Rail Efficiency: Cost Research and Its
Implications for Policy
Draft Discussion Paper
Prepared for the Roundtable:
Efficiency in Railway Operations and
Infrastructure Management
18-19 November 2014,
International Energy Agency, Paris, France
Christopher Nash
Andrew S.J. Smith1
Institute for Transport Studies
Leeds University,
United Kingdom
1st
Draft October 2014
1
We also acknowledge the contribution of Phil Wheat to material on which this paper is partly based.
2
THE INTERNATIONAL TRANSPORT FORUM
The International Transport Forum at the OECD is an intergovernmental organisation with
54 member countries. It acts as a strategic think-tank, with the objective of helping shape the
transport policy agenda on a global level and ensuring that it contributes to economic growth,
environmental protection, social inclusion and the preservation of human life and well-being. The
International Transport Forum organises an annual summit of Ministers along with leading
representatives from industry, civil society and academia.
The International Transport Forum was created under a Declaration issued by the Council
of Ministers of the ECMT (European Conference of Ministers of Transport) at its Ministerial Session
in May 2006 under the legal authority of the Protocol of the ECMT, signed in Brussels on 17
October 1953, and legal instruments of the OECD.
The Members of the Forum are: Albania, Armenia, Australia, Austria, Azerbaijan, Belarus, Belgium,
Bosnia and Herzegovina, Bulgaria, Canada, Chile, People’s Republic of China, Croatia, Czech
Republic, Denmark, Estonia, Finland, France, Former Yugoslav Republic of Macedonia, Georgia,
Germany, Greece, Hungary, Iceland, India, Ireland, Italy, Japan, Korea, Latvia, Liechtenstein,
Lithuania, Luxembourg, Malta, Mexico, Republic of Moldova, Montenegro, the Netherlands, New
Zealand, Norway, Poland, Portugal, Romania, Russian Federation, Serbia, Slovak Republic,
Slovenia, Spain, Sweden, Switzerland, Turkey, Ukraine, United Kingdom and United States.
The International Transport Forum’s Research Centre gathers statistics and conducts co-operative
research programmes addressing all modes of transport. Its findings are widely disseminated and
support policymaking in Member countries as well as contributing to the annual summit.
Discussion Papers
The International Transport Forum’s Discussion Paper Series makes economic research,
commissioned or carried out at its Research Centre, available to researchers and practitioners. The
aim is to contribute to the understanding of the transport sector and to provide inputs to transport
policy design.
ITF Discussion Papers should not be reported as representing the official views of the ITF or of its
member countries. The opinions expressed and arguments employed are those of the authors.
Discussion Papers describe preliminary results or research in progress by the author(s) and are
published to stimulate discussion on a broad range of issues on which the ITF works. Comments on
Discussion Papers are welcomed, and may be sent to: International Transport Forum/OECD, 2 rue
André-Pascal, 75775 Paris Cedex 16, France.
For further information on the Discussion Papers and other JTRC activities, please email:
itf.contact@oecd.org
The Discussion Papers can be downloaded from:
www.internationaltransportforum.org/jtrc/DiscussionPapers/jtrcpapers.html
The International Transport Forum’s website is at: www.internationaltransportforum.org
This document and any map included herein are without prejudice to the status of or sovereignty
over any territory, to the delimitation of international frontiers and boundaries and to the name of
any territory, city or area.
3
Abstract
In this paper we first consider alternative measures of efficiency. We explain why simple
partial productivity measures are inadequate as the basis of overall measures of efficiency,
and outline two alternative approaches. The first is technical efficiency – the degree to which
output is maximised for a given level of inputs – and the second is cost efficiency, the degree
to which costs are minimised for a given level of output. Cost efficiency implies technical
efficiency but also allocative efficiency – choosing a cost minimising mix of inputs. We
explain why we prefer to measure cost efficiency, both in terms of what governments and
regulators are interested in and in terms of practical data problems.
We then examine applications of cost function analysis to two areas. The first is rail
privatisation in Britain. British experience has seen a large increase in traffic, but also a
similar increase in costs. We review attempts to understand and explain both the increase in
passenger train operating cost and infrastructure cost using cost function analysis. The second
is European rail reform. Countries in Europe have adopted a wide variety of approaches to rail
reform, and studies using a mix of European and other countries should be able to shed light
on the important question of what works best in different circumstances. Finally we consider
how efficiency analysis techniques need to develop in future to address current weaknesses
and tackle new challenges.
1. Introduction
Studies of rail efficiency usually have one of two motivations. Firstly they may aim to
identify which railways are efficient and which are not, in order to draw lessons as to the level
of improvement that may be required. An example of this is the benchmarking studies
conducted on behalf of the British rail regulator in deciding on the financial requirements of
Network Rail, the infrastructure manager discussed below (Smith et al, 2010). Secondly
studies may seek to draw policy conclusions about which policies regarding industry
structure, competition and regulation will be most beneficial. That is the approach we
emphasise in this paper.
In sectors of the economy in which markets are a reasonable approximation to perfectly
competitive, a reasonable measure of overall efficiency may simply be the profitability of the
firm. Under perfect competition, prices are not influenced by the individual firm and therefore
the more profitable the firm, the more it has been able to minimise costs of production and to
produce the most valuable combination of goods in the eyes of consumers.
4
But rail is a long way from being a perfectly competitive industry. In some sectors (e.g. coal,
commuters) rail operators still have considerable monopoly power, whilst for this and other
social reasons rail prices are often regulated by governments, who also play a key role in
specifying passenger sector outputs. If the aim is to examine the efficiency of railway
management, these factors must be allowed for. To the extent that railway managers (at least
in the European passenger sector) have limited control over their outputs, the key issue is
whether they produce them at minimum cost.
