a stochastic frontier analysis to estimate the …a stochastic frontier analysis to estimate the...
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A stochastic frontier analysis to estimate the relative efficiencyof Spanish airports
Juan Carlos Martın Æ Concepcion Roman ÆAugusto Voltes-Dorta
Published online: 14 January 2009
� Springer Science+Business Media, LLC 2009
Abstract There exists a common belief among researchers
and regional policy makers that the actual central system of
Aeropuertos Espanoles y Navegacion Aerea (AENA) should
be changed to one more decentralized where airport man-
agers could have more autonomy. The main objective of this
article is to evaluate the efficiency of the Spanish airports
using Markov chain Monte Carlo (MCMC) simulation to
estimate a stochastic frontier analysis (SFA) model. Our
results show the existence of a significant level of ineffi-
ciency in airport operations. Additionally, we provide
efficient marginal cost estimates for each airport which also
cast some doubts about the current pricing practices.
Keywords Airport efficiency � Stochastic frontier �Bayesian inference � Markov chain Monte Carlo
JEL Classification C15 � D24 � L93
1 Introduction
Nowadays, airports may be more than essential facilities
for cities or regions. In order to compete globally, regions
need efficient airport infrastructures. Knox (1997) recog-
nizes the important role of airports in changing the local,
regional and national cities’ economic functions by new
emerging nodal points in global commodity chains. In this
context, a few cities will acquire world city status because
of their involvement in linking and shaping whole com-
plexes of commodity chains. In fact, he describes an
interesting process which reinforces this argument. ‘‘By
decentralizing back-office functions to offshore locations,
companies can save even more in labor costs. Several New
York-based life insurance companies, for example, have
established back-office facilities in Ireland, situated con-
veniently near Ireland’s main international airport,
Shannon Airport. The companies ship insurance claim
documents from New York via Federal Express, process
them, and beam the results back to New York via satellite
or transatlantic fiber-optic line’’ (p. 26).
An airport has generally four types of effects on the
economy of the region (Button and Taylor 2002):
1. Primary effects: the benefits of construction or expansion
of the airport, e.g. design of the facility, construction of
terminals and hangars, and the installation of the air
traffic navigation system. There are direct effects (local
employment in construction) and indirect effects (ben-
efits of the wages and other incomes following from this
employment and spend in the region, and tax revenues
available to local governments).
This paper draws on some results from a case study prepared for the
EU Commission (Research project Generalisation of Research on
Accounts and Cost Estimation (GRACE)). We acknowledge support
under the sustainable surface transport priority programme of the 6th
FP for RTD. We also want to express our gratitude to our colleagues
C. A. Nash, H. Link and E. Van de Voorde for helpful comments on
an earlier draft. This paper has been written while Prof. Martın and
Roman were visiting the Institute of Transportation Studies at the
University of California Berkeley. They wish to thank to Samer
Madanat and Mark Hansen for being considerate hosts during their
stay. The usual disclaimer applies.
J. C. Martın (&) � C. Roman � A. Voltes-Dorta
Universidad de Las Palmas de Gran Canaria,
35017 Las Palmas, GC, Spain
e-mail: [email protected]
C. Roman
e-mail: [email protected]
A. Voltes-Dorta
e-mail: [email protected]
123
J Prod Anal (2009) 31:163–176
DOI 10.1007/s11123-008-0126-2
2. Secondary effects: the longer-term effects associated
with the local economic benefits of running and
operating the airport, such as employment involved
in maintaining the facility and handling the aircraft,
passengers and cargo. Again, there are direct and
indirect impacts.
3. Tertiary effects: these longer-term effects stem from
benefits in the regional economy as the result of
companies and individuals having air transport services
at their disposal. This holds particularly true for
employees of high-technology companies, as they fly
1.6 as much as those employed in traditional industries.
4. Perpetuity effects: these very long-term effects refer to
a development in which once started economic growth
in a region becomes self-sustaining and may be even
accelerated. Infrastructure investment, like that in an
airport, may act as a catalyst for such a development.
However, despite these commented benefits it is clear
that not every city can develop a sustainable airport in its
area. So national and regional planners usually have to face
an important dilemma about airport investments: quantity,
location and moment. There is also a trend to privatize
airports. For example, the former British Airports
Authority (now BAA) was privatized by a public flotation
in July 1987. After this experience some other countries
have privatized totally or partially the airports. Today,
these airport operators are a good example of privatized
firms operating in regulated markets. Some studies suggest
that privately owned companies can achieve higher levels
of operational efficiency than its state owned counterparts,
but other are not so conclusive.
Thus, it does not matter if airports are privatized or
not, there are always different stakeholders, viz., regional
planners, regulators or investors who need information on
the cost structure and efficiency of airports. For example,
regional planners need information about the efficiency
of the regional airport to see how they can foster an
improvement in the competitiveness of the region. Regu-
lators need information on the development over time of
an airport’s efficiency in order to constrain its behavior,
especially if the prices of the airports are regulated via price
caps. Investors may be more willing to invest in a relatively
efficient airport, since it may have higher expected profits.
