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]
Trang 1Measurement of productive ef ficiency 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 Coruña, 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 5 May 2009
Received in revised form 9 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 essentially ex ante efficiency 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
© 2010 Elsevier B.V All rights reserved
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
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.
2
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 this figure will rise to more than 6000 MW by the end of 2012.
0140-9883/$ – see front matter © 2010 Elsevier B.V All rights reserved.
Contents lists available atScienceDirect
Energy Economics
j o u r n a l h o m e p a g e : w w w e l s ev i e r c o m / l o c a t e / e n e c o
Trang 2the 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 do not break the
principle whereby, with the same those weights, no other unit
overcomes the maximum reachable value of efficiency, which is equal
to 1 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 between ex ante and ex post efficiency
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 single firm 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.
5 For an overview of the concepts related to efficiency, and the main methods used
in its evaluation, see Coelli 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
7
See Gong and Sickles (1992) and Ruggiero (2007) , from a theoretical perspective, and as a practical application the comparison of methods made by Hjalmarson et al (1996)
8
See Mortimer (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 highlight Seitz (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.
10 For an overview of these works, in the case of the DEA methodology see Zhou et al (2008) , who analyse applications in the energy and environmental fields In relation to econometric studies, see the survey of Ramos-Real (2005) And for a brief revision of
Trang 3Barros 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: an ex ante level, 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, an ex post level, 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 of electrical energy delivered to the grid, while the inputs would be the capital, which basically includes the wind turbines, the labour, and the fuel, 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:
where E is the electrical energy, K the capital, L the labour and F the 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:
2 ×ρ × S × v3
ð2Þ
whereρ is the air density, S the interposed surface and v the 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
14 A 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
Wind farms were excluded from the sample for a given year if during that year
Trang 44.2 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 do 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 do not believe that there is any
inconvenience in adopting the option of strong disposability both in
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 = 1
xjλj; y≤ ∑n
j = 1
yjλj;λj≥0; j = 1; 2; :::; n
with the CCR model
EPV ðx; yÞ : x≥ ∑n
j = 1
xjλj; y≤ ∑n
j = 1
yjλj;λj≥0; ∑n
j = 1 λj= 1; j = 1; 2; :::; n
with the BCC model
where x is the inputs vector, y is the outputs vector andλ is 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 1 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 four cross-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 a pooled 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 use averaged 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 2 and 3
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 1
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 supposed ρ=1.22 kg/m 3 , taking into account that the group of wind farms face analogous general weather conditions and have a similar altitude (500–800 m).
16 That 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
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
The first DEA application of this type made it possible to measure the efficiency evolution of different units of aircraft maintenance for the United States Air Force
Trang 5CCR-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 do not exceed 70% of efficiency with any
option, afigure which drops to five 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 do 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 2
CCR-O efficiency scores.
Farm Cross-section Pooled Averaged Farm Cross-section Pooled Averaged Farm Cross-section Pooled Averaged
20
In fact, the most efficient thing would be to install just one wind turbine at the
Trang 6In 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
where y is the output, x is the inputs vector,β is a vector of unknown
production parameters andε is a random disturbance which includes
statistical noise (v) and technical inefficiency (−u) As for the
subindexes, i denotes each one of the wind farms (i = 1, 2, , 57)
and t the 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, where f (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 the ex ante efficiency 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 do 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 (variable u): 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 4
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+β4x21+β5x22+β6x23
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 of x1and x3were 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 ante efficiency measure under study, because this productive factor plays the key role during the operating and maintenance phase The x1 square was significant at 10%, and the interaction term between x1 and x2was significant at 5%
Table 3
BCC-O efficiency scores.
Farm Cross-section Pooled Averaged Farm Cross-section Pooled Averaged Farm Cross-section Pooled Averaged
21 In this sense, the DEA analysis of the previous section reinforces this choice.
22 On the other hand, note that, as Kumbhakar 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
Trang 7We contrasted the null hypothesis that x2, the quadratic terms and
the interaction terms could be supposed jointly equal to zero,
producing a p-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
and x3) would be adequate This Cobb–Douglas function24would be
expressed by:
The main results of this estimate are shown inTable 5 The Wald
and z statistics 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 6 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 2 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)
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 (ư0.6064) 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 + 0:0530 Time trend + 0:0304 Age
0:07
U = 0:3617 + 0:0108Time trendư0:0002Unitary surface
4:30
The results indicate that the time trend variable is not significant.28 The other two variables reveal a certain explanatory power, with a
Table 4
Descriptive statistics of the variables used in the SFA model.
Standard deviation 0.4348 0.3982 0.4764 0.4510
24
This function (with only capital and fuel as inputs) resembles the engineering
approach of Cowing (1974)
25 Gamma is the proportion of the total variance of ε (ε=error term=vưu) that is
due to the inefficiency term (ưu).
26 This 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.
27 Barros and Peypoch (2008) have carried out recent and innovative research in this field.
28
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.
Trang 8higher t-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 a t-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
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 do 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 5
Time-invariant random effects model, 2 inputs.
Log likelihood 143.7063 Wald chi2(3) = 1026.84
ProbNchi2=0.000
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
Table 6
SFA efficiency scores and ranking.
Trang 9which 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 on ex ante efficiency 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
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 by Jamasb and Pollitt
(2001)
31
On this question, see Junginger et al (2005) In the case of the Galician farms this
fact is endorsed with a correlation of 0.4492 between the farms' age and the wind
Trang 10important 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 to ex ante decisions 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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