Economists are very used to distinguishing between technical efficiency and allocative
efficiency. Technical efficiency is measured by whether output is maximised for a given level
of inputs (or conversely inputs are minimised for a given output). The standard economic
approach to examine this is to estimate a production function, although in recent times a non
parametric method – data envelopment analysis – has been most commonly used. This
approach is considered further in the next section.
Allocative efficiency considers whether the correct mix of inputs is used to minimise cost for
a given level and quality of output. Cost efficiency, which is the product of technical and
allocative efficiency, and thus takes both into account, is the subject of the following section.
We then examine evidence on both the efficiency of the approach to railway reform taken in
Britain, and the relative efficiency of the variety of approaches taken around Europe before
seeking to reach conclusions.
2. Technical efficiency
2.1 Introduction
The material in this section is drawn partly from Smith (2004), and Nash, C.A. and Smith, A.S.J.
(2007).
Before turning to discuss more advanced measures it is first worth considering why it is
important to go beyond simple partial productivity measures - such as train kilometres per
member of staff or per locomotive - which are often used as measures of technical efficiency.
The first point to note is that they are partial measures and cannot therefore lead to
conclusions about overall efficiency (unless the same railway is more efficient on every
measure). Further, they are often impacted significantly by capital substitution effects (where
capital is substituted for labour, therefore improving labour productivity). In a multi-input,
multi-output environment such as the railways, the concept of total factor productivity (TFP)
provides a more informative indicator of technical efficiency.
TFP is a measure of the ratio of all outputs to all inputs (with the different inputs and outputs
weighted in some way). Under perfect competition, prices may be used as the weights so the
measure returns to one of the ratio of the value of outputs to the value of inputs, or in other
5
words profitability. Of course, the underlying assumptions of constant returns to scale /density
and marginal cost pricing are highly restrictive, especially in the context of the world’s
railway systems, which are characterised by high quasi-fixed costs and are heavily regulated.
These restrictive assumptions mean that TFP measures are unable to distinguish changes in
technical efficiency from underlying technical change and from changes in TFP resulting
from scale or/ density effects or departures of prices from marginal cost. Figure 1 illustrates,
for the single input, single output case, how inefficiency (the gap between a firm’s inputoutput
combination and the frontier) differs from productivity effects (moving along the
production frontier).
Figure 1: Single input production frontier
One way of dealing with this problem is to estimate a cost function using econometric
methods (see section 3 below). This approach allows the estimation process to calculate the
extent of returns to scale, to/ density, the elasticities of cost with respect to the outputs,
productivity growth resulting from technical change, and changes in efficiency. Data
envelopment analysis (DEA) is an alternative index number method for deriving productivity
and efficiency measures. It is a non-parametric approach, in which the efficiency frontier is
computed using linear programming techniques (rather than estimated, using econometric
methods; see section 3). The method permits the assumption of variable returns to scale and
Malmquist productivity indices can be computed from such models that also allow the
decomposition of TFP changes into technical efficiency, scale efficiency and technical
change.
f(x)
x
y
x2
y
0
g(x)
x1x3
6
One challenge that the DEA approach faces is its difficulty in characterising the technology,
since the introduction of numerous inputs and outputs into the DEA tends to result in all firms
being on the frontier. It can thus be hard to distinguish between, for example, economies of
scale and density. One way in which the approach can be augmented to deal with this
criticism is through the use of a second stage, in which the efficiency scores from the first
stage are regressed on a range of factors, such as train density and load factor and indeed
policy variables, such as the degree of competition). However, the approach then starts to look
much more like an econometric model, and it raises a question as to why adopt a two stage
approach, and instead simply estimate an econometric model. A remaining, major weakness
of DEA, however, is its inability to take account of random noise, meaning that measures of
inefficiency can be overstated (or efficiency understated).
One supposed advantage, historically, of DEA has been its ability to deal with multiple inputs
and outputs without recourse to potentially restrictive behavioural assumptions (for example,
cost minimisation, as required in econometric cost function estimation). Another is the fact
that it does not require the specification of a functional form for the underlying technology.
However, both these advantages have been largely eliminated by the widespread use of
flexible functional forms (e.g. the translog) and by the development of econometric methods
for estimating distance functions (see Groskopf et al, 1997).
Overall, the most advanced approaches and widely used approaches in the academic literature
for estimating technical efficiency are econometric distance functions (see for example,
Kennedy and Smith and Coelli and Perelman, 1999) and DEA (see, for example, Canto et. al.,
2010. However, as will be discussed in section 3, eonometric cost function / cost frontier
estimation has numerous benefits, and this approach dominates the empirical discussion.
Importantly, whatever approach is adopted, a decision is needed as to what should be the
relevant outputs and inputs, as well as associated output characteristic variables.
2.2 Outputs
At its simplest, transportation output may be regarded as the transport of passengers or
freight. Thus measures such as passenger kilometres and freight tonne-kilometres are the
usual starting point for output measurement. However, there are grave shortcomings with
such simple measures of output.
Multiplicity of outputs is a common feature of transport firms. Strictly, an output needs to be
described in terms of the provision of transport of a specific quality from a specific origin to a
specific destination at a specific point in time. Thus an operator of rail passenger services
running trains between ten stations ten times per day and offering two classes of travel is
already producing 1800 different products. A large European railway will have literally
millions of products on offer. Of course, it is not possible to provide cost or performance
measures that separately identify each product.
This is only really a problem if the different products have significantly different cost
characteristics, and traffic on them is growing or declining at different rates. For instance, if it
costs a similar amount to transport passengers (per km) between London and Leeds and
7
London and Manchester, then performance measures will not be distorted by regarding these
as the same product. On the other hand, failure to identify different traffic having very
different costs will be very distorting. For instance, part of the rapid improvement in
productivity of British Rail freight wagons in the 1980s was because of the decline and
eventual abolition of movement of single wagonloads in favour of movement of traffic in full
trainloads.