So in summary, given that airports are capital intensive
units, there are many stakeholders who need to be aware of
the cost structure and efficiency of the airports.
The interest in airport performance is not new and it will
be increased in the future. This type of studies can be very
helpful in policy decisions to choose the best framework to
organize the airport system. Especially in those cases
wherein the management of the whole airport network lies
in a single (public) company such as in Spain, AENA
Spanish Airports and Air Navigation; Ireland, Aer Rianta;
Finland, Civil Aviation Administration of Finland; Swe-
den, Swedish Civil Aviation Administration; and Portugal,
ANA Portuguese Airports and Air Navigation.
The aim of this paper is to evaluate the efficiency of
the Spanish airports using Markov chain Monte Carlo
(MCMC) simulation that estimates a stochastic frontier
analysis (SFA) model. Our results show the existence of a
significant level of inefficiency in airport operations.
Additionally, we provide efficient marginal cost estimates
for each airport which also cast some doubts about the
current pricing practices of AENA.
The rest of the paper is organized as follows. The next
section develops the background issues of the model.
AENA, the public corporation that controls and owns the
Spanish airport system, and the data are presented in
Sect. 3. The model with the results is presented in Sect. 4,
and Sect. 5 summarizes the major findings of this study.
2 Models to measure the relative efficiency in airports
Total factor productivity (TFP) and data envelopment
analysis (DEA) have been the two most employed methods
to measure the performance of airports. Stochastic frontier
analysis (SFA) has only been used in very scarce occa-
sions. The choice among them is a weighted decision
between personal beliefs, competence of researchers and
data availability. TFP is the ratio of output over input.
When there is more than one input and/or output, it
requires weights to be specified, which are usually based on
price information. In the airports field, Oum and Yu (2004),
Hooper and Hensher (1997) and Yoshida (2004) have
employed this type of analysis. Nevertheless, this meth-
odology presents a very serious caveat as the differences
between two TFP measures cannot be further decomposed
in technical change, technical and scale efficiency change,
or allocative efficiency. This decomposition requires the
estimation of a production (or cost) frontier. The other
two main approaches are used to construct frontiers, and
therefore their data requirements are considerably higher.
DEA is a non-parametric technique which uses linear
programming to fit a linear surface over the data points. It
is by far the most popular methodology in airport bench-
marking and has been applied in a large number of studies,
such as Parker (1999), Gillen and Lall (1997), Sarkis
(2000), Pels et al. (2001) and Martın and Roman (2001).
DEA presents some advantages related to the identification
of some peer firms to which the rest of firms should be
compared attending to its operational similarity. Addi-
tionally it does not require a functional form or
distributional assumption, as SFA does, for both the fron-
tier and the inefficiency term. However some caveats are
164 J Prod Anal (2009) 31:163–176
123
also present, for example the theoretical restrictions for
production/cost frontiers cannot be easily tested and most
important, the estimation can be affected by noise of many
unpredictable and uncontrollable factors which make it
difficult the obtaining of sensible policy recommendations.
SFA models resolve some of these shortcomings. This
model is based on an econometric method that estimates a
cost frontier as follows:1
Ci ¼ f ðyi;wiÞ þ ui þ vi ð1Þ
where y is the output vector, w is the vector of input prices,
v is the white noise which captures the effects of those
unpredictable perturbations and u is a disturbance term
which is usually interpreted as an indicator of the economic
inefficiency2 of each airport. It is worth noting that all
inefficiency components should follow a one-sided distri-
bution, since they can only take positive values.
Oum et al. (2008) studied the effects of ownership forms
on airports’ cost efficiency by applying stochastic frontier
analysis to a panel data of the world’s major airports.
Barros (2008) analyzed the technical efficiency of UK
airports using a random stochastic frontier model and
ranked the airports according to their productivity for the
period 2000–2005.
Different distributions have been proposed in the liter-
ature, such as the exponential (Meeusen and van den
Broeck 1977); the half-normal (Aigner et al. 1977; Ste-
venson 1980); the gamma (Greene 1990). Battese and
Coelli (1992) introduced a model, in which the firm effects
are assumed to be truncated normal random variables that
can also systematically vary with time.
Coelli et al. (1998) argue that the main advantages of
SFA are as follows:
• It is easy to deal with environment variables.
• It allows conducting statistical tests of hypotheses
concerning any parameter restrictions associated with
economic theory.
• It allows an easier identification of outliers.
However, the estimation results are sensitive to distri-
butional assumptions on the error terms, and the model
requires large samples for robustness. Pels et al. (2003)
used SFA in airports estimating two stochastic production
frontiers, both for air traffic movements (ATM) and air
passenger movements (APM). They used the first predic-
tions as an intermediate input for the second frontier. They
found that European airports were relatively inefficient,
using data from 34 European airports for the period
1995–1997.
