the pair time trend-age (6) and another with the pair time trend-unitary surface (7) This way the results of both inefﬁciency effects models would be (t-ratios between parentheses): U= 0:0920 + 0:0530Time trend+ 0:0304Age

0:07

ð Þ ð0:23Þ ð2:37Þ ð6Þ

U= 0:3617 + 0:0108Time trend−0:0002Unitary surface 4:30

ð Þ ð0:51Þ ð−3:10Þ ð7Þ

The results indicate that the time trend variable is not signiﬁcant.28

The other two variables reveal a certain explanatory power, with a

Table

Descriptive statistics of the variables used in the SFA model

y x1 x2 x3

Mean 17.9514 3.1948 1.2457 2.8257

Median 17.9606 3.1781 1.3863 2.8778

Standard deviation 0.4348 0.3982 0.4764 0.4510 Skewness −0.1656 −0.0916 −0.5749 −0.4548

Kurtosis 2.3350 3.0728 2.4252 2.9372

24

This function (with only capital and fuel as inputs) resembles the engineering approach ofCowing (1974)

25Gamma is the proportion of the total variance ofε(ε= error term =v−u) that is due to the inefﬁciency term (−u)

26This change provokes a slight decrease of the average efficiency of the group of farms, regarding the original DEA models with labour, with reductions of less than 3% In relation to the correlations between farms, regarding both positions (Spearman) and efficiencies (Pearson), in all the cases values higher than 0.85 are reached when comparing the new models with the original ones This fact agrees with the results of inputs slacks obtained when applying the DEA programs, where the labour factor was the one that showed more slacks and the one that on average participated less in the explanation of the radial efficiencies

27Barros and Peypoch (2008)have carried out recent and innovative research in this ﬁeld

28

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highert-ratio of the unitary surface This fact means that as the wind turbine unitary size increases, inefficiency decreases, in accordance with the logic of the evolution of the sector, where the diameter of the machines is increasingly large If we use age as explanatory variable for inefficiency, it is also significant, with at-ratio of 2.37, indicating that the greater the age, the higher the inefficiency Given the corre-lation between unitary surface and age, there is a combined effect of both that is summarized by the variable of highest explanatory power, i.e the surface

In relation to the former result it can be pointed out that the most efficient farms in the group according to the DEA and SFA methodologies show a higher unitary size This feature is present in those efficient farms that became operational in 2003 and 2004, which means that a great deal of the farms installed previously is considered inefficient, as we pointed out in Section 4.2 This fact confirms that the year of installation has a certain explanatory power of the inefficiency The relationship between both variables, unitary surface and age, is not perfect because the installation of large machines has not been staggered over time.29

The aforementioned points indicate that it would be possible to increase efﬁciency levels, and therefore production rates, of the farms with wind turbines that are smaller than the average size and which tend to be the oldest This process is known as‘repowering’ and involves incorporating larger and more powerful wind turbines

Generally speaking, the explanations for the inefﬁciency shown by each wind farm are linked to the decisions on the productive process shown inSection 4.1

Taking into account the high availability factors for operation of the sample of wind farms, our DEA and SFA models are focused on isolating an efficiency score which essentially represents ex ante decisions The results not show significant changes in the annual efficiency scores for each farm There are no global trends or consistent evolution paths during this short period at the beginning of lifetime, facts that reinforce the adopted approach Within this context, the sources of inefficiency–which are closely interrelated– can be systematized as follows:

1) Erroneous assessment of the resources available on site: less wind than expected, excessive wind or changes in direction that affect the efﬁciency of the design

2) Choice of machine type: inadequate selection of machinery (in terms of its nominal power, diameter, height, generator type or mechanical capacity) and non-compliance of the technologist's technical speciﬁcations

3) Farm design: this includes particularly positioning the wind turbines in the wrong direction, or in inadequate sites in function of the topography or the altitude The distance from the connection point on the electric grid is also important, due to transport losses

At all events, external factors exist that are beyond the control and decisions of developers and operators, such as unforeseen weather conditions, grid restrictions, administrative reasons, sabotages, etc.,