In passenger rail transport, longer distance, faster moving traffic and traffic moving in large
volumes generally costs less per passenger-kilometre to handle than short distance traffic or
traffic that must move slowly and in small volumes. This is because of the spreading of
terminal costs and the economies of operating longer trains. Peaks in demand also lead to
poor productivity by requiring the provision of a lot of resources that are only used for a small
part of the day. Thus a fundamental distinction is between types of passenger traffic in rail
such as inter-city, suburban and regional. Such peaks in demand are likely to be an issue in
urban public transportation operations, with some services being more peaked than others.
Likewise bus services can be provided at a lower unit cost (per passenger-km and bus-km)
where there are large volumes as operators exploit economies of density (see section 5
below). Economies of density occur when adding more traffic to the same network leads to a
less than prolirtionate increase in cost, whereas economies of scale occur when a given
increase in both nework size and traffic leads to a less than proritonate increase in cost.
In any event, frequency of service is an important quality attribute. A transportation manager
who was simply wishing to minimize costs – for a given number of passenger kilometres might
run one high capacity service per day, but this would not be very attractive to
customers. No sensible transportation manager will provide the frequency of service that
minimizes costs if a more frequent service will improve net revenue or benefits. This suggests
that, unless a way can be devised of adjusting passenger and freight-tonne-kilometres for the
quality of service provided, a more radical change to the output unit to train-kilometres rather
than passenger- or freight-tonne-kilometres might be desirable (it will still be necessary to
disaggregate train-kilometres according to their cost characteristics, as it costs much more to
shift a 5000 tonne freight train than a two-car branch line passenger train). The use of vehiclekilometres
in place of train-kilometres may be a helpful further refinement of the trainkilometre
measure, although this measure will still not correct for different weights of train.
Certainly, to regard operations where rolling stock is grossly overloaded, as for instance in
some developing countries, as therefore performing well - even if they are producing the
service itself very inefficiently - seems mistaken.
Freight traffic is particularly complex because of the lack of a homogenous unit of
measurement; at least in passenger transport we are always dealing with people. A tonne of
freight may cost very different amounts to transport according to whether it is a dense product
or not (for a dense product a single wagon will contain far more tonnes than for a product that
is not dense) and the form it is in (bulk solids or liquids may be loaded and unloaded much
more simply than manufactured goods, although the latter will be easier to handle if they are
containerized). It follows that loaded-wagon-kilometres may be a better unit of measurement
than tonne-kilometres, and that distinctions may be needed between trainload, wagonload and
container or intermodal traffic. If tonne-kilometres are used, a distinction by commodity is
important; for instance, a railway that has declining coal traffic and rapidly growing
8
intermodal traffic will almost certainly show declining productivity if tonne-kilometres are the
measure.
2.3 Inputs
Providing a rail service requires locomotives, passenger coaches or freight wagons (or selfpowered
vehicles), track, signalling, terminals and a variety of types of staff (train crew,
signalling, track and rolling stock maintenance, terminals and administration). While
ultimately all may be regarded as forms of labour and capital, the length of life of the assets
and government intervention over employment and investment will often mean that at a
particular point in time an undertaking will not have an optimal configuration of assets and
staff (see section 2.3 below). This renders attempts to measure inputs simply as labour and
capital difficult, as measures of the value of capital stock will need to allow for excess
capacity and inappropriate investment. An alternative is to simply look at physical measures
of assets (e.g. kilometres of track, numbers of locomotives, carriages and wagons for
railways), but this obviously makes no allowance for the quality of the assets.
2.4 Problems in measuring technical efficiency
A key problem in measuring technical efficiency is that of joint costs and economies of scale
/and density. For instance, a single-track railway may carry both passenger and freight traffic,
a passenger train first- and second-class passengers, and a freight train a variety of
commodities. In this situation, only some of the costs can be specifically attributed to one of
the forms of traffic; the remaining costs are joint. The result is that railways typically are
characterized by economies of scope; i.e. the costs of a single railway handling a variety of
types of traffic are less than if each distinct product were to be handled by a different railway.
Moreover, most evidence suggests that railways are subject to economies of traffic density.
Putting more traffic on the same route generally reduces unit costs and raises measures of
total factor productivity, unless the route is already heavily congested.
The result is that apparent rises in productivity may be caused by diversification into new
products or by increased traffic density rather than being relevant to the measurement of
performance. Of course, under conditions of economies of density, running more services
(and possibly different types of service) on the network does lead to a genuine improvement
in productivity. The argument here, however, is that the improvement in productivity arises
naturally as a result of the shape of the cost function, and not because of any improvement in
working practices.
The operating environment will also exert a strong influence on railway performance through
its impact on the nature of the traffic carried. This has already been considered above.
However, geography has other influences as well; gradient, climate and complexity of the
network are all likely to influence costs. The quality of the service delivered will also impact
on costs, for example in terms of the rolling stock used (e.g. air conditioned trains; trains that
give greater access for disabled users), and more widely the punctuality and reliability of
services. Other factors, such as the extent of passenger information provided and the quality
9
of on-board catering services for rail will also affect costs. Particularly in the case of rail, the
quality of the service will depend critically also on the capability of the infrastructure.
Of course, to the extent that the method used contains relevant measures of outputs and output
characteristics such that it can capture some of these features of the technology (e.g. scale and
density effects; quality; network complexity), then it should be possible to obtain measures of
technical efficiency after having taken account of these effects. We consider that econometric
methods, as opposed to DEA or partial or TFP measures give the best opportunities for
getting at underlying technical efficiency; though as noted, DEA combined with a second
stage econometric model is a useful alternative. As we will argue in section 3, we consider
cost econometric models to be the most suitable to achieving the objectives set out earlier,
namely assessing relative efficiency, and understanding the impact of industry structure.