SFA models are also based on a flexible3 functional
form for the cost frontier. Of all the flexible forms, the
translog functional form is the one which has been most
frequently used.4 It provides a second order approximation
to any cost structure and allows a great variety of substi-
tution patterns. Regularity conditions5 can be imposed by
linear restrictions to the parameters. The general structure
of the functional form with logged variables is as follows:
lnCðw;yÞ¼aoþX
j
aj lnyjþX
i
bi lnwi
þX
i
X
j
cij lnyi lnwjþ���
þ1
2
X
j
X
h
djh lnwj lnwhþX
i
X
k
qik lnyi lnyk
" #
ð2Þ
The translog function is commonly estimated using also
the cost minimising factor share equations by means of a
seemingly unrelated regression (SURE) (Zellner 1962) by
maximum likelihood estimators. Cost minimising factor
shares can be obtained by applying Shephard’s lemma.
This procedure allows researchers to including (m - 1)
additional equations to the cost function where m is the
number of inputs6 that have been considered in the model
specification. As no additional parameters are included, the
estimation becomes more efficient.
si ¼wiXi
C¼ oC
owi
wi
C¼ o ln C
o ln wi
¼ bi þXm
j¼1
dij ln wj þXs
j¼1
cji ln yj ð3Þ
1 Duality ensures that both production and cost functions give the
same information (Shephard 1953). Cost function estimation also
allows for an easier calculation of marginal costs and economies of
scale (Jara-Dıaz 1983).2 Kumbhakar and Wang (2006) show that, aggregating both technical
and allocative effects produce biased estimations of parameters, scale
and price elasticities and inefficiencies. This method has been
extended taking into account a separation of the economic ineffi-
ciency into two different terms, viz. allocative and technical
inefficiency (Kumbhakar 1997; Kumbhakar and Tsionas 2005).
3 Caves et al. (1980) argue that flexible functional forms are
characterized because they do not impose any prior restrictions on
the first and second order derivatives. For example, although the
Cobb–Douglas cost function is consistent with the theory of
production and costs, it has some rather restrictive properties, as the
elasticity of total cost with respect to output is a constant, no matter
whether the firm is small or large. If this elasticity is less than unity,
then there will be economies of scale for all outputs, and the average
cost schedule will be declining for all outputs as well.4 Jeong (2005) shows in a recent survey on airports cost function
estimation that the majority of the studies have used the trans-
logarithm functional form. However, it can be seen that all the studies
have supposed that airports are efficient without questioning the neo-
classic assumption that all the firms are minimizing costs.5 C must be nonnegative, real valued, nondecreasing, strictly positive
for positive output, and linearly homogeneous and concave in w for
each output vector.6 This is necessary condition in order to avoid the singularity of the
disturbance covariance matrix.
J Prod Anal (2009) 31:163–176 165
123
Additionally, for panel data, it would also be interesting
to account for technological change (Stevenson 1980).
Viewing the time variable time (t) as a proxy for the level
of technological development (Td), so we can incorporate t
into the model by specifying a truncated third-order tran-
slog functional form. Therefore, we must take into account
the following issues: (1) the functional form of the cost
frontier model; (2) the factor share equations in order to
increase the efficiency of estimations; (3) the parameter
restrictions in order to have a well behaved cost frontier
model; and (4) the distributional assumptions about the
inefficiency error term. There are some statistical packages
that have incorporated some routine to treat these problems
empirically. However, Bayesian methods are also more
flexible, and take parameter uncertainty into account in
deriving the efficiency posterior density, as economic
grounds guide us in forming our prior ideas, but they do not
provide us its exact functional form (van der Broeck et al.
1994). In this context, we apply a Bayesian method which
is based on a Markov chain Monte Carlo (MCMC) sampler
following Griffin and Steel (2007).
3 Spanish airports
We estimate, therefore, a technical efficiency stochastic
frontier for a long run multiproduct cost function system in
Spanish airports’ industry using Bayesian methods. The data
have been obtained from the Spanish Entity that controls
and owns the assets of the Spanish airport system AENA
(Aeropuertos Espanoles y Navegacion Aerea). AENA is a
public owned company that manages the total airport system
and air traffic control in Spain, being the organization in the
European Union that operates the largest and the most
geographically diverse airport network.
The structure of the Spanish airports is really diverse,
and there are different types of airports depending on the
traffic they handle. Madrid/Barajas and Barcelona are the
primary airports with the highest traffic turnover. They are
the main hub airports for international and domestic flights.
Other important airports are dominated by a high per-
centage of non-scheduled tourist flights. These are mainly
located on the Canary Islands, Balearic Islands and
Malaga. Although these tourist-dominated airports share
common features with respect to peak and off-peak peri-
ods, they also have significant seasonal differences. The
Balearic and Malaga airports have a peak concentration
during the summer months. Meanwhile, the traffic in the
Canary Islands is more evenly distributed throughout the
year. There are medium-sized airports in which the normal
traffic consists of scheduled domestic and European flights,
with connections to Madrid and Barcelona being the pre-
dominant characteristic.
Our sample includes 37 Spanish airports that have dif-
ferent size. We used data of the Spanish airports formed by
a symmetric panel for a seven year period from 1991 to
1997 with 259 observations. We measure output with two
variables: the air traffic movements (ATM), and the work
load units (WLU)7 which are defined by the number of
passengers and the number of tons of cargo transported in
the airport. The input variables are classified according to
the type of expenditures and were divided as follows:
labour, capital and materials. We have also considered the
full time equivalent number of employees as a variable in
order to obtain the labour input price for each airport. The
rest of input prices have been more problematic to estimate
and we have employed a standard normalization proce-
dure dividing the total expenses by ATMs and WLUs,
respectively.
