cost and revenue inefficiencies in the european railways
TRANSCRIPT
COST AND REVENUE INEFFICIENCIES
IN THE EUROPEAN RAILWAYS*
Pedro Cantos, José M. Pastor and Lorenzo Serrano**
WP-EC 2002-10
Correspondence to P. Cantos: Universitat de València. Edificio Departamental Oriental. Campus dels Tarongers, s/n. 46022 Valencia (Spain). Tel.: 34 96 382 87 87 / Fax: 34 96 382 82 49 / E-mail: [email protected].
Editor: Instituto Valenciano de Investigaciones Económicas, S.A.
Primera Edición Mayo 2002
Depósito Legal: V-1779-2002
Los documentos de trabajo del IVIE ofrecen un avance de los resultados de las investigaciones económicas en curso, con objeto de generar un proceso de discusión previo a su remisión a las revistas científicas.
* The authors acknowledge the helpful comments and suggestions of an anonymous referee. The authors also wish to thank the CICYT SEC98-0895 and the Generalitat Valenciana GV99-103-1-08 for financial support. ** P. Cantos: Universitat de València; J.M. Pastor y L.Serrano: Universitat de València and Ivie.
1
COST AND REVENUE INEFFICIENCIES IN THE EUROPEAN RAILWAYS
Pedro Cantos, José M. Pastor and Lorenzo Serrano
A B S T R A C T
This study analyses cost and revenue inefficiencies for a sample of European railway companies. On the basis of a DEA model we calculate cost and revenue inefficiencies, decomposing them into inefficiencies of a technical or allocative type. It is observed that inefficiencies in revenues are greater than those in costs, indicating that the study of inefficiencies in costs is only a partial analysis of the problem. Also, technical inefficiencies are greater than the allocative type. Finally, the most independent companies, with least external intervention in their decisions, are also the most efficient in both costs and revenue. Keywords: Cost Inefficiency, Revenue Inefficiency and European Railways.
R E S U M E N Éste trabajo analiza las ineficiencias en costes y en ingresos de una muestra de
compañías ferroviarias europeas. Los indicadores de eficiencia en costes y en ingresos se calculan utilizando la técnica DEA y se descomponen en sus en ineficiencias técnicas y asignativas. Los resultados indican que las ineficiencias en ingresos son mayores que las ineficiencias en costes, indicando que el estudio de las ineficiencias en costes constituye un análisis parcial del problema. Asimismo, las ineficiencias técnicas son mayores que las de tipo asignativo. Finalmente, las compañías más independientes, con menor intervención externa en sus decisiones, son también las mas eficientes en costes y en ingresos. Palabras clave: Ineficiencias en costes, ineficiencias en ingresos y Compañías ferroviarias europeas.
2
1. Introduction
In recent years several studies have evaluated changes in the productivity and
efficiency of European railway companies. Oum et al. (1999) give a wide ranging
review of the different studies that have evaluated the productivity and efficiency of
railway companies. The techniques used have been diverse. Oum and Yu (1994)
evaluate the changes in technical efficiency for a sample of European railway
companies using a non-parametric approach. Cowie and Riddington (1996) combine
different techniques in the estimation/calculation of efficiency levels. Gathon and
Pestieau (1995) and Cantos and Maudos (2000) estimate respectively production and
cost functions of a stochastic nature which allow advances in productivity to be
decomposed into technical change and changes in efficiency. Similarly, Cantos et al.
(1999) obtained, on the basis of non-parametric techniques, indices of productivity
growth that are also separated into technical change and efficiency.
One result common to these studies is that during the last two decades there have
been significant improvements in productivity, explained basically by technological
advances rather than by the better management or greater efficiency of the companies.
For this reason, one of the recommendations deriving from these studies is to promote
improved management of the companies, since this is a potential source of productivity
growth. Taking as reference the study by Cantos et al. (1999), figure 1 shows how
during the 70-95 period, and particularly, in the 82-95 sub-period, the productivity of
the railway industry grew notably. However, it has been observed that despite these
increases in productivity, the companies have been incapable of improving their
financial results. On the contrary - in most cases the financial losses during this period
grew substantially (see figure 2). In recent years there has also been great concern on
the part of the European Commission and the EU countries themselves to solve the
financial problem of this sector.
3
Figure 1. TFP evolution
Source: Cantos et al. (1999).
Figure 2. Accounting losses
(in millions of $US of 1990)
(*) Data refers to a sample ot seventeen European railways. Data for the period 1970-73 does not include
BR.
0,8
0,9
1
1,1
1,2
1,3
1,4
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
-2000-1800-1600-1400-1200-1000-800-600-400-200
0
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
4
All this makes us think that simultaneously with the problem of the slow
reduction of costs, companies' commercial revenue policies have been clearly unable to
curb their growing financial losses. We consider that a firm is inefficient in revenue
when, given prices for outputs and levels of inputs, the company does not reach its
maximum level of revenue. Similarly, a company is inefficient in costs when, given the
prices of inputs and levels of outputs, it does not reach its minimum level of costs. Note
that the joint analysis of the cost and revenue efficiency does not imply to impose either
assumption about the capacity of the railways to choose the levels of inputs or outputs.
For example, in the calculation of the cost efficiency indicators, we assume that ouputs
are given, but these can be determined by the firm, a governmental entity, the market, or
by a determined mixture of these three aspects.
One of the objectives of this study is to analyse the relative importance of
inefficiencies in revenue and in costs in order to explain the poor financial results of the
companies. One firm will be completely efficient only if it is efficient in costs and in
revenue at the same time. Therefore, it is interesting to try to distinguish if the sources
of the inefficiency come from the cost or the revenue side. The type of appropriate
strategies to reduce one type or another of inefficiency can be very different.
For the special case of banking, there are some papers (Berger et al., 1996,
Berger and Mester, 1997, and Rogers, 1998) that have estimated and compared revenue
and cost efficiency. Recently, Cantos and Maudos (2001) have estimated using a
stochastic frontier approach the revenue inefficiencies for the rail sector, showing the
importance to taking into account this effect.
In pursuit of this objective we will apply a non-parametric approach based on
linear programming to calculate the efficiencies in revenue and in costs for a sample of
European railway companies during the period 1970-1995. The methodology applied,
called Data Envelopment Analysis (DEA), enables us to differentiate whether the
inefficiency, in revenue or in costs, is of a technical or allocative kind. Moreover, it
allows us to analyse what part of technical inefficiency is associated with the size or
scale of the company (scale inefficiency).
5
There are many studies centered on the estimation of the principal factors
explaining the companies' levels of technical or cost inefficiency. Such is the case of
Oum and Yu (1994), Gathon and Pestieau (1995), Cantos et al. (1999) and Cantos and
Maudos (2000). All the studies found that the companies with a higher degree of
autonomy and independence of management, and lower dependence on public
subsidies, are the most efficient ones. However, there are not works that analyse the
commercial behaviour of the railways.
