1968
T. Coelli and S. Perelman
are public services, which are often submitted to high
regulation.
This paper is organized into sections. The following sec-
tion provides a discussion of methods that may be used to
model multioutput technologies, including a detailed
description of the distance functions methods that are
used in the empirical analysis. In Section III, technical e -
ciency in European railways is investigated using a variety
of estimated distance functions, and in the ®nal section
some concluding comments are made.
The three characteristics described above are common to
all 17 European railways companies considered in this
study (see Table 2 for a list of these companies). All of
the companies produce both passenger and freight services
and are state-owned (during the sample period).2 All com-
panies hold a natural monopoly position in rail transporta-
tion, but in return, their activity is constrained to varying
degrees by public authorities and, in most cases, by
European Union regulations.
II. MULTIOUTPUT PRODUCTION A ND
DISTA NCE FUNCTIONS
A multioutput dual cost function approach has been
used by a number of authors in analyses of the North
American railways industry (e.g., Caves and Christensen,
1980; Caves et al., 1981). This method is unlikely to be an
appropriate method of analysis in the state-owned
European industry, where cost-minimization is an objective
which rarely has a high priority. In fact, in terms of per-
formance measurement, Pestieau and Tulkens (1993) argue
forcefully that technical e ciency measurement is probably
the only appropriate way to compare the performance of
enterprises operating in such environments. They observe
that the technical e ciency objective, that is, the maximi-
zation of physical outputs for a given combination of
physical inputs3 is, in fact, the only objective that is com-
patible with all other objectives ®xed by various control
authorities and, for this reason, appears to be an unavoid-
able goal. Hence, in this study, we focus upon the use of
technical e ciency as our measure of performance in
European railways.
The majority of econometric studies that have attempted to
model a multiple-output technology have either: (a) aggre-
gated the multiple outputs into a single index of output
(this index may be simply aggregate revenue or perhaps a
multi-lateral superlative index such as a Tornqvist4 or
Fisher index); or (b) modelled the technology using a
dual cost function.5 These approaches, however, require
certain assumptions to be made. The ®rst of these methods
require that output prices be observable (and re¯ ect rev-
enue maximizing behaviour), while the latter approach
requires an assumption of cost-minimizing behaviour.
There are a number of instances, however, when neither
of these requirements are met. The public sector contains
many examples. One example being the case of European
Railways, where the vast majority of organizations are
both government-owned and highly regulated.
Some recent parametric frontier papers have also
attempted to solve the multiple output problem by estimat-
ing the production technology using either: (a) an input
requirements function (e.g., Gathon and Perelman, 1992)
in which a single (possibly aggregate) input is expressed as
a function of a number of outputs; or (b) an output- or
input-orientated distance function (e.g., Lovell et al., 1994;
Grosskopf et al., 1997) which can accommodate both mul-
tiple inputs and multiple outputs. The input requirements
function approach has the advantage of permitting mul-
tiple outputs but at the cost of restricting the production
technology to a single input. The distance function
approach, however, requires no such restriction. We now
discuss the distance function approach in some detail.
This study, hence, has two principal objectives. The ®rst
is to measure the technical e ciency of European railways,
while the second objective is to provide a detailed illustra-
tion and discussion of distance function methods, which is
believed to have signi®cant potential in applied econo-
metric analyses of multioutput industries. The analysis
includes a comparison of the distance function results
with results obtained from a single-output production
function, where the single-output measure is an aggregate
measure of passenger and freight services. The results indi-
cate that output aggregation can have a substantial in¯ u-
ence upon both parameter estimates and technical
e ciency measures. In addition to this, the results also
identify a signi®cant improvement in railways technical
e ciency over the past decade. A phenomenon that can
be interpreted as the result of a catching-up process,
which is expected to be primarily due to the gradual intro-
duction of European Commission regulations restricting
the use of government subsidies.
Distance functions
We begin by de®ning the production technology of the ®rm
using the output set, P x , which represents the set of all
… †
2 The privatization process of some British Railways activities started in April 1994. For a description of this process see Dodgson (1994).
3 Or alternatively minimizing the inputs required to produce given outputs.
4 See Caves et al. (1982).
5 For example, see Ferrier and Lovell (1990). Also note that a dual pro®t or revenue function could alternatively be considered.