Jara-Dıaz (1983) explains clearly how aggregation of
output over any dimension (commodity, time, or space)
involves a loss of information associated with the transport
processes generated by the decisions of the managers of
transport firms. As is evident, spatial aggregation destroys
information on the geographical context of the origin–
destination system in which a transport system operates.
Aggregation of output over time may cause distortions
when estimating cost functions if periods of distinctive
mean flows are being averaged. Finally, commodity
aggregation may affect cost estimation since the (mini-
mum) cost of moving the same aggregate weight or volume
will generally depend on the composition of that output.
We sustain here that the aggregation of inputs or the cal-
culus of input prices with some output aggregate or other
conventional input multi-lateral indices can be also prob-
lematic. However, previous literature has not dedicated the
same emphasis to this issue.
Additionally, in order to provide an easy interpretation
of parameter estimates, all explanatory variables8 are
defined in deviations with respect to an approximation
point. For example, we have calculated and normalized the
values of ATMs as follows:
atm ¼ lnðATMÞ � lnðATMÞ
As we use a panel data to estimate our models, all the
expenses may be contaminated by the effect of price
variation, both temporal and spatial. For this reason, we
deflate this variable by the general consumer prices index
of the National Statistics Agency (INE). These variables
7 WLU is equivalent to one passenger or 100 kg of cargo.8 This is a usual practice which allows a simple calculation of
outputs’ cost elasticities and the Hessian values of the cost function,
which are essential in identifying mean economies of scale (S) and
cost subadditivities (Jara-Dıaz 1983). In our case, we have logged and
normalized all the variables except time, which is not logged but only
deviated.
166 J Prod Anal (2009) 31:163–176
123
have a clear meaning and the fact that the source of the
data is AENA, clearly helps in reducing the problems of
comparability which are present in other studies which
analyze the performance of airports internationally. This
comment is especially true in reference to the capital costs.
Some differences in accounting practices usually difficult
the comparison of these variables in the studies of airport
with distinct nationalities or type of ownership. We have
tried to expand our sample period to include more recent
years. However, AENA is reluctant to allow us to update
this information because an important debate has arisen
in the recent policy arena regarding what role the
Autonomous Regions of Spain may play in the control
and management of the airports located in each of the
territories of Spain.
4 Model specification and results
The basic model specification relates the airport’s total
costs (TC) to a minimum cost frontier, which depends on
output quantities (atm & wlu) and input prices of capital,
materials and personnel (wc, wm & wp). We use a sec-
ond-order translog specification including all second order
interactions between the aforementioned variables plus
the first and a second order interaction between these
variables and the time t. Additionally, in order to include
the maximum information to the system, all the three
(capital, materials and personnel) factor share equations
are included, as the flexibility of the Bayesian approach
does not oblige researchers to exclude one share equation
of the system. Linear homogeneity in w is imposed using
the common linear restrictions on the parameters. The
symmetry conditions on the Hessian matrix are also
imposed.
Regarding the Bayesian structure of the model, we fol-
low Griffin and Steel (2007) where the dependent variable
is said to be normally distributed, with the above men-
tioned frontier as mean and r2v as variance. Besides,
inefficiencies uiare assumed to be exponentially distributed
with mean k�1:
yi�Nðaþ x0ibþ ui; r2vÞ ð4Þ
ui� expðkÞ ð5Þ
Prior distributions are assigned to the parameters, such as
the multivariate normal to the vector of regressors b, a
gamma distribution (a0,a1) for the white noise precision
ðr�2v Þ; and another exponential for the k parameter which
allows us to impose our priori ideas about the mean
efficiency ð�rÞ in the Spanish airport industry. Finally, firm-
specific efficiency estimates (ri) are calculated as functions
of the inefficiency terms.
b�Nð0;RÞr�2
v �Gða0; a1Þk� expð� log �rÞri ¼ expð�uiÞ
ð6Þ
In our case, a stochastic translog cost frontier model is
formulated using a 0.75 prior efficiency for the Spanish
airport industry.9 Other priors about the precision and the
specifications for the parameters need also to be included.
In this paper, we have followed the suggestions made by
Griffin and Steel (2007), that is, the values of the param-
eters of the gamma distribution for the white noise are set
at 0.001 and the prior distribution for the beta parameter
vector was also set at 0.01. This ensures very diffuse prior
information.
Of course, the speed of convergence of the chain is
affected by these values. Faster convergence is obtained
with values which allow larger posterior densities. Once,
the model, data and initial values have been entered, the
model is compiled to perform an MCMC algorithm for
sampling from the posterior distribution. There are several
options regarding burn-in, multiple chains and thinning of
the chain. In Table 1, we present the results of a chain
which was run with a burn-in of 10,000 iterations, with
20,000 retained draws and a thinning to every 5th draw.