In very regulated frameworks as the rail sector, we can presume that companies
will try to minimise costs, given the level of outputs and prices on inputs, instead of
maximise revenue. This fact may explain that, for most of the companies, revenue
inefficiencies obtained in our work are higher than cost inefficiencies. In any case, it is
interesting to analyse both problems.One company may be cost efficient, for example,
but very revenue inefficient. And additionally, a company can be cost and revenue
inefficient at the same time.
In frameworks that are being increasingly deregulated as this sector, it is
necessary to analyse its comercial behaviour. In other words, given the quantities of
inputs, do the companies do the sufficient efforts to maximise revenue?. The answer of
this question is fundamental in order to improve the financial viability of the sector, and
to fulfil one of the main objectives of the European Commission (see, for instance, the
objectives fixed in the 107th Round Table of the CEMT).
The results of this study point to the greater importance of inefficiency in
revenue than of that occurring on the cost side. In turn, technical inefficiency is always
greater than allocative inefficiency on both the cost side and the revenue side.
Inefficiencies of scale are not very important, and are always lower than technical
inefficiencies, showing that a reorientation of the literature is required. Our study also
obtains the result that the most efficient companies on the cost side are also the most
efficient on the revenue side. Furthermore, the companies with greater independence
from the government are the most efficient in all the categories of inefficiency defined.
Finally, in the light of our results, it has to be said that the measures taken to restructure
the companies in the period 1970-95 in order to favour, among other things, their
financial health, have not had the results that were hoped for.
6
The paper is structured as follows. Section 2 describes briefly the most important
institutional changes occurring in the industry during recent years. Section 3 presents a
description of the concepts used. Section 4 describes the methodology and section 5 the
data and variables used. Section 6 presents the results obtained, and finally Section 7
describes the main conclusions and recommendations deriving from the study.
2. Institutional framework.
The period covered by our study (1970-95) includes some years in which
important institutional changes took place in the railway service industries of the
countries analysed. One of the main concerns in the designing of European railway
policy is the control over the growing public subsidies received by the railway
companies. The first measures grew from the directives on the obligations of public
service and standardisation of accounts (1191/69), and on financial aid for transport
(1107/70). Subsequently, in 1989, the Commission presented a series of proposals for
requiring companies to have greater commercial and financial independence as well as
clearer and more accurate accounting.
Directive 91/440 also advocated a system of competitive access to the
infrastructures, based on the principle of vertical disintegration between infrastructure
and operations. This separation was compulsory in the accounting aspect, but voluntary
from the point of view of the organisation of the companies. The directive also
promoted the creation of specific public service contracts between states and companies
in order to regulate the activities relating to the management of the infrastructure and
the regional and local services. All other railway activities should be self-financing.
Vertical disintegration would also imply free access to infrastructures, and transit over
them, by any operator who so requested.
Finally, the various reports presented by the European Commission in 1996 and
1998 continue to acknowledge the problem of the financial health of the companies. In
this context some of the objectives indicated by the recents Round Tables of the CEMT
point to the need to recover the costs of infrastructure provision (including the finance
7
necessary for the investment), the encouragement of efficient behaviour in the operators
and of measures to favour competition.
At a practical level the processes of change in most of the companies during the
last 20 years have taken place very slowly. In the 1980s the companies introduced
decentralised methods of management by sectors or business units in order to encourage
an increase in the efficiency of the different services and in the control and
responsibility of management. It was hoped that these measures would also place the
industry's finances on a sound basis.
With regard to the separation of infrastructure and operations, the case of
Sweden represents the pioneering experience in the European context. 1988 saw the
separation of the ownership of the infrastructure (in the hands of the state agency
Banverket) from operations (in the hands of the public operator Statens Jarnvagar).
Though there is a system of free access by a system of tenders, very few routes have
been granted to private operators. Recently, however a private consortium has obtained
the concession for two important licences: the Stockholm commuter service and the
West Coast Main Line.
The most radical experience in the process of vertical separation is that of Great
Britain. The infrastructure was placed in the hands of a new company (Railtrack) which
was privatised in 1996. Passenger trains were to be run by twenty-five private operators,
who were allotted franchises of from five to fifteen years.
Other, less extreme, de-regulation experiences are those of Germany and the
Netherlands. After re-unification in 1994 of the former West German and East German
railway companies, the most important reform has been the introduction of free access,
which has allowed the entry under a licensing system of some private operators other
than the predominant public company (Deutsche Bahn AG). In the Dutch case, as well
as total separation between infrastructure and services, there is also a system of free
access, although new entrants have been limited to a small number of freight services
and a single passenger operator which competes directly with the public company NS.
Other countries, such as France and Spain, have created a body entrusted with
the management of the infrastructure, which aims to work towards the separation
8
between infrastructure and services. However, in practice the reforms do not seem to
have had much effect for the moment.
3. Efficiency measures
Efficiency measures are based on prior estimation or calculation of the frontier
of production, costs or revenue. The frontier can be defined in each case for a set of
observations, indicating that it is not possible to find any observation above it (in the
case of revenue and production functions) or below it (in the case of cost functions).
More specifically, the production frontier is the maximum level of output
achievable for a company with a given level of inputs, or the minimum level of inputs
that enables a company to reach a given level of output. Likewise, the cost frontier
corresponds to the minimum level of cost at which it is possible to produce a given
vector of output at given input prices. Finally, the revenue frontier is associated with the
maximum revenue achievable for a company, given output prices and input levels.
The common feature of these frontiers is optimality, specifying the maximum or
minimum value that can be achieved under certain conditions imposed by prices and
technology. That is to say, they describe a limit or frontier. Efficiency measures are
obtained by comparing the observed values for each company with the optimum,
defined by the estimated frontier. When the optimum is defined by the production
frontier the efficiency measure obtained is called technical efficiency. On the other
hand, if the comparison is made by considering an optimum defined in terms of an
economic objective that companies are assumed to pursue (minimisation of costs or
maximisation of revenue), the efficiency measure obtained is called economic
efficiency. In this case, we can distinguish two types of efficiency: cost and revenue
efficiency.
The two types of efficiency analysed -cost and revenue- correspond to two
economic objectives, respectively minimisation of costs and maximisation of revenue,
and are based on comparison of the observed values (of costs and revenues) with the
optimum values, determined by the relevant frontier.
9
3.1. Cost efficiency (CE)
Cost efficiency is defined as the quotient of the minimum cost at which it is
possible to obtain a certain vector of outputs determined by the frontier (C*) and the
cost actually incurred (C). Thus a cost efficiency value of CE=C*/C implies that it
would be possible to produce the same vector of outputs with a saving in costs of
(1−CE)100%, efficiency being restricted to between zero and one.