2.5 Conclusion
There are many studies of railway technical efficiency using total factor productivity or DEA
approaches. However, in addition to the problems of measuring outputs and inputs, there is a
severe difficulty in terms of the data for this form of analysis. Typically, such approaches
include physical measures of the labour input, combined with physical measures of the
infrastructure and rolling stock measured in simple terms (track-km and number of rolling
stocks). Usually other inputs are excluded which, given that there are varying degrees of
subcontracting in the rail sector (rolling stock may be leased, maintenance and cleaning of
rolling stock and stations may be contracted out, as may track maintenance and renewals and
so on), this risks giving misleading results. For that reason as well as the technical reasons
given above, we prefer studies based on costs, which should be comprehensive measures
including all contracted out items. Moreover, it is costs ultimately that governments and
regulators are most interested in, not measures of physical productivity.
3. Cost function estimation
3.1 Introduction
In addition to the reasons outlined for preferring the approach of estimating cost functions,
there is an additional practical reason, namely that data is more reliable, although there remain
problems of inconsistencies in treatment of costs such as depreciation and interest,
particularly in international comparisons, but even in one country over time. The problem is
not simply different assumptions about asset lives. In some cases, where assets are purchased
with grants, no depreciation or interest is entered into the accounts. In some cases historic
debts have been written off; in other cases interest is still charged on them. Getting consistent
data remains a challenge.
10
The problems regarding how to measure inputs and outputs also remain, as does the issue of
the operating environment. How these problems may be handled in cost function analysis is
considered below. However, overall, the cost function approach does at least ensure that all
inputs are considered and the allocative efficiency (or inefficiency) associated with using
different input combinations accounted for. This compares to technical efficiency analysis
which first of all does not, of course, take account of allocative efficiency, but perhaps more
importantly for analysis of railways, often neglects some inputs (i.e. those represented by
other costs; see section 2).
3.2 Cost function estimation
Derived from assuming cost minimisation in a production process, the cost function relates
costs (C) to the level of outputs (Y) and input prices (P) and, where data is available over
time, some measure of how costs change over time as a result of technical change. Thus
 tPYCC ititit ,, (1)
It therefore automatically allows for one key issue in comparing costs between railways in
different countries, and in a single country over time, namely different input prices.
There have been a vast array of forms proposed. Notable developments include the constant
elasticity of substitution (CES, Arrow et al (1961)) and generalised Leontief (Diewert, 1971).
The most widely employed cost function is the Translog (Christensen, Jorgenson and Lau
1971, 1973). The Translog nests the simpler, and widely-used Cobb Douglas function (see,
for example Beattie and Taylor, 1985) as a special (restricted) case, however it is not derived
from any production function using duality theory. Instead the Translog cost function is
usually presented as a functional form which is a second order approximation to any cost
function rather than being derived directly from economic theory2
. The general form of the
Translog cost function for m outputs and n inputs is represented as:


  
 


m
1i
n
1i
jiij
n
1i
n
1i
jiij
m
1i
m
1i
jiij
n
1i
ii
m
1i
ii0
wlnyln
2
1
wlnwln
2
1
ylnyln
2
1
wlnylnCln
(2)
The function includes both first and second order terms in all variables. As such the Translog
cost function (like the generalised quadratic) is called a second order flexible functional form
whereas the Cobb Douglas (and the linear) are called first order flexible forms since they
include only first order terms. Importantly, the use of second order approximations allows for
elasticities and marginal costs to vary flexibly with the level of outputs and prices. In this
2
This justification can also be applied to the generalized quadratic functional form which nests the linear as a
special case.
11
sense the Translog does have appealing economic characteristics, such as the ability to deal
with varying degrees of returns to scale and density as firm size varies.
There are a number of requirements that a functional form has to obey to be consistent with
economic theory. Some, such as symmetry and homogeneity of degree one in input prices,
can be imposed through suitable parameter restrictions. However others such as concavity in
input isocurves cannot be directly imposed in the Translog cost function. Instead these
restrictions have to be tested at each data point in a sample. As such, the function will not
necessarily be globally consistent with economic theory, but the researcher should test
whether it is locally consistent. This illustrates the general difficulty of choosing sufficiently
flexible functional forms while maintaining requirement that the function has proper
economic properties.
Finally we note that the Translog cost function is often estimated along with the factor share
equations. Factor share equations are expressions for the proportion of total cost used by each
input and are derived using Shephard’s (1953) lemma as the partial derivative of the cost
function with respect to each input price. Estimation can then proceed using Zellner’s (1962)
Seemingly Unrelated Regression (SUR) which is more efficient (in terms of estimation) than
single equation ordinary least squares.
When it comes to measuring outputs, the need to distinguish between scale and density effects
or the choice between passenger and freight tonne or train or vehicle km is only part of the
wider issue of how to account for the heterogeneity of railway outputs. One way to deal with
the heterogeneity in outputs is to group outputs (denoted y) into m groups and include a
further set of r variables which characterise the outputs (denoted q):
 n1r1m1 w,,w,q,,q,y,,yC  (3)
The move from potentially hundreds or thousands of outputs to a more manageable number of
m outputs is obviously a simplification. However the inclusion of output characteristic
variables is an attempt to reintroduce heterogeneity in outputs back into the model. Such
variables may include revenue measures (such as passenger-km and freight tonnes-hauled)
where available measures are adopted as output and vice-versa. As such it can become a little
ambiguous as to what variables represent outputs versus output characteristics versus network
size.
The inclusion of characteristic variables in the cost function specification has prompted new
definitions of economies of scale and density to be proposed to allow for the possibility of
characteristics of outputs changing along with the outputs or network size themselves. See
Oum and Zang (1997) for a discussion. The ideas are similar to the discussion in Caves et. al.