The reporting results are the posterior mean, median and
standard deviation with a 95% posterior confidence inter-
val. Estimates show good performance and significance of
major parameters,10 time variable estimates point out into
the existence of a small degree of technical progress (see
Appendix 1 for density pictures of all the parameters).
Another very interesting feature of this approach
regarding its flexibility is that the model can be used to
obtain a logical node which is function of the estimated
parameters. Thus, we can obtain the same summary or even
the posterior density graph for any defined stochastic node.
As an interesting useful example, we can calculate the
inverse of the sum of the first order output parameters
beta(2) and beta(3). This node gives indication on the mean
degree of the returns to scale in the industry. As we can see
in Fig. 1, all probability mass lies in the increasing returns
to scale (IRS) zone with an average figure of 1.296, which
clearly rejects the assumption of constant returns to scale
(CRS). This represents an alternative approach to the
classic Wald Coefficient tests obtained with classical
9 This prior informative value is based on previous studies carried out
with this database (Martın and Roman 2001, 2006, 2007).10 Following a Bayesian approach, it is enough to observe whether 0
is included or not in the interval. However, the figures of the posterior
density kernels can help researchers in order to decide whether a
parameter is significant or not even in the cases in which 0 is included
in the interval.
J Prod Anal (2009) 31:163–176 167
123
econometric procedures, and give us a better idea on how a
confident interval looks like.
In stochastic frontier analysis, the efficiency estimates of
each airport are usually a very important object of interest.
Airport-specific efficiencies have been generated by the
sampler and their full posterior distributions are available.
Our model presents an overall 83% of average efficiency,
which is a bit higher than expected due to previous analysis
in which we study the performance of the airports using
data envelopment analysis (DEA).11 Table 2 shows the
point estimation of economic efficiencies for each indi-
vidual airport. It can be seen that economic inefficiencies
are quite significant for the Spanish airports during this
period. Whether this economic inefficiency comes from
allocative or technical inefficiency cannot be answered
with this type of models. However the resolution of this
type of uncertainty (the problem of Green) is out of the
scope of this paper. What our model shows is that eco-
nomic inefficiencies are significant and they need to be
considered in order to have better estimations of the rest of
parameters. The results indicate that production factors
could be employed more efficiently (technical efficiency)
and/or the variable input mix is not optimal, and costs
could therefore be reduced through a more efficient allo-
cation of inputs (allocative efficiency).
It is especially significant the very poor efficiency that
presents Cordoba—the smallest airport of our sample with
a 27% of average efficiency. Murcia and Vitoria are also
two airports which present a very poor performance with
their 95% confident interval lying under the sample mean
efficiency. Table 2 shows the level of efficiency of each of
the Spanish airports using different distributions to address
the inefficiency error term. In Appendices 2 and 3, we
present both a box plot of all the efficiencies of the airports
included in the sample and graphs of posterior densities.
These figures are very useful when one compares the
performance of the Spanish airports. It is interesting to
Table 1 Cost frontier parameter estimates
Node Mean SD MC error 2.5% Median 97.5% Start Sample
constant beta[1] 13.3100 0.0387 0.0008 13.2300 13.3100 13.3800 10,001 20,000
atm beta[2] 0.2954 0.0877 0.0015 0.1180 0.2964 0.4635 10,001 20,000
wlu beta[3] 0.4776 0.0726 0.0012 0.3380 0.4771 0.6219 10,001 20,000
wc beta[4] 0.3387 0.0112 0.0001 0.3166 0.3387 0.3608 10,001 20,000
wm beta[5] 0.2009 0.0111 0.0001 0.1792 0.2009 0.2227 10,001 20,000
wp beta[6] 0.4604 0.0112 0.0001 0.4384 0.4602 0.4826 10,001 20,000
atm*wc beta[7] 0.0833 0.0455 0.0004 -0.0053 0.0829 0.1737 10,001 20,000
atm*wm beta[8] -0.0898 0.0437 0.0003 -0.1756 -0.0897 -0.0038 10,001 20,000
atm*wp beta[9] 0.0065 0.0379 0.0003 -0.0677 0.0066 0.0809 10,001 20,000
wlu*wc beta[10] -0.0582 0.0370 0.0003 -0.1305 -0.0583 0.0141 10,001 20,000
wlu*wm beta[11] 0.1216 0.0380 0.0003 0.0472 0.1215 0.1960 10,001 20,000
wlu*wp beta[12] -0.0688 0.0326 0.0003 -0.1322 -0.0691 -0.0048 10,001 20,000
wm*wc beta[13] -0.0665 0.0284 0.0002 -0.1223 -0.0665 -0.0107 10,001 20,000
0.5*wm*wm beta[14] 0.1248 0.0343 0.0003 0.0574 0.1249 0.1922 10,001 20,000
0.5*wc*wc beta[15] 0.1078 0.0340 0.0003 0.0416 0.1079 0.1750 10,001 20,000
wm*wp beta[16] -0.0701 0.0336 0.0003 -0.1349 -0.0702 -0.0046 10,001 20,000
wc*wp beta[17] -0.0273 0.0338 0.0003 -0.0926 -0.0273 0.0386 10,001 20,000
0.5*wp*wp beta[18] 0.1470 0.2356 0.0017 -0.3161 0.1465 0.6066 10,001 20,000
0.5*atm*atm beta[19] 0.3016 0.1382 0.0024 0.0304 0.3033 0.5716 10,001 20,000
0.5*wlu*wlu beta[20] 0.2453 0.0780 0.0008 0.0938 0.2454 0.3982 10,001 20,000
atm*wlu beta[21] -0.2536 0.0990 0.0014 -0.4485 -0.2541 -0.0593 10,001 20,000