The costs of an organisation depend on the vector of outputs (y), the vector of
prices of the inputs used (w) and on the level of cost efficiency (uc). Thus the cost
frontier determines the minimum cost that each company could reach, for a given vector
of outputs (y) and a given vector of prices of inputs (w). Once the cost efficiency (CE)
has been obtained, the next step is to analyse whether the reason why companies do not
achieve minimum costs is because they use more inputs than necessary, or because,
given the prices of inputs, they use them in other than cost-minimising proportions. In
the first case we would be looking at the concept of technical efficiency (input
oriented), in the second at cost allocative efficiency (CAE).
Figure 3 illustrates the concepts for the case of a company A which uses a vector
of inputs x=(x1, x2) at prices w=(w1, w2) to produce a vector of outputs y=(y1, y2) at
prices r=(r1, r2). The upper part of the figure illustrates the measurement of cost
efficiency (CE), which is represented by the ratio between the minimum cost
(CE=w1xE1+w2xE
2), represented by the isocost line tangent with the isoquant, and the
observed cost of company A (CA=w1xA1+w2xA
2), represented by its isocost line, i.e.
CE=CE/CA.
10
Figure 3. Cost and Revenue Efficiency
yA
yE
yA*
IsoqP(x)
y2
y1
xA
xE xA*
IsoqL(y)
x2
x1
11
Technical Cost inefficiency (θ) is obtained from the distance between the
isoquant defined for the vector of inputs xA, and the isoquant associated with the vector
xA*, i.e. from the ratio CA*/CA. This distance indicates the reduction of inputs that could
be applied to company A so that it would still be able to produce the same. Allocative
efficiency in costs (CAE) is measured by means of the ratio of the costs of economically
efficient companies (xE) to the technically efficient combination (xA*) i.e. by means of
the ratios CAE=CE/CA* (graphically, through the difference between the two isocost
lines). A company is efficient from the allocative point of view when its choice of
inputs is the optimum for minimising costs. That is to say, it chooses a combination
whereby the relative prices are equal to the relative marginal productivities (graphically,
when the slopes of the isocost line and isoquant coincide). There must therefore be more
than one input for allocative inefficiency to occur. Note that we can breakdown the cost
efficiency measure (CE) between its two components (cost technical efficiency, θ, and
cost allocative efficiency, CAE). In particular θCAECC
CC
CCCE A
*A
*A
E
A
E
=== .
3.2. Revenue efficiency (RE)
Unlike cost efficiency, revenue efficiency relates the revenue generated by a
given vector of production (R) to the maximum possible revenue associated with that
vector, as determined by the frontier (R*). The revenue frontier assumes that companies
take prices of outputs as given1. Given the vector of prices of outputs (r) and the
quantities of inputs (x), the railway company tries to maximise revenue by adjusting the
vector of outputs.
As occurred with cost efficiency, revenue efficiency is defined as the quotient
between the maximum revenue attainable (R*) as determined by the frontier given the
prices of outputs, and the observed revenue (R). Thus, a revenue efficiency (RE) value
of RE=R*/R implies that the company could obtain revenue of (RE−1)100% higher than
it does.
1 In the case of the railway sector this assumption is reasonable given the existence of government regulations on prices of railway services. Rail prices have traditionally been regulated, under government control. Only recently some companies have liberalised their pricing policies (see Campos and Cantos, 2000).
12
Finally, we will analyse whether companies do not achieve maximum revenue
because they do not produce the maximum possible output (technical efficiency), or
because, given the prices of outputs, they do not produce them in the right proportions
to maximise revenue (allocative efficiency).
The lower part of Figure 3 illustrates the measurement of revenue efficiency (RE).
This is measured by the ratio of the maximum revenue (RE=r1yE1+r2yE
2), represented by
the isorevenue tangent to the frontier of production possibilities, to the observed revenue of
company A (RA=r1yA1+r2yA
2), represented by its isorevenue line; this measurement is
therefore expressed as RE=RE/RA. Technical Revenue efficiency (ϕ) is obtained as the
distance between the revenue associated with the isorevenue line given for yA and the
revenue associated with the isorevenue line for yA*, i.e. the ratio RA*/RA. This distance
indicates the potential increase in output that the company could obtain using the same
inputs. Revenue allocative efficiency (RAE) is measured by the ratio of the revenue of
economically efficient companies (yE) to that of the technically efficient combination (yA*),
i.e. by the ratio RAE=RE/RA* (graphically, through the difference between the two
isorevenue lines). A company is efficient from the allocative point of view (RAE=1) when
its choice of outputs is the optimum for maximising revenues. Note that we can again
breakdown the concept of revenue efficiency (RE) between its two components (revenue
technical efficiency, ϕ, and revenue allocative efficiency, RAE). In particular,:
ϕRAERR
RR
RRRE A
A
A
E
A
E
===*
* .
4. Methodology: Cost and revenue efficiency by means of non-parametric techniques.
Although there are many studies that analyse cost efficiency, only a few
compare it with profit or revenue efficiency. In particular, only Berger and Mester
(1997) compare cost and profit efficiency, for a single sample in the US banking sector,
using a parametric stochastic frontier approach (SFA). As the authors themselves
acknowledge, SFA has to make distributional assumptions which in most cases are quite
arbitrary (see Berger and Mester, 1997, page 906). Furthermore, the studies in which the
true distribution of inefficiencies has been compared with the assumed distributions
13
have found that the distributions are much more symmetrical than those usually
imposed, e.g. half-normal (see Bauer and Hancock, 1993, and Berger, 1993). The
availability of panel data allows efficiency to be estimated by means of a parametric
frontier without assuming any distributional form for inefficiency. However, such
techniques only allow estimation of one inefficiency per company, common to the
whole period. This implies assuming that the companies do not vary their style of
management during the period analysed, and the longer this is, the riskier the
assumption2.
The use of non-parametric techniques to calculate the frontier is in many cases
preferable to parametric techniques, because they enable efficiency measures to be
obtained without needing to assume any distribution function for inefficiencies or to
specify any functional form for the frontier. Also, unlike panel techniques, they do not
avoid the problem of assuming a distribution function for inefficiency in exchange for
doing without the time dimension of efficiency. However, these techniques do not
consider the existence of an error term, so its existence may skew the results.
This study uses the non-parametric DEA technique to calculate efficiency (cost
and revenue efficiency and their technical and allocative components). The frontier is
obtained by means of linear combinations of efficient companies in the sample, and
therefore the frontier is piece-wise linear unlike the general frontiers represented in
figure 3. Although cost efficiency has been widely obtained by non-parametric
techniques, they have never been used to calculate cost or revenue efficiency for the
railways. In this section we present two non-parametric DEA models to calculate cost
and revenue efficiency.
