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: jcmartin@daea.ulpgc.es

C. Roman

e-mail: croman@daea.ulpgc.es

A. Voltes-Dorta

e-mail: avoltes@becarios.ulpgc.es

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

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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

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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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