time beta[22] -0.0117 0.0073 0.0001 -0.0261 -0.0116 0.0025 10,001 20,000
wc*t beta[23] 0.0020 0.0063 0.0000 -0.0103 0.0021 0.0143 10,001 20,000
wm*t beta[24] -0.0005 0.0057 0.0000 -0.0119 -0.0005 0.0107 10,001 20,000
wp*t beta[25] -0.0040 0.0073 0.0001 -0.0183 -0.0040 0.0104 10,001 20,000
11 Studying the efficiency of the container port industry, Cullinane
et al. (2006) found a high degree of correlation between the efficiency
estimates derived from DEA and SFA models, and concluded that
results are relatively robust to the DEA models applied or the
distributional assumptions under SFA. Nevertheless, with the excep-
tion of the model based upon the assumption of a half-normal
distribution, the average efficiency estimates derived from SFA yield
higher efficiency scores than those from the DEA models. The
comparison between both methods is out of the scope of this paper but
it can be analyzed in the future.
168 J Prod Anal (2009) 31:163–176
123
remark, that we have obtained a positive correlation
between profits and efficiency. Related to this point, it is
also important to recognise that the estimated efficiency
scores may also be a function of the pressure or incentives
that exist upon management in order to be efficient. So it
seems that airports which cross-subsidize the whole system
present upper levels of efficiency. This result could explain
why airports which are commercially viable are more
efficient than those which are not.
A simple comparison between two major groups in our
sample, the big airports with more than a million annual
passengers and the rest of the airports, will again show the
flexibility of the Bayesian approach. Results can be pre-
sented in such a way that allows us to check whether some
group presents a better performance regarding its level of
efficiency. Posterior densities are shown in Fig. 2, and it can
be seen that the group of the bigger airports presents a
significant better performance. These results are in con-
cordance with previous studies, as major airports benefit
from scale economies and hubbing ‘‘activities’’. However,
the group of small airports presents some peculiar disad-
vantages such as a very low level of outsourcing in all those
activities which are not considered ‘‘core’’ activities, e.g.,
ground handling, commercial activities and cleaning ser-
vices. While SFA do not identify the specific causes of why
inefficiencies exist, their results are usually used as the basis
for the analysis of relationships between the estimated
efficiency estimates and other more structural characteris-
tics. In this sense, the efficiency estimates can be analyzed
with the extent of outsourcing practices of the airports
under study. In fact, the final purpose of these studies is to
inform policy makers or stakeholders on the provision or
implementation of appropriate incentives or regulatory
instruments for enhancing the performance of airports.
Now we explore the problem of airport financing ana-
lyzing the estimation of efficient marginal costs for each
airport. The full airport charging system is also scheduled
by AENA which imposes little variation on landing or
passenger charges in order not to discriminate in a signif-
icant way according to the specific characteristics and costs
of each airport. On one hand, some politicians and AENA
managers defend the network system because it holds the
respectable principles of equity and solidarity between all
the Spanish regions. On the other hand, this cross subsi-
dization may be hiding and burdening the development of
other more successful locations where airport managers are
not free to negotiate fare agreements with low-cost carriers,
so they cannot compete in order to attract more traffic to
their regions.
Individual estimates of efficient marginal costs for both
ATM and WLU are presented both in Fig. 3 and Table 2.
Mathematically, our marginal cost estimates are calculated
according to the predicted efficient costs (that is the inef-
ficiency behaviour of the airports is not considered) instead
of actual costs:
oC
oyi¼ o ln C
o ln yi
C
yið7Þ
Figure 3 also shows the presence of important economies
of scale, revealing that: (1) marginal cost pricing is not
financially viable, therefore, network sustainability12
requires of a strong public subsidization; and (2) a very
rigid pricing scheme does not seem suitable for the Spanish
airports.
The economies of scale are not exhausted at any output
level, and we also observe some slight degree of techno-
logical progress. This technological progress can be seen in
the value and the density graph of the parameter b22.
Regarding long-run efficient marginal cost estimations,
some reasonable values are obtained for ATMs and WLUs
in the average airport, which are 175.45 and 5.88 euros,
respectively. These figures are difficult to compare with
other findings of previous studies. Link et al. (2009)
reported a marginal labour cost of an extra aircraft move-
ment of 22.6 euros, a result that is of the same magnitude
as earlier findings for US airports. Morrison and Winston
(1989) report for maintenance, operation and administra-
tion of US airports a marginal cost of $22.09 per aircraft
which after conversion is 32.97 euros in 2000 prices. Of
course, these figures are not directly comparable to the
ones presented in this paper because capital and materials
have also been included in our study.