To illustrate the non-parametric methodology for calculating cost efficiency, let
us suppose there are N companies (i=1,…,N) which produce a vector of q outputs
yi=(yi1,…,yiq) ∈ ℜ q++ which they sell at prices of (ri1,…,riq) ∈ ℜ q
++ using a vector of p
inputs xi=(xi1,…,xip) ∈ ℜ p++ and paying for them a price of wi=(wi1,…,wip) ∈ ℜ p
++.
2 In the context of panel data, this assumption of invariant inefficiency can be relaxed by using different specifications of the efficiency term (see a survey of these specifications in Cornwell and Schmidt, 1995). However, a structure has to be imposed on the type of variation.
14
Given the particular nature of the railway business, in which companies operate
with very heterogeneous lengths of track (LT), in order to avoid the bias that this could
lead to, the standard DEA problem has been adapted to the case of the railway
companies by adding the restriction ∑ ≤i
jii LTLTλ . This implies that company j will
be compared with a linear combination of companies that operates in countries with
equal or lesser length of track. With this restriction we try to make comparisons
between companies with similar network characteristics, and therefore with similar
infrastructure characteristics.
4.1. Cost inefficiency3
The cost efficiency of company j can be calculated by solving the following
linear programming problem.
N,...,1i;0
LTLT
pxx
qyy.t.s
xwMin
i
ijii
ijpipi
ijqiqi
pjpjp
=≥
≤
∀≤
∀≥
∑
∑
∑
∑
λ
λ
λ
λ
[1]
The solution, x*j=(x*
j1,…, x*jp), corresponds to the vector of demand for inputs
which minimises costs with given input prices, and is obtained from a linear
combination of companies that produces at least as much of each of the outputs using
the same amount of inputs or less. If this hypothetical company had the same vector of
input prices as company j it would have a cost of C*j =∑wjp x*
jp which by definition
would be less than or equal to that of company j (Cj =∑wjp xjp).
3 See, for example, Ferrier and Lovell (1990).
15
Having obtained the solution to the problem, the cost efficiency of company j
can then be calculated as follows:
∑∑
==
pjpjp
p
*jpjp
j
*j
j xw
xw
CC
CE [2]
where CEj ≤1 represents the ratio of the minimum costs (C*j) –associated with use of the
vector of inputs that minimises costs (x*j)— and the observed costs (Cj) for company j.
4.2. Revenue efficiency4
Similarly to cost efficiency, revenue efficiency can be calculated for company j
by solving the following linear programming problem:
N,...,1i;0
LTLT
pxx
qyy.t.s
yrMax
i
ijii
ijpipi
ijqiqi
qjqjq
=≥
≤
∀≤
∀≥
∑
∑
∑
∑
λ
λ
λ
λ
[3]
The solution corresponds to the vector of outputs y*j=(y*
j1,…,y*jq) that maximise
revenue given the price of the outputs. This solution is obtained from a linear
combination of companies that produces at least as much of each of the outputs, using
an equal or lesser amount of inputs, and operate with an equal or lesser length of track
(LT). If this hypothetical company was subject to the same output prices as company j it
would have revenue of R*j=∑rjq y*
jq which by definition would be greater than or equal
to that of company j (Rj=∑rjq yjq).
4 See Färe et al. (1997).
16
Having solved the above problem, revenue efficiency (REj) can be calculated as
follows:
∑∑
==
qjqjq
q
*jqjq
j
*j
j yr
yr
RR
RE [4]
where REj ≥1 represents the ratio of maximum revenue (R*j) and observed revenue (Rj)
– associated with the production of the vector of outputs y*j which maximise the
revenue of company j.
4.3. Technical, allocative and scale efficiency
One of the advantages of DEA is the ease with which cost inefficiency can be
decomposed into its technical, allocative and scale components. The measurement of
technical cost efficiency (input-oriented) under variable returns to scale is obtained by
solving the following problem:
Ni
LTLT
pxx
qyyts
Min
iii
ijii
ijp
VRSjipi
ijqiqi
VRSj
,...,1;1;0
..
==≥
≤
∀≤
∀≥
∑
∑
∑
∑
λλ
λ
θλ
λ
θ
[5]
From the solution of this problem for each of the N companies of the sample we
obtain N optimal solutions. Each optimum solution θVRS is the input-oriented technical
efficiency measure of each company which, by construction, satisfies θVRS≤1. Those
companies with θVRS<1 are considered cost technical inefficient, while those with θVRS=1,
17
are catalogued as cost technical efficient, since they stand at the frontier 5. Note that if the
restriction ∑ =i
i 1λ is removed from the linear programming exercise defined in [5] we
obtain the technical inefficiency under constant returns to scale (θCRS). Therefore, the
input-oriented scale inefficiency (SEI) can be calculated by means of the following ratio CRSVRSI /SE θθ= .
The measurement of output-oriented technical efficiency under variable returns to
scale is obtained in a similar way, by solving the following problem:
Ni
LTLT
pxx
qyyts
Max
iii
ijii
ijpipi
ijq
VRSjiqi
VRSj
,...,1;1;0
..
==≥
≤
∀≤
∀≥
∑
∑
∑
∑
λλ
λ
λ
ϕλ
ϕ
[6]
Similarly, each one of the N optimal solutions ϕVRS will be the technical revenue
efficiency of each company (output-oriented) which, by construction, satisfies ϕVRS≥1.
Those companies with ϕVRS>1 are considered technically inefficient, while those with
ϕVRS=1 are catalogued as technically efficient6. Again, we can calculate the output-
oriented scale inefficiency by means of the following ratio VRSCRSOSE ϕϕ /= .
5 From an intuitive point of view, to analyse the efficiency of the productive scheme of company j (yj, xj) the problem constructs a feasible scheme as a linear combination of the schemes of the N companies of the sample which using θj xj inputs produces at least yj. Thus (1-θj ) indicates the maximum radial reduction to which the vector of inputs of company j can be subjected without altering the observed levels of output, so that θj is the indicator of technical efficiency. In the case where θj =1, this means that no linear combination of companies can be found that with less input obtains the same amount of output, so the company is catalogued as efficient. In all other cases, θj<1, indicating that the productive scheme of company j is inefficient, as there is a feasible alternative scheme that obtains the same quantity of output using θj xj inputs, its over-use of resources being quantified by comparison with the alternative scheme as (1-θj )xj.
6 Note that on the assumption of constant returns to scale the output-oriented and input-oriented measurements of technical inefficiency, θCRS and ϕCRS, are equivalent (θCRS =1/ϕCRS). However, they are not equivalent under variable returns to scale. See Färe and Lovell (1978).