Table

Time-invariant random effects model, inputs

Log likelihood 143.7063 Wald chi2(3) = 1026.84 ProbNchi2 = 0.000

Coefﬁcient Standard deviation z p-value Conﬁdence interval 95%

x1 0.5649 0.0425 13.28 0.000 0.4816 0.6483

x3 0.3950 0.0290 13.63 0.000 0.3382 0.4518

cons 15.2375 0.0975 156.24 0.000 15.0463 15.4286

/mu 0.1653 0.0907 1.82 0.068 −0.0124 0.3430

/lnsigma2 −3.5687 0.4297 −8.30 0.000 −4.4109 −2.7265

/ilgtgamma 1.8975 0.5172 3.67 0.000 0.8839 2.9111

sigma2 0.0282 0.0121 0.0121 0.0655

gamma 0.8696 0.0586 0.7076 0.9484

sigma_u2 0.0245 0.0121 0.0008 0.0483

sigma_v2 0.0037 0.0005 0.0026 0.0047

29

It is important to bear in mind that it is a very short time period, so different types of machines have been intercalated in the time evolution, due to delays in construction or administrative matters

Table

SFA efﬁciency scores and ranking

Farm Efficiency Position Farm Efficiency Position Farm Efficiency Position

1 0.6962 52 20 0.7435 44 39 0.8009 34

2 0.8308 28 21 0.7316 46 40 0.6359 55

3 0.9293 22 0.8519 23 41 0.9611

4 0.9155 12 23 0.7521 43 42 0.8123 32

5 0.9299 24 0.6139 57 43 0.6264 56

6 0.8432 26 25 0.9198 11 44 0.6635 53

7 0.8461 25 26 0.9670 45 0.9148 13

8 0.7024 49 27 0.9284 46 0.9045 14

9 0.8591 22 28 0.8842 15 47 0.8779 17

10 0.9198 10 29 0.7660 41 48 0.8688 20

11 0.6969 51 30 0.8025 33 49 0.8805 16

12 0.7980 37 31 0.7979 38 50 0.8741 18

13 0.8003 35 32 0.8377 27 51 0.8282 30

14 0.8138 31 33 0.9617 52 0.8722 19

15 0.8286 29 34 0.8616 21 53 0.7951 39

16 0.6383 54 35 0.7141 48 54 0.7630 42

17 0.7187 47 36 0.9246 55 0.7007 50

18 0.9476 37 0.9807 56 0.7334 45

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which can affect the efﬁciency results, asKrokoszinski (2003)pointed out

5.3 Applications of the scores obtained

The interest in efficiency information is immediate for those directly involved in the sector Specifically, engineers and developers can draw significant conclusions, mainly if they are able to interpret the causes of the inefficiency that have been systematized in the previous section In this sense, it is important to point out the effects on costs linked to improvements in the different wind energy learning systems defined byJunginger et al (2005)in order to draw global experience curves Wind farm development (deployment) allows for learning-by-doing, learning-by-using and innovation generated by RD&D (learning-by-searching process), redesigning and upsizing These advances are important not only for the installation of wind farms in new areas, but also for the repowering processes They would also lead to the improved assessment of the on-site wind resource, the use of more efficient wind turbines and enhanced wind farm design and layout

From the regulator's point of view, since the farms' economic remuneration is directly linked to production, in principle linking efﬁciency scores to remuneration would not appear to be of particular use.30 Indeed, in a price support system, a disparity of efﬁciency

among farms could imply the possibility of widely varying profit levels between farms, since the less efficient units possibly mark a threshold of minimum profitability in order to remain in the sector Economic efficiency studies would be required in order to appropri-ately channel this conclusion

The technological impact must be kept in mind when comparing farms installed at varying stages of the technological evolution process, due to the clear advantages in terms of production of those built later and which benefited from the sector's steady technological progress The regulator will assess the value of putting into practice differentiated price support systems for these circumstances, which can be determined in accordance with the efficiency scores In this regard, the enhanced and therefore more efficient technology of modern farms is regularly compensated in production terms by the better wind resources of the older farms, due to their pioneering nature within the sector.31

Efficiency scores can also be useful for the regulator when exploitation authorizations are temporary Once the authorization period has finished, the characteristics of each site –that may be uncertain atfirst–are known, and the efficiency scores can be used as a location reassignment criterion for that operator, or for another that has shown greater efficiency levels in their exploitations In general, the scores can be used to endorse the technical capacity of a technologist or a developer to assess authorization procedures

Finally, it should be pointed out that the average values of the sector efﬁciency scores reveal how close is to an optimum assignment of resources for society This question is of particular interest in terms of sustainability, given the intensive land use of wind technology in comparison with other electricity generation technologies ( Rama-nathan, 2001)