(1985) regarding the need to consider changes in unobserved network effects in EoS
described above, however in Oum and Zang (1997) these relate to changes in observed rather
than unobserved variables.
While this formulation does simplify the problem to a tractable level, the resulting function
may be very complicated given the number of variables in and possible interaction and higher
order terms for each. As a result the cost function may still not be suitably parsimonious.
12
Spady and Friedlaender (1978) developed a hedonic cost function, which restricts the cost
function in equation (3) to:
  m1r1 w,,w,q,,q,yC  (4)
Two things distinguish equation (4) from (3). First there is only one output as opposed to n
outputs (this is relaxed in some applications e.g. Bitzan and Wilson (2008) and Wheat and
Smith (2014)). Second the output and output characteristic variables enter into their own
function and this then enters into the general cost function. This is important as once a
functional form is chosen for C( ) such as Translog, the use of hedonic output (  ) imposes
several restrictions on the model in equation (4). The benefit of this approach is a more
parsimonious model; however this may represent an unacceptable simplification of the cost
relationship.
It is perhaps surprising that there have not been too many applications of hedonic cost
functions in transportation operations. One example in transport operations is that by Wheat
and Smith (2014) who estimated such a function with three outputs (train hours, route length
and number of stations operated) and many characteristic variables relating to the train hours
output. This analysis provided rich insights into the impact of output heterogeneity on
economies of scale and density (see section 4), whilst enabling a parsimonious model.
3.3 Stochastic frontier methods: introduction
The above discussion has focused on the relationship between costs, outputs, output
characteristics and input prices. As noted earlier, a key motivation for policy makers is to
understand the relative cost efficiency of transport operators. The cost function relationships
discussed above can be augmented to allow the relative efficiency of companies to vary and
for this degree of variation to be estimated.
The efficiency measurement literature cites three functions which may be estimated,
depending on the appropriate behavioural assumption: cost functions, production functions or
distance functions (the latter two are focused on technical efficiency; see section 2). Most
applications in railways are based on cost functions, reflecting the fact that, due to the highly
regulated environment in which most railways operate, it is appropriate to view railways as
seeking to minimise cost for a given level of output (where the latter is more or less
determined by government). In this section we focus on cost function relationships or, more
precisely now that we are introducing inefficiency into the approach, cost frontier
relationships.
The simplest econometric approach is to use the method of corrected ordinary least squares
(COLS). This method proceeds by ordinary least squares (OLS), but then shifts the regression
line down by the amount of the largest negative residual (for the cost function case), thus
translating an “average” cost line into a cost frontier. However, like DEA, the COLS method
is a deterministic approach which does not distinguish between genuine inefficiency and
statistical noise when looking at deviations from the frontier. It is however, with suitable
adjustments, widely used by UK economic regulators, in part due to its simplicity.
13
The alternative and more widely used method in the academic literature (and increasingly by
economic regulators) is stochastic frontier analysis (SFA); see equation (5) below. The
stochastic cost frontier model can be represented as:
itittitititit uvNPYfC  );,,,(  (5)
where the first term ( );,,,( tititit QPYf ) is the deterministic component, and itY is a vector
of output measures, itP is a vector of input prices, itN is a vector of exogenous network
characteristic variables, t is a vector of time variables which represent technical change and
 is a vector of parameters to be estimated. itC represents the cost variable to be explained.
The i and t subscripts refer to the number of firms and time periods respectively. Whilst some
applications may use only cross sectional data, most railway applications utilise panel data,
and this type of data greatly expands the possibilities for increasing the richness of the
analysis in a number of ways as discussed further below. The itv term is a random component
representing unobservable factors that affect the firm’s operating environment. This term is
distributed symmetrically around zero (more specifically assumed to be normally distributed
with zero mean and constant variance). A further one sided random component is then added
to capture inefficiency ( itu ).
For cross-sectional data, it is necessary to make distributional assumptions concerning the
one-side inefficiency term, and the estimation proceeds via maximum likelihood. This is a
significant limitation as these assumptions may not be valid. For panel data, there are
additional estimation possibilities. Before turning to the panel data approaches it is worth
summarising the benefits of the econometric methods for studying the structure of railway
costs and relative efficiency performance.
Compared to cost function (or average response function estimation) it is clear that frontier
methods are a significant development since they explicitly allow for the possibility of
variation in efficiency performance between railways and over time. Compared with the DEA
approach, econometric methods provide estimates of the underlying structure of production /
costs, for example, the elasticity of costs with respect to different cost drivers, such as traffic
volumes - which DEA does not. In addition, through the development of stochastic frontier
analysis, econometric techniques are also able to distinguish between random noise and
underlying inefficiency effects. However, econometric approaches do require the choice of an
appropriate functional form, and the more flexible forms (such as the translog) are not always
straightforward to implement due to the large number of parameters to be estimated. In
addition, the choice of distribution for the inefficiency term in stochastic frontier analysis is
arbitrary. The precise method that researchers should use will therefore depend on a range of
factors, and in many academic papers more than one method is used in order to provide a
cross-check against the other approaches.
14
3.4 Stochastic frontier methods: panel data approaches
The existence of panel data offers a number of important benefits. First of all, by combining
cross-sectional and time series observations it provides additional degrees of freedom for
estimation. This may be very important, particularly if the number of companies for which
data exists is small as it often is for economic regulators. Second, it provides an opportunity to
simultaneously investigate inter-firm efficiency disparities, changes in firm efficiency
performance over time, as well as industry-wide technological change over the period of the
study. Third it can, for some models, permit the estimation of firm efficiency without recourse
to potentially restrictive distributional assumptions. Finally, it offers the prospect of
disentangling inefficiency from unobserved factors. This latter benefit may be particularly
important for railways, where substantial differences exist between railways both within and
between countries, but where it is hard to capture these differences in a set of variables to be
included in the model.