18
Cost allocative efficiency (CAE) for each company is calculated by means of the
quotient between the measurements of cost efficiency (CE) and the corresponding
technical efficiency under constant returns to scale (θ CRS), CAE=CE/θ CRS. The revenue
allocative efficiency (RAE) for each company is calculated by means of the quotient of
the measurements of revenue efficiency (RE) and the corresponding technical efficiency
under constant returns to scale (ϕCRS), RAE=RE/ϕCRS.
5. The data
The sample covers the period 1970-1995, though not completely in the case of
BR (1973-95) and VR (1970-94). The data are taken from the reports published by the
Union Internationale des Chemins de Fer (UIC). Seventeen companies were included;
they appear in table 1. During the period analysed no important institutional change
took place, except for the process of vertical separation between infrastructure and
operations in the Swedish company SJ in 1988. The radical process of restructuring
carried out in the UK began in late 1995, so its effects are not reflected in our sample.
Throughout the period, the companies of the sample were state owned, although in
recent years all the companies have been transformed into autonomous organisations
with different degrees of independence from governmental control.
To represent revenue (R), we differentiated between the revenues from
passenger traffic and from freight traffic. As variables representing the vector of
outputs we used the number of passenger-km (y1) and freight ton-km (y2). We chose this
specification for two reasons. The first is that the prices of outputs can be proxied
simply, as the quotient of the revenue generated by each output and its volume, and that
is how it was computed here. The second reason, noted by some authors such as Oum
and Yu (1994), is that this variable for output is desirable when the basic aim of the
study is the analysis of government policies. In this sense, the levels of efficiency
evaluated with this type of measurements reflect the combined effects of the more or
less efficient performance of the companies and of the restrictions imposed by the
regulating authority. Finally, the prices of outputs were calculated as already indicated
(r1 and r2 represent respectively the prices of passenger and freight outputs).
19
To calculate cost efficiency, we took first the operating costs of the companies
(C). These include the costs of staff, energy, and those deriving from materials and
external services. Introducing other types of costs, such as those associated with
infrastructure and its maintenance (track, signalling, stations, buildings, etc.) would
have brought with it serious problems of homogeneous valuation of the sample, due to
the different accounting systems used to estimate infrastructure stock, depreciation and
interest rates. We introduce the number of kilometres of track as a proxy for the capital
stock, because it is proportional to the total volume of infrastructure and capital of each
company. This is the approach used in some papers, due to the problems to estimate the
capital inputs, and mainly, its prices. 7
The factors of production usually considered are those inputs that generate the
three types of costs mentioned above. On this point we must make some comments.
Firstly, in 1990 there was a change in accounting procedures, such that it is no longer
possible to distinguish between material and energy costs. Secondly, we only have
physical units for the labour factor, whereas for energy, materials and external services
the information is only available in monetary terms.
To solve the first problem, we opted to aggregate energy and material costs and
external services in a single cost concept, thus allowing us to use all the information
available. Besides, energy costs represent a relatively low percentage of total costs
(around 5%), so the problem of aggregation is not important. On the second question,
since energy and material costs are clearly proportional to the distances travelled by the
companies (see Nash, 1985), each kilometre travelled was considered a unit of
consumption generating these costs8. Thus the price of input for energy and materials
(w2) was obtained by dividing the quantity of costs generated by this input by total train
kilometres generated by the company. This approximation for calculating the price of
inputs is habitual in the literature (see, among others, Preston, 1994; Preston and Nash,
1996; and Cantos and Maudos, 2000). Finally, the price of the labour factor (w1), was
7 There are many studies that have considered the number of km of track as a fixed or quasi-fixed input representing the company's capital and infrastructure (see for instance, Caves, Christensen and Swanson, 1981, Gillen, Oum and Tretheway, 1990, Friedlander et al., 1993).
8 The correlation coefficient between the kilometres travelled by the companies and the energy and material costs for the total sample period is 0.90.
20
calculated as the quotient between the labour costs and the number of workers. The
monetary variables were expressed in constant dollars of 1990 through the Purchasing
Power Parity (PPP) indices. Table 1 shows the average values for the variables included
in the sample
Table 1. Average values for the variables (1970-1995).
LT y1
(*) y2(*) C(**) R(**) w1 w2 r1 r2
BR (U. K.) 17,387 31,085 17,636 5,235,865 3,491,127 19.3 4.7 76.3 64.1CFF (Switzerl.) 2,960 9,586 7,067 1,387,433 1,053,941 26.5 3.5 55.9 71.3CFL (Luxemb.) 272 234 658 156,927 44,797 36.4 3.8 37.8 55.6CH (Greece) 2,494 1,687 695 240,235 77,034 13.6 3.7 22.7 58.7CIE (Ireland) 2,064 1,007 590 327,974 137,019 14.5 9.1 98.7 45.2CP (Portugal) 3,434 4,940 1,272 390,299 255,144 12.3 3.6 38.5 42.3DB (Germany) 29,130 41,977 61,364 10,882,421 6,551,283 29.0 3.9 74.8 54.1DSB (Denmark) 2,227 4,081 1,793 542,541 260,398 15.9 4.1 39.2 51.5FS (Italy) 16,257 40,680 18,912 6,863,061 3,063,077 23.6 7.3 51.8 46.1NS (Holland) 2,851 9,928 3,114 902,908 557,919 21.8 2.7 41.2 39.4NSB (Norway) 4,180 2,097 2,694 374,085 209,502 16.4 3.5 46.5 40.5OBB (Austria) 5,781 7,536 11,203 2,086,125 1,019,549 17.5 7.8 50.1 56.0RENFE (Spain) 13,083 15,361 11,441 1,921,283 1,045,985 20.3 4.8 38.5 39.9SJ (Sweden) 11,110 5,741 16,595 1,007,711 693,081 18.0 4.1 52.7 23.2SNCB (Belgium) 3,975 6,940 8,235 2,015,804 898,874 27.7 6.2 81.0 42.5SNCF (France) 34,716 54,967 60,519 7,302,492 5,265,459 21.4 5.0 50.2 40.9VR (Finland) 5,941 3,027 7,617 409,453 362,537 13.4 2.1 37.0 31.9
(*) Data in millions of 1990 $US. (**) Data in thousand of 1990 $US. LT: number of track kilometres; y1: number of passenger-km; y2: number of ton-km; C: total operating costs by company; R: total commercial revenue by company; w1: price of labour; w2: price of energy and materials; r1: price of passenger output; r2: price of freight output.
Two additional considerations must be made at this point. Firstly, the inclusion
in the model of only two operating inputs is justified by the need to calculate the price
of each input. It is obvious that technical efficiency can be obtained introducing a higher
number of inputs (see Oum and Yu, 1994, Cantos et al, 1999), but to calculate cost
inefficiency, it is necessary to have many items of high quality financial and accounting
data, which are not available. Secondly, as already indicated, we have introduced into
our problem a variable representing capital stock or infrastructure (network length)
which controls for the different size of network with which companies operate.