Fig. 1 Scale economies in
Spanish airports
12 We refer here to sustainability in a dual till sense, i.e., the
aeronautical activities should generate enough revenues to cover
aeronautical costs.
J Prod Anal (2009) 31:163–176 169
123
Finally, we explore how different distributions to mea-
sure the inefficient behaviour of airports affect the results.
Coding any feasible inefficiency distributions for the dis-
turbance term such as half or truncated Normal or Gamma
is very simple and intuitive, therefore, we refer directly to
Griffin and Steel (2007) for further details on code and
prior distributions. Final estimates for three different
selected models are presented in Table 2.13 It can be seen
that, in spite of the existence of differences in the mean
average efficiency, airport rank orderings remain almost
Table 2 Spanish airport marginal costs and efficiency level
No. Airport Pax Distribution of inefficiency Marginal costs
Exponential Half normal Gamma Euros
103 Mean SD Mean SD Mean SD atm wlu
1 Alicante 4,398 0.84 0.07 0.77 0.08 0.87 0.08 84.15 1.78
2 Almeria 714 0.79 0.07 0.70 0.07 0.82 0.08 136.70 3.27
3 Asturias 595 0.84 0.07 0.73 0.08 0.87 0.08 114.48 3.55
4 Badajoz 18 0.96 0.03 0.95 0.04 0.97 0.03 248.87 15.10
5 Barcelona 14,561 0.84 0.10 0.71 0.11 0.86 0.10 72.90 1.22
6 Bilbao 1,970 0.93 0.05 0.84 0.08 0.94 0.05 88.84 1.98
7 Cordoba 1 0.28 0.08 0.35 0.09 0.27 0.08 1063.62 74.41
8 Fuerteventura 2,440 0.96 0.03 0.92 0.06 0.97 0.03 76.76 1.78
9 Girona 507 0.77 0.08 0.68 0.09 0.80 0.09 257.29 5.73
10 Gran Canaria 7,927 0.85 0.08 0.75 0.08 0.86 0.08 88.66 1.60
11 Granada 447 0.79 0.07 0.69 0.07 0.82 0.08 148.71 4.08
12 Hierro 97 0.87 0.07 0.78 0.08 0.90 0.07 214.84 6.48
13 Ibiza 3,528 0.91 0.06 0.84 0.08 0.93 0.06 81.52 1.47
14 Jerez 453 0.86 0.07 0.76 0.08 0.88 0.07 118.87 5.06
15 La Coruna 398 0.84 0.07 0.74 0.08 0.87 0.08 120.85 3.73
16 La Palma 696 0.91 0.06 0.81 0.08 0.93 0.06 117.89 2.81
17 Lanzarote 4,005 0.95 0.04 0.92 0.06 0.96 0.04 58.08 0.92
18 Madrid 23,122 0.81 0.10 0.73 0.12 0.83 0.11 87.89 1.35
19 Malaga 7,190 0.79 0.08 0.71 0.07 0.81 0.09 93.38 1.87
20 Melilla 352 0.90 0.07 0.78 0.09 0.92 0.07 100.50 1.84
21 Menorca 2,232 0.92 0.06 0.84 0.08 0.93 0.06 93.17 1.74
22 Murcia/San Javier 108 0.67 0.07 0.59 0.07 0.69 0.08 170.06 5.85
23 Palma De Mallorca 16,449 0.87 0.08 0.81 0.10 0.88 0.08 76.88 1.54
24 Pamplona 288 0.79 0.07 0.68 0.07 0.82 0.08 101.55 2.81
25 Reus 518 0.94 0.05 0.88 0.08 0.95 0.05 76.04 2.92
26 Salamanca 44 0.88 0.08 0.80 0.12 0.90 0.09 413.94 13.66
27 San Sebastian 173 0.81 0.07 0.72 0.07 0.84 0.08 170.49 4.21
28 Santander 204 0.73 0.07 0.64 0.07 0.76 0.08 194.98 4.46
29 Santiago 1,283 0.72 0.07 0.62 0.06 0.75 0.08 113.62 2.32
30 Sevilla 1,543 0.78 0.07 0.67 0.07 0.81 0.08 169.42 4.07
31 Tenerife Norte 2,042 0.88 0.07 0.75 0.08 0.91 0.07 83.54 1.55
32 Tenerife Sur 7,438 0.89 0.07 0.84 0.08 0.91 0.07 78.90 1.38
33 Valencia 1,912 0.82 0.08 0.69 0.08 0.85 0.09 105.03 2.34
34 Valladolid 191 0.93 0.05 0.87 0.08 0.95 0.05 94.04 2.42
35 Vigo 556 0.87 0.07 0.76 0.08 0.89 0.07 126.96 2.82
36 Vitoria 145 0.62 0.06 0.53 0.06 0.64 0.07 137.38 4.52
37 Zaragoza 244 0.75 0.08 0.63 0.08 0.78 0.09 108.68 3.74
Average airport 2,940 0.83 0.07 0.74 0.08 0.85 0.07 175.45 5.88
13 Note that exponential distribution was chosen as it allows the
easiest implementation of prior ideas and direct interpretation of
parameter estimates was straightforward.