One way of dealing with a panel is to treat each data point as a separate firm. In this case,
each observation, including observations for the same firm over multiple time periods, is
given a separate efficiency score. In the case of econometric estimation this assumption may
not be appropriate, since it assumes that inefficiency is independently distributed across
observations, even though it might be expected that an inefficient firm in one period is likely
to retain at least some of that inefficiency in the next period.
The alternative and more usual approach, is explicitly to recognise the panel nature of the data
set. Within this alternative, there are two further options. Firstly, to estimate the model using
traditional panel data methods (fixed effects or random effects (GLS)); see Schmidt and
Sickles (1984). Alternatively, Pitt and Lee (1981) offer a maximum likelihood version of the
same approach. In both cases, inefficiency is assumed to be “time-invariant” and each firm is
given one efficiency score for the whole period, rather than one score per firm for each period
as in the simple pooled approach. The advantage of the traditional panel approach (fixed and
random effects) is that it does not require distributional assumptions concerning the
inefficiency term as in the maximum likelihood equivalent. This benefit does come at a cost
though, as it requires the assumption that inefficiency does not vary over time, which is
restrictive.
For long time periods, the assumption of time invariant inefficiency is clearly problematic,
and a number of approaches which allow for inefficiency to vary, whilst retaining some
structure to the variation, have been developed. Time varying models have been developed for
both the traditional panel data methods (e.g. Cornwell, Schmidt and Sickles (1990), and the
maximum likelihood approach (e.g. Battese and Coelli (1995); Cuesta (2000). Kumbhakar
and Lovell (2000) describe these approaches in detail. A key distinction in the literature is
between those models which make the assumption of independence in inefficiency over time
(e.g. pooled SFA; Battese and Coelli (1995)) and those which permit firm inefficiency to
change in a structured and not random way over time ( Cuesta (2000)). The latter seem to
have advantages from a regulatory and economic perspective
An important and relatively recent development in the literature has revolved around the
problem of disentangling inefficiency from unobserved heterogeneity. In the standard panel
literature, fixed and random effects are assumed to represent unobserved, time invariant
15
factors that vary between firms. As noted, in the efficiency literature, these models have been
applied as efficiency estimation approaches, with the firm effects re-interpreted as
inefficiency. This approach risks badging unobserved factors – genuine heterogeneity
between railways – as inefficiency. Methods have therefore been developed in the literature to
address this (Greene, 2005; Farsi et. al., 2005; Kumbhakar et. al., 2014; Colombi et. al.,
2014). One version of Greene’s approach includes a firm-specific dummy, to capture
unobserved heterogeneity between firms, which is assumed to be time invariant (e.g.
environmental factors, such as topography or climate) as well as the one-side inefficiency
term (which varies over time). The decomposition therefore relies on the assumption that
inefficiency varies randomly over time whereas unobserved heterogeneity is time invariant (as
well as on the distributional assumptions of the model). The model is then estimated via
maximum likelihood. This is one of the so-called “true” models, and there is also a random
effects version of this approach.
The Farsi et al. (2005) approach separates inefficiency from unobserved heterogeneity by
making the assumption that the former is assumed not to be correlated with the regressors
whilst the latter may be (inefficiency being a function of the ability of management to control
costs given the exogenous set of output requirements and input prices that it faces – hence this
would not be expected to be correlated with the regressors). Finally, the approaches set out by
Kumbhakar et al., 2014; Colombi et al., 2014 seek to go further and separate the model
residual into four components: random noise, time varying inefficiency, time invariant
inefficiency and time invariant unobserved heterogeneity. This model relies entirely on
distributional assumptions to make this separation, which is a limitation. It further assumes
that unobserved heterogeneity is uncorrelated with the regressors, which may not be valid. It
is worth noting that these are relatively new approaches with relatively few applications as
yet, and none, to our knowledge in railways.
3.5 Conclusion
To conclude, then, there exists a wide range of methods for estimating cost inefficiency in the
literature, some of them relatively simple and widely used, particularly by regulators, and
others more complex. However, some of the more complex methods are now entering the
economic regulation sphere in the UK, for example, ORR has adopted a range of advanced
methods, and others, such as OFWAT, have considered these approaches at least, though to
date has fallen back on simpler methods, given the data and results obtained3
. Panel methods
offer much more scope for a rich analysis of the cost structure (economies of scale and
density) and inefficiency and these are the most widely used in railways. The question of
dealing with random noise and heterogeneity (observed and unobserved) remains a key issue
for all regulators in railways and other sectors. Ultimately, the choice of technique will
depend on a number of factors, including the number of data points, availability of cost driver
data, model performance, economic theory and practical considerations. Usually, it is
appropriate to run a range of approaches and compare the results and in some cases it will not
be possible easily to choose between them. Economic regulators in that case tend to average
the efficiency results across a range of models.
3
Andrew Smith has been advising ORR and OFWAT on the use of these methods.
16
4. Rail privatisation in Britain
4.1 Introduction
Over the period 1994-97, the British rail system underwent the most radical transformation of
any European railway. Infrastructure was separated from train operations, and the new
infrastructure company (Railtrack) privatised by sale of shares. The freight sector was
privatised essentially as two companies and open access for new entrants permitted. The
passenger sector was largely franchised out in the form of 25 franchises, offered for a period
in most cases of 7-10 years, on a net cost basis but with requirements as to what services
should be operated and restrictions on the levels of some fares.
In the period since privatisation (1995 to 2010) passenger-km growth has been faster than in
all other major European railways (Brown, 2013). To provide a few specific examples,
between 1995-2010, passenger km increased 84% (Britain); 65% (Sweden); and 17%
(Germany)4
. Between 1995 and 2013 freight volume (in tonne km) increased by around 70%.