21
6. Results
Figures 4 and 5 present the average evolution of revenue and cost efficiency and
its components for the period analysed. It must first be pointed out that, in general, the
average inefficiencies deriving from revenue are higher than those deriving from costs.
This indicates that the analysis of costs alone is only a partial analysis, for it leaves
aside a very important element in the study of the performance of companies, i.e. the
evolution of their commercial revenue and hence of their financial results. But the
variations in both cost and revenue inefficiency are not very great during the sample
period. We only observe a certain increase in the level of revenue inefficiency at the end
of the sample period.
In any case, this result shows that the railways have been mainly cost minimisers
during the period of analysis. One of the implications of this behaviour has been the
genereal revene inefficiency of most companies. The reduction of the revenue
inefficiency during the last years may be explained by the introduction of measures
oriented to an improvement in the commercial undertaking of the railways.
Figure 4.
Revenue efficiency and its components
0,80
0,90
1,00
1,10
1,20
1,30
1,40
1,50
1,60
7 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 8 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 9 0 9 1 9 2 9 3 9 4 9 5
Rev. eff. (RE) Rev. alloc. eff. (RAE) Rev. tech. eff. ( ) Scale eff. (SE )ϕVRS O
22
Figure 5. Cost efficiency and its components
Tables 2 and 3 present respectively the levels of companies' revenue and cost
inefficiency for different periods. With regard to revenue inefficiency (RE), some
companies are observed to have behaved efficiently throughout the period. Such is the
case of the companies SJ, NS, CFF, VR and FS. Others, on the contrary, were clearly
inefficient, especially CH, CIE, DSB, NSB or BR. In the case of these companies these
results show the existence of a margin of improvement in their revenue policy which
can be used to advantage.
On the cost side, the most efficient companies throughout the sample period
were NS, SJ, CFF and SNCF, and the most inefficient CIE, CH, NSB, BR and DSB.
This result points to the idea that the companies most concerned to reduce their costs
were also those that developed most effective commercial and revenue policies.
Therefore, the companies that are good performers in controlling their costs, are also
good performers in their commercial policies, and vice-versa. The companies that are
fully efficient in both costs and revenue throughout the period of analysis, like the
0,40
0,50
0,60
0,70
0,80
0,90
1,00
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
Cost eff. (CE) Cost alloc. eff. (CAE) Cost tech. eff. ( ) Scale eff. (SE )θVRS I
23
Swedish SJ and the Dutch NS, are therefore companies with profit-maximising
behaviour.9
Table 2. Revenue efficiency (RE)
1970-75 1975-80 1980-85 1985-90 1990-95 1970-95
BR 1.56 1.52 1.59 1.47 1.66 1.56 CFF 1.00 1.00 1.00 1.00 1.00 1.00 CFL 1.00 1.00 1.00 1.03 1.24 1.06 CH 2.25 2.02 2.22 2.15 3.02 2.37 CIE 2.18 1.86 1.87 1.78 1.71 1.88 CP 2.00 1.18 1.00 1.00 1.09 1.27 DB 1.15 1.18 1.03 1.02 1.29 1.14 DSB 1.65 1.76 1.77 1.63 1.64 1.69 FS 1.00 1.00 1.00 1.00 1.00 1.00 NS 1.00 1.00 1.00 1.00 1.00 1.00 NSB 1.75 1.69 1.64 1.66 1.80 1.71 OBB 1.24 1.22 1.17 1.04 1.09 1.15 RENFE 1.02 1.08 1.41 1.08 1.23 1.16 SJ – BV 1.00 1.00 1.00 1.00 1.00 1.00 SNCB 1.09 1.20 1.26 1.00 1.00 1.11 SNCF 1.00 1.00 1.00 1.00 1.02 1.01 VR 1.10 1.00 1.00 1.00 1.00 1.02 TOTAL 1.35 1.28 1.29 1.23 1.34 1.30
Table 3. Cost efficiency (CE)
1970-75 1975-80 1980-85 1985-90 1990-95 1970-95
BR 0.59 0.58 0.60 0.68 0.58 0.61 CFF 1.00 1.00 0.96 1.00 1.00 0.99 CFL 1.00 0.98 0.81 0.81 0.74 0.87 CH 0.61 0.59 0.56 0.56 0.45 0.55 CIE 0.30 0.34 0.36 0.41 0.45 0.37 CP 0.64 0.86 1.00 0.99 0.90 0.87 DB 0.79 0.79 0.98 0.97 0.72 0.85 DSB 0.72 0.63 0.71 0.74 0.63 0.69 FS 0.85 0.92 0.87 0.89 0.85 0.88 NS 1.00 1.00 1.00 1.00 1.00 1.00 NSB 0.56 0.59 0.60 0.59 0.57 0.58 OBB 0.59 0.60 0.73 0.81 0.81 0.71 RENFE 0.96 0.97 0.85 0.90 0.85 0.91 SJ – BV 1.00 1.00 1.00 1.00 1.00 1.00 SNCB 0.78 0.63 0.62 0.99 0.97 0.80 SNCF 1.00 1.00 1.00 1.00 0.94 0.99 VR 0.79 0.74 0.86 0.79 0.81 0.80 TOTAL 0.77 0.78 0.80 0.83 0.78 0.79
9 These results for the cost efficiency rankings are similar to those obtained in Cantos and Maudos (2000 and 2001), but there are some differences for the revenue efficiency. Note that the inputs used are different. Furthermore, in this paper we introduce a variable (the length of track) that controls for the different size of network with which railways operate, and finally, the techniques employed are different.
24
As we saw in section 3, revenue inefficiency (RE) can be attributed to technical
causes (the output produced is not the maximum,ϕVRS>1), allocative causes (the
combination of outputs is non-optimal, RAE>1), or scale effects (the size of the
company is also non-optimal, SEO>1). Thus table 4 presents the levels of revenue
efficiency attributed to technical, allocative and scale effects. It is observed that, on
average, technical inefficiency is clearly greater than allocative and scale inefficiency.
This indicates that companies should make an effort to improve the utilisation of their
resources and thus increase their levels of output and therefore revenue.
Similarly, cost inefficiency (CE) can be attributed to technical causes (the input
is not the minimum, θVRS<1), allocative causes (the combination of inputs is non-
optimal, CAE<1), or scale effects (the size of the company is non-optimal, SEI<1).