170 J Prod Anal (2009) 31:163–176
123
unaltered no matter what distribution is used for addressing
the inefficiency term. We performed three Spearman Rank
Correlation Tests obtaining 71% as the lower value.
Therefore, in our case, and taking into account the ‘‘rela-
tive’’ nature of how to measure the efficiency in airports
performance, it can be said that the election of any specific
distribution does not have any major influence in airport
benchmarking.
5 Conclusions
In this paper, we have reviewed the principal aspects of the
methodology that has been applied in our empirical exer-
cise. Flexibility has been cited as one of the principal
advantages regarding the implementation of basic infor-
mation structures promoting the use of Bayesian methods
for making inference in SFA models. We proposed a
translog cost function to evaluate economic inefficiencies,
economies of scale and even marginal costs in the Spanish
airport industry.
We provided an empirical application of this model to
study important industry parameters in the airport industry
of Spain, using a balanced panel database for 37 com-
mercial airports observed over the period 1991–1997.
These airports are controlled, owned and managed by
AENA and are characterised by a lack of incentives on the
part of the agents who manage commercial airports to
adopt the criterion of cost minimisation.
We estimated a stochastic frontier model by imposing
three different distributions in order to address the ineffi-
ciency component in the structure of the error term. Results
indicate that economic inefficiencies range in the interval
15–26% for the average airport. It has also been shown that
the use of different distributional assumptions on the error
component which encapsulated the inefficient behaviour of
airports does not produce any significant differences with
respect to the benchmarking of Spanish airports. We also
carried out a simple comparison trying to analyze whether
size plays a role regarding the performance between big
and small airports, and results show that bigger airports are
more efficient.
The actual regulation of operations of Spanish airports
does not have adequate incentives to induce CEOs of each
individual airport to perform efficiently. It is a system
where cross-subsidies exist because all the airports are
operated under the control of a single entity. In fact, the
presence of this anachronistic regulatory body ‘‘AENA’’
could underline the existence of these inefficiencies. The
existence of some airports is based more on a statutory
Fig. 2 A comparison
of the level of efficiency
of the Spanish airports
according to its size
R2 = 0.7396
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00
0 3,000,000 6,000,000 9,000,000 12,000,000 15,000,000 18,000,000
wlus
MC
Fig. 3 Stochastic frontier
marginal costs (WLU)
J Prod Anal (2009) 31:163–176 171
123
pre-condition or the status quo. There is not any social
justification for its existence with the exception of some
airports located in the islands. Some politicians and AENA
managers defend the network system because it holds the
respectable principles of equity and solidarity between all
the Spanish regions.
The estimation of efficient marginal costs for each
airport has been used to analyze the airport financial sus-
tainability and the adequacy of the pricing scheme adopted
by AENA. It has been shown that the imposition of little
variation on landing or passenger charges in order not to
discriminate in a significant way according to the specific
characteristics and costs of each airport can only be justi-
fied by social cohesion or political pressures. However, the
existing situation of cross subsidies may be hiding and
burdening the development of other more successful
locations where airport managers could be free to negotiate
fare agreements with low-cost carriers, attracting more
traffic to their regions. Therefore, the actual rigid pricing
scheme does not seem suitable for the Spanish airports.
We showed the existence of important economies of
scale which are not exhausted at any output level, as well
as, some slight degree of technological progress. Regarding
long-run efficient marginal cost estimations, some reason-
able values are obtained for ATMs and WLUs in the
average airport, which are 175.45 and 5.88 euros,
respectively.
Regarding other technical issues, we argued first that
obtaining good financial information about airports is
usually very difficult, and this difficultness is even more
acute if we need the data to be homogeneous and compa-
rable. Our database does not have any problem of
homogeneity and comparability as long as all figures come
from a single national entity like AENA, which applies the
same accounting and valuation policies in all the airports
included in the sample. Such a plethora of extremely good
and actualised data is expected to be available for future
research. The second issue concerns the capital prices,
whose calculation should be more related to capital mea-
sures than to output variables. And thirdly, in order to
properly account for systematic cost differences, and due to
the extreme complexity of the airport activities, some
hedonic approach could also be carried out by enriching the
specification with indicators such as regional location, slot
coordination, percentage of long haul traffic or percentage
of hubbing traffic.
Appendix 1
Posterior density plots of cost frontier parameters.
172 J Prod Anal (2009) 31:163–176
123
Appendix 2
Box plot of Spanish airports’ efficiency level (exponential
distribution).
[1][2]
[3][4] [5] [6]
[7]
[8]
[9][10]
[11]
[12] [13] [14] [15] [16] [17] [18][19]
[20] [21]
[22]
[23]
[24]
[25] [26][27]
[28][29]
[30]
[31] [32][33]
[34] [35]
[36]
[37]
box plot: eff
0.0
0.25
0.5
0.75
1.0
J Prod Anal (2009) 31:163–176 173
123
Appendix 3
Posterior density plots of efficiency level (exponential
distribution).
174 J Prod Anal (2009) 31:163–176
123
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