Most studies conclude the main reasons for this growth,were not to do with privatisation, but
that privatisation was a contributory factor. However, the story regarding passenger train and
infrastructure costs is not so positive (Table 1)
Under strong regulatory pressure, Network Rail’s costs have been falling in recent years,
although the company is not improving efficiency as quickly as the regulator would like.
To understand the drivers behind these trends we will first consider studies of passenger train
operating costs and then infrastructure costs to try to understand the reasons for this increase.
4
Source: European Commission Transport in Figures.
17
Table 1: Rail Industry Costs in Britain (Infrastructure and Passenger Train
Operations): 1997 to 2012
4.2 British passenger train operating costs
There have been many studies of passenger train operating costs in Britain, including, Affuso,
Angeriz, and Pollitt (2003); Cowie (2002a, 2002b, 2005 and 2009); Smith and Wheat (2012),
Wheat and Smith (2014) and Smith, Nash, and Wheat (2009). Preston (2008) provides a
review of, inter alia, previous cost studies of the British rail sector. The above papers have
Costs (£b2011/12 prices) 1996/97 2005/6 2011/12
Infrastructure expenditure
Maintenance 1.1 1.4 1
Renewals and enhancements 1.5 3.7 4.6
Other operating costs 1 1.4 1.5
3.5 6.5 7.1
TOC costs less access charge
payments
4.2 5.8 5.9
Total passenger rail costs 7.7 12.3 13
Unit cost measures (£)
Total passenger rail costs per
passenger train km
20.2 27 25.4
Infrastructure costs per
passenger train km
9.2 14.4 13.9
TOC costs (excluding access
charges) per passenger train km
11 12.6 11.5
18
utilised a variety of methods including non-parametric DEA (Affuso et al., 2003; Cowie,
2009, Merkert et al., 2009) and index number approaches (Cowie, 2002a; Smith et al., 2009),
as well as parametric estimation of cost functions (Cowie, 2002b; Smith and Wheat, 2012,
Wheat and Smith, 2013), production functions (Cowie, 2005) and distance functions (Affuso
et al., 2003). Clearly the former methods (DEA and index number approaches) can only
consider cost or technical efficiency and produce no estimates regarding the actual cost
structure.
Importantly, of the British TOC cost studies, only four cover the crucial period after 2000
when TOC costs started to rise substantially, these being Cowie (2009), Smith et al. (2009),
Smith and Wheat (2012) and Wheat and Smith (2014). Cowie (2009) covers the period to
2004, whilst the two further papers cover the period to 2006. Wheat and Smith (2014) provide
analysis up to 2010.
An important issue is whether to include an infrastructure input in any analysis of train
operating costs. Clearly the infrastructure input may be an important part of the
transformation function and so should be considered for inclusion in any analysis. The four
papers by Cowie all include some measure of infrastructure input in the analysis which is
some combination of route-km and access charges paid by operators to the infrastructure
manager (to form a price if applicable).
This in turn raises two important and related problems: (1) the infrastructure input is hard to
measure (see the previous discussion for particular measurement issues in Britain); and (2) the
inclusion of this input turns the analysis into an assessment of rail industry costs/production,
rather than being targeted on the TOCs. In their study, Affuso et al. (2003) produce two
models: one including the infrastructure input, and one not. The results differ as a
consequence, although this problem is less severe during the early period after privatisation
(which the study covers), since access charges and infrastructure costs were fairly stable
during that period. Whilst there are good reasons for capturing the infrastructure input in a
study of TOC performance, to capture the possibility that this input affects the TOC
transformation function, Smith and Wheat (2012) and Wheat and Smith (2014) argue that,
given the measurement problems noted above, infrastructure inputs are best left out of the
analysis. The dependent variable in their paper is thus defined as TOC costs, excluding fixed
access charges. Route-km is also included as an explanatory variable in their model, not as a
measure of the infrastructure input, but to distinguish between scale and density effects.
The focus of Smith and Wheat (2012) was on the impact on cost efficiency of contract
regimes following several renegotiations and temporary contracts being introduced following
franchise failure. It used a panel data stochastic frontier framework which allowed efficiency
to evolve over time (based on the model by Cuesta, 2000; see section 3). They also included
dummy variables in the cost function to allow the extent of cost effects of different contract
types to be directly estimated.
The focus of the Wheat and Smith (2014) work, in contrast, was how to best model the cost
structure of the industry. This work utilised a hedonic cost function (see section 3.2) and the
description of the data used is given in Table 2. In particular they defined three generic
outputs (Route-km, Train-hours and number of stations operated) and defined nine
characteristics of train services which go into the Train-hours output function ( 2 ). These
19
characteristics control for the heterogeneity in train service provision. They also define two
inputs and associated prices.
Table 2. Data used in Wheat and Smith (2014)
Symbol Name Description Data Source
Generic Outputs ( )
11 y
1y Route - km Length of the line-km operated by the
TOC. A measure of the geographical
coverage of the TOC
National Rail Trends
929282827272626252524242322212
32221222
qqqqqq
eeeeeeqqqy 
 
2y Train Hours Primary driver of train operating cost National Modelling Framework
Timetabling Module
12q Average vehicle length of
trains
Vehicle-km / Train-km Network Rail
22q Average speed Train-km / Train Hours National Modelling Framework
Timetabling Module
32q Passenger Load Factor Passenger-km / Train km Passenger-km data from National
Rail Trends. Train-km data from
Network Rail.