Table 5 shows the different components of cost inefficiency. We observe that,
depending on the company, the results are different. For some companies (CFL, CH,
CIE, CP, DB, SNCB, FS and VR) allocative inefficiency is higher than technical
inefficiency. However, on average, technical inefficiency is the main source of cost
inefficiency. As already noted in the studies that decompose productivity into changes
in efficiency and technical progress, potential sources of productivity growth do exist if
companies improve their management and make more efficient use of their resources
(see Gathon and Pestieau, 1995, Cantos et al., 1999, and Cantos and Maudos, 2000).
25
Table 4. Components of Revenue Efficiency (RE)
1970-75 1975-80 1980-85 1985-90 1990-95 1970-95 1970-75 1975-80 1980-85 1985-90 1990-95 1970-95 1970-75 1975-80 1980-85 1985-90 1990-95 1970-95BR 1.17 1.21 1.23 1.14 1.32 1.22 1.27 1.20 1.17 1.19 1.23 1 .21 1.05 1.05 1.12 1.09 1.02 1.06CFF 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1.00CFL 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.01 1.08 1 .02 1.00 1.00 1.00 1.02 1.14 1.04CH 1.18 1.35 1.32 1.14 1.16 1.22 1.19 1.09 1.07 1.13 1.28 1 .16 1.61 1.37 1.58 1.67 1.97 1.66CIE 1.49 1.52 1.62 1.53 1.26 1.47 1.22 1.11 1.10 1.14 1.37 1 .20 1.22 1.10 1.05 1.02 1.01 1.08CP 1.08 1.00 1.00 1.00 1.00 1.02 1.09 1.01 1.00 1.00 1.02 1 .03 1.69 1.16 1.00 1.00 1.06 1.19DB 1.00 1.00 1.00 1.00 1.00 1.00 1.11 1.06 1.00 1.01 1.16 1 .07 1.04 1.11 1.03 1.01 1.11 1.06DSB 1.20 1.37 1.24 1.21 1.44 1.29 1.06 1.04 1.03 1.03 1.05 1 .04 1.30 1.23 1.38 1.31 1.09 1.26FS 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1.00NS 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1.00NSB 1.60 1.52 1.49 1.52 1.56 1.54 1.08 1.10 1.10 1.08 1.11 1 .10 1.01 1.01 1.01 1.01 1.03 1.01OBB 1.16 1.14 1.06 1.00 1.03 1.08 1.02 1.05 1.04 1.02 1.04 1 .04 1.04 1.02 1.06 1.01 1.02 1.03RENFE 1.00 1.03 1.15 1.04 1.10 1.06 1.00 1.01 1.02 1.01 1.06 1 .02 1.01 1.04 1.21 1.03 1.06 1.07SJ-BV 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1.00SNCB 1.08 1.16 1.15 1.00 1.00 1.08 1.00 1.01 1.01 1.00 1.00 1 .01 1.01 1.03 1.08 1.00 1.00 1.02SNCF 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.02 1 .00 1.00 1.00 1.00 1.00 1.00 1.00VR 1.04 1.00 1.00 1.00 1.00 1.01 1.02 1.00 1.00 1.00 1.00 1 .00 1.04 1.00 1.00 1.00 1.00 1.01TOTAL 1.12 1.14 1.13 1.09 1.11 1 .12 1.06 1.04 1.03 1.04 1.08 1 .06 1.12 1.07 1.09 1.07 1.09 1.09
Technical efficiency (ΨVRS) Scale efficiency (SEO ) Revenue Allocative efficiency (RAE)
26
Table 5. Components of Cost Efficiency (CE)
1970-75 1975-80 1980-85 1985-90 1990-95 1970-95 1970-75 1975-80 1980-85 1985-90 1990-95 1970-95 1970-75 1975-80 1980-85 1985-90 1990-95 1970-95BR 0.71 0.64 0.69 0.74 0.68 0.70 0.89 0.93 0.90 0.93 0.90 0.91 0.94 0.97 0.98 0.99 0.96 0.97CFF 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 0.96 1.00 1.00 0.99CFL 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 0.99 0.83 0.96 1.00 0.98 0.81 0.82 0.89 0.90CH 0.88 0.78 0.78 0.90 0.91 0.86 0.81 0.87 0.91 0.86 0.75 0.84 0.86 0.86 0.78 0.72 0.65 0.77CIE 0.77 0.72 0.67 0.74 0.87 0.76 0.74 0.84 0.84 0.78 0.68 0.77 0.53 0.57 0.64 0.71 0.77 0.64CP 0.93 1.00 1.00 1.00 1.00 0.98 0.91 0.99 1.00 1.00 0.98 0.97 0.75 0.87 1.00 0.99 0.92 0.90DB 1.00 1.00 1.00 1.00 1.00 1 .00 0.80 0.80 0.99 0.98 0.78 0.87 0.99 0.98 0.99 0.99 0.92 0.97DSB 0.84 0.71 0.76 0.79 0.71 0.77 0.92 0.91 0.95 0.94 0.93 0.93 0.94 0.99 0.99 0.99 0.95 0.97FS 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1 .00 0.85 0.92 0.87 0.89 0.85 0.88NS 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1 .00NSB 0.66 0.70 0.71 0.70 0.69 0.69 0.88 0.86 0.86 0.87 0.83 0.86 0.96 0.99 0.98 0.97 0.99 0.98OBB 0.79 0.77 0.88 1.00 0.94 0.88 0.99 1.00 0.94 0.96 0.96 0.97 0.75 0.78 0.88 0.85 0.90 0.83RENFE 1.00 0.97 0.87 0.96 0.89 0.94 1.00 1.00 0.99 0.99 0.97 0.99 0.97 1.00 0.99 0.94 0.98 0.98SJ-BV 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1 .00SNCB 0.88 0.73 0.72 1.00 1.00 0.87 1.00 0.98 0.98 1.00 1.00 0.99 0.88 0.88 0.87 0.99 0.97 0.92SNCF 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 0.98 1 .00 1.00 1.00 1.00 1.00 0.96 0.99VR 0.97 1.00 1.00 1.00 1.00 0.99 0.98 1.00 1.00 1.00 1.00 1 .00 0.83 0.74 0.86 0.79 0.81 0.81TOTAL 0.91 0.88 0.89 0.93 0.92 0.91 0.94 0.95 0.96 0.96 0.92 0.95 0.90 0.91 0.92 0.92 0.91 0.92
Cost technical efficiency (θ VRS ) Scale Efficiency (SEI) Cost allocative efficiency (CAE)
27
6.1. Analysis based on correlation coefficients
Tables 6a and 6b show the correlation coefficients between the various
efficiency measures. We introduced an additional variable to represent companies'
degree of autonomy (AUTO). This variable, defined by Gathon and Pestieau (1995) has
been used in other studies (Oum and Yu, 1994, Cantos et al. 1999) and has proved to be
very important in explaining levels of technical efficiency10. Since the indicators of
technical, allocative and scale inefficiency are different depending on whether cost or
revenue efficiency is being calculated, we have introduced separately the results of the
correlations for the various concepts of inefficiency, though the results are not very
different.