6 Conclusions

DEA and SFA frontier methodologies are able to discriminate in terms of efﬁciency against the productive behaviour of the group of

farms analysed Furthermore, it can be claimed that there is a high correspondence between the results of technical efficiency obtained by means of both methods This fact reinforces the validity of the efficiency scores and, in turn, complements the studies with the specific information that each methodology provides

From a theoretical point of view, the SFA technique questions the basic production relationship in the generation of wind electricity, which links the electricity delivered output with the capital, labour and fuel inputs In this sense, it excludes the labour factor, which would affect DEA methodology, one of the weaknesses of which is its sensitivity to output and input specifications Nevertheless, in practical terms, the non-incorporation of labour does not suppose a serious setback, considering that we have focused onex anteefficiency and also that within this context it is more important for both developers and operators to show efficiency in the other inputs In a cost efficiency study, the labour factor has a very limited impact on this kind of facilities in comparison with the global investment However, this does not imply that this factor is of no interest; on the contrary, it is important in order to keep the wind farms operating

For future studies, in an assessment of the ex post efficiency, especially with regard to operation and maintenance costs, a sufficient number of years in operation (at least more than half the useful life) would provide efficiency scores that would allow us to identify those wind farm operators that have implemented the best operating strategies In this sense, the availability factor is an important reference, and could be an output for this efficiency measure

In relation to wind input, in our models the effects of the quality of wind resources have been included within the fuel input This implies that no operator is penalized for possessing poor resources The economic impact of this is of considerable interest, as according to the method adopted by the regulator for the assignment of wind farm sites, some operators benefit from higher production by using an input that is free, although it is linked to a site with economic value In order to isolate this effect, from a technical efficiency point of view, it could be possible to put forward DEA and SFA models which replace the fuel input for the land occupied by the wind farms For the purpose of cost efficiency analysis, this implies that this input would be included through the value of land At all events, this means that information on the wind resource quality is not required in order to obtain efficiency scores In this sense, and in terms of economic rationality, it would be logical for land prices to reflect the quality of wind resources for electric generation purposes

With regard to the assessment of the results, DEA and SFA methodologies have shown that the average technical efﬁciency is high, exceeding 75% in all cases However, the results must be considered with caution given the limited number of both farms and years studied

SFA methodology has enabled us to confirm the existence of technical inefficiency in the farm sample, with a gamma value of 0.8696 Moreover, it provides parameters that are useful to define the characteristics of the productive environment, such as the scale behaviour On the other hand, DEA methodology enables us to draw individualized conclusions, including those relating to comparison groups for the inefficient units and the slacks, in this case in inputs, detecting that some recently-created farms belong to most of the comparison groups It also tells us that the scale is not a question that significantly affects efficiency, although it reveals the presence of decreasing returns to scale due to the productive logic, with more wake effects between wind turbines as wind farms have more installed capacity This fact leads us to conclude that the use of BCC-O models may be more appropriate for comparisons between farms, as these models present the highest correlation of efficiencies and rank with regard to SFA methodology

This paper has offered an explanation for the efﬁciency scores obtained, establishing the signiﬁcance of the average size of the standard wind turbine used in farms, which in turn shows an

30

Although, in the electric sector, energy distribution and transmission activities are regularly remunerated in many countries in accordance with efﬁciency scores Numerous studies have addressed this topic, such as the one byJamasb and Pollitt (2001)

31

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important correlation with the year of installation This fact indicates technological advances, albeit not in terms of the evolution of each farm over time, as no repowering processes have taken place, but instead in the inclusion of new units in the group of farms—in this respect it must be remembered that setting up a farm implies a high investment inﬁxed assets, with the result that changes in the capital factor are not immediate

Furthermore, we have systematized the inefficiency sources that in general can exist in a wind farm as a productive unit, since this knowledge can help with the interpretation and practical use of the efficiency scores calculated In this sense, the information obtained can be of interest for the installation of future wind farms, in terms of improvements in the technology used, farm design and other questions related toex antedecisions Furthermore, where appropri-ate, and taking into consideration the theoretical background to the methodologies, the efficiency scores can also be used by the sector regulator when establishing incentives or granting exploitation concessions

Future research over longer periods and more observations could lead to the use of alternative DEA and SFA models Within thefield of the inputs and outputs specifications, we could also incorporate variables such as the environmental or socioeconomic impact of farms into the analyses, thereby constituting a wider means of measuring efficiency

Acknowledgments

The authors thank two anonymous referees for their helpful comments, which contributed to clarifying and improving the paper The usual disclaimer applies

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