Table 6a. Correlations among efficiency measures (input oriented)
Revenue eff. (RE)
Cost eff. (CE)
Technical eff. (θVRS)
C. Alloc. eff. (CAE)
Scale eff. (SEI) AUTO
Revenue efficiency (RE)
1.00 (1.00)
0.91 (0.85)
0.84 (0.73)
0.51 (0.49)
0.88 (0.84)
0.54 (0.46)
Cost efficiency (CE)
1.00 (1.00)
0.82 (0.84)
0.44* (0.68)
0.83 (0.86)
0.61 (0.47)
Cost technical efficiency (θVRS)
1.00 (1.00)
0.28* (0.25*)
0.76 (0.65)
0.45 (0.31*)
Cost allocative efficiency (CAE)
1.00 (1.00)
0.47 (0.54)
0.55 (0.40*)
Scale efficiency (SEI)
1.00 (1.00)
0.46 (0.29*)
AUTO (Autonomy index)
1.00 (1.00)
Upper rows show ranking´s correlation, lower rows (between parenthesis) are the Pearson’s correlation coefficients. In order to facilitate the whole understanding of Tables 6a and 6b the sign for some of these coefficients was changed. Therefore, a positive coefficient indicates that the companies which are efficient in one measure are also efficient in the another one. The values with * are non statistically significant at 5%.
10 This variable was constructed on the basis of a questionnaire sent to the European companies, containing a variety of questions on railway activity, from human resources management to financial policy, or from marketing and pricing to technical operations. In summary, the objective of the index is to provide information on the companies’ degree of autonomy. The problem is that the information is only available for one year. We are assuming, then, that the variations in any year in the level of this autonomy are negligible for each company. In any case we have opted to introduce this variable, despite its obvious problems, since no more suitable information was available.
28
Table 6b. Ranking´s correlations with efficiency measures (output oriented)
Revenue
eff. (RE) Cost eff.
(CE) Technical eff. (ϕVRS)
R. Alloc. eff. (RAE)
Scale eff. (SEO) AUTO
Revenue efficiency (RE)
1.00 (1.00)
0.91 (0.85)
0.90 (0.79)
0.79 (0.77)
0.93 (0.81)
0.54 (0.46)
Cost efficiency (CE)
1.00 (1.00)
0.88 (0.86)
0.60 (0.43*)
0.84 (0.85)
0.61 (0.47)
Revenue technical effic. (ϕVRS)
1.00 (1.00)
0.66 (0.25*)
0.81 (0.71)
0.50 (0.40*)
Revenue allocative effic. (RAE)
1.00 (1.00)
0.74 (0.45)
0.51 (0.36*)
Scale efficiency (SEO)
1.00 (1.00)
0.41*
(0.11*) AUTO (Autonomy index)
1.00 (1.00)
Upper rows show ranking´s correlation, lower rows (between parenthesis) are the Pearson’s correlation coefficients. In order to facilitate the whole understanding of Tables 6a and 6b the sign for some of these coefficients was changed. Therefore, a positive coefficient indicates that the companies which are efficient in one measure are also efficient in the another one. The values with * are non statistically significant at 5%. The values with * are non statistically significant at 5%.
The degree of rank correlation among all the efficiency measures is positive and
statistically significant in all cases but three. As we have noted, there is a notably high
correlation between the cost inefficiencies and revenue inefficiencies; this leads to the
conclusion that the companies that best managed their revenue were also those that best
managed their costs. Furthermore, the most efficient companies from a technical, scale
and allocative viewpoint are also the most efficient in revenue and in costs. The study
therefore reinforces the idea that the companies that are good performers in one aspect,
are also good in all the others.
Very interesting results were obtained from the correlation of the variable
representing the degree of autonomy with those representing inefficiency. This result
indicates that the degree of autonomy with which companies operate (i.e. their greater
or lesser freedom to decide fares, service levels, or opening or closure of lines) is
relevant not only for their technical efficiency (as found in Cantos et al, 1999, and Oum
and Yu, 1994) but also for them to be able to reduce costs and improve their levels of
revenue. Outstanding in this respect is the positive coefficient of correlation between the
autonomy index and revenue efficiency. This result can be explained by the high degree
29
of regulation of the industry, in terms of control over fares, level and quality of services,
etc., which justifies the importance of the revenue inefficiencies obtained in this study.
7. Conclusions.
This study has attempted an integral analysis of efficiency for a sample of
European railway companies. This analysis studies the concept of efficiency not only
from the perspective of the potential decrease in costs, but also from that of potential
gain in revenue. The results obtained indicate that the potential increases in revenue
(revenue inefficiency) are generally greater than the potential decreases in costs (cost
inefficiencies). Therefore, companies' efforts should be devoted not only to improving
the utilisation of their productive inputs, but also to improving their commercial and
revenue policies. This result reinforces the idea that railways have been more cost
efficient than revenue maximisers.
The sample period analysed shows that no significant changes occurred in
efficiency, whether in costs or in revenue.11 Therefore the policies current in most
European countries in the 1980s of creating a public body to manage railway operations
in the framework of a program-contract with the State do not seem to have had a
positive effect on the companies' efficiency, whether from the point of view of costs or
of revenue. Nevertheless, although in the period 1985-1990 a certain improvement can
be observed in the levels of revenue inefficiency, these decline again in the last stage
(1990-1995). This result may indicate the exhaustion of this type of policies.
If we decompose the inefficiencies of revenue and of costs into their technical,
allocative and scale components, we can appreciate that technical inefficiencies are the
most important. However, the results are different depending on the company
considered. Another important result is that the most cost efficient companies are also
those most efficient in revenue. Companies like the Swedish SJ, the Dutch NS, or the
French SNCF have shown very efficient behaviour on both the revenue side and the cost
11 An ordinary least square regression between average inefficiency indexes of cost and revenue against time was calculated, but the estimated parameter was clearly non significant (Student t-statistics were respectively 0,95 and -0,56).
30
side. On the other hand, companies like the Greek CH or the Irish CIE are clearly
inefficient on both sides. This indicates, therefore, that those companies that concern
themselves most with improving the utilisation of their resources are also the ones that
apply the most effective commercial and revenue policies.
The coefficients of correlation obtained indicate that the greater the companies'
autonomy and independence of management, the greater is their efficiency in costs and
in revenue. Furthermore, it is to be highlighted that the companies traditionally most
independent in their decisions on prices, levels of service, closure and opening of
services, etc. (such as the aforementioned SJ and NS) are also the most efficient in the
three different components of cost and revenue efficiency.
31
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