42q Intercity TOC Proportion of train services intercity in
nature
National Rail Trends for the
categorisation of TOCs into
intercity, LSE and regional. Where
TOCs have merged across sectors a
proportion allocation is made on an
approximate basis with reference to
the relative size of train-km by each
pre-merged TOC
52q London South Eastern
indicator
Proportion of train services into and around
London
(in general commuting services)
62q 5242qq Interaction between Intercity and LSE
proportions
72q  524242 1 qqq  Interaction between intercity and regional
(non-intercity and non-LSE services)
proportions
82q  524252 1 qqq  Interaction between LSE and regional
proportions
92q Number of rolling stock types
operated
Number of “generic” rolling stock types
operated
National Modelling Framework
Rolling Stock Classifications
33 y
3y Stations operated Number of stations that the TOC operates National Rail Trends
Prices
1P Non-payroll cost per unit
rolling stock
TOC accounts for cost, Platform 5
and TAS Rail Industry Monitor for
rolling stock numbers
2P Staff costs (on payroll) TOC accounts (both costs and staff
numbers)
Source: Reproduced from Table 1 in Wheat and Smith (2013).
Using the notation in Table 2, Wheat and Smith (2014) estimate the following system of two
equations using non-linear least squares. This represents a full Translog hedonic cost function
(S refers to the cost shares for each input):
20
       
  
 
  



































































































 
tln
P
P
ln.2S
t
P
P
lntlnt
P
P
lnln
P
P
ln
lnln
2
1
t
P
P
lnln
P
C
ln
Tm
3
1l
litlm
it2
it1
1111
2
TT
it2
it1
1Tlit
3
1l
Tl
3
1l it2
it1
lit1l
2
it2
mit1
11
3
1l
bitlit
3
1b
lbT
it2
it1
1
3
1l
litl
it2
it
(3.11)
Findings on the cost structure of passenger train operations
In this sub-section we present some results of the work undertaken to date to illustrate the
richness and usefulness of the methods employed. As described above, returns to scale (RtS)
and returns to density (RtD) can be defined specifically for operations (as distinct from
infrastructure). RtS measure how costs change when a firm grows in terms of geographical
size. RtD measures how costs change when a firm grows by running more services on a fixed
network.
The DEA analysis yields few results with relation to economies of scale or density. Indeed the
paper by Cowie imposes constant returns to scale. Merkert et al (2009) did estimate a variable
returns to scale model and found that British and Swedish TOCs were below minimum
efficient scale, while the largest German operators were above. Of the parametric papers,
Cowie (2002b) estimates a cost model which provides evidence on economies of scale. Cowie
finds evidence for increasing returns to scale and that these are increasing with scale. There is
no attempt to differentiate between scale and density economies in the analysis.
Smith and Wheat (2012) put forward a model which yields estimates of the extent of both
economies of scale and economies of density, where the primary usage output is train-km.
They found constant returns to scale and increasing returns to train density. The policy
conclusion of this finding is that whilst there would not be scale benefits from merging
franchises, such mergers may reduce costs by allowing greater exploitation of economies of
density (a single operator running trains more intensively down a given route); though see
further discussion on economies of density and heterogeneity below. One limitation of the
Smith and Wheat (2012) work was the inability to estimate a plausible Translog function.
Instead, a restricted variant was estimated, selected on the basis of general to specific testing
and on whether key elasticities were of the expected sign. This implicitly restricts the
variation in economies of scale and economies of density.
Further work by Wheat and Smith (2014) estimated a Translog simultaneously with the cost
share equations and adopt a hedonic representation of the train operations output in order to
include characteristics of output in a parsimonious manner. This work provides new insights
into the scale and density properties of train operations, since it allows RtS and RtD to vary
21
with the heterogeneity characteristics of output. Figures 2 and 3 summarise the findings on
RtD and RtS.
Figure 2. Returns to density for different TOC types holding other variables constant
Source: Reproduced from Wheat and Smith (2013).
Figure 2 shows that all TOC types exhibit increasing RtD and that this does fall with density,
although RtD are never exhausted within the middle 80% of the sample. At any given train
hours per route km level, intercity TOCs exhibit the lowest RtD, while LSE (commuter
services into London) exhibit the strongest (and indeed even at the 90th percentile density in
sample the RtD estimate is in excess of 1.2). Intuitively, the curve for mixed TOCs is
somewhere in-between the curves for intercity and regional. The policy conclusion from the
analysis of RtD is that most TOCs should be able to reduce unit costs if there is further
growth in train hours (on a fixed network) in response to future increases in passenger
demand
Figure 3 provides a similar plot for RtS. This shows that for all of the central 80th percent of
the train hours distribution, intercity (and mixed) TOCs exhibit decreasing RtS. LSE TOCs
exhibit increasing returns to scale only for the very smallest in sample, whilst regional TOCs
are the only TOC type to have an appreciable range of scale exhibiting increasing returns to
scale. The results are consistent with a u-shaped average cost curve, although it would appear
that most TOCs are operating at or beyond the minimum unit cost point. This finding has
important implications for examining the optimal size of TOCs and is relevant to the recent
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.5 1 1.5 2 2.5 3 3.5
Train Hours per Day per Route-km
Intercity Regional LSE Mixed
22
franchise policy change that has resulted in substantial franchise re-mapping, and in turn
larger franchises.
Figure 3. Returns to scale for different TOC types holding other variables constant
Source: Reproduced from Wheat and Smith (2013).
The overall conclusion from this section is that modelling returns to scale and density in
passenger train operations potentially requires a rich model to fully capture the effects. The
initial work published in Smith and Wheat (2012) based on a restricted translog model
suggested broadly constant returns to scale combined with fairly strong economies of density.
This may suggest that there could be a case for making franchises smaller, which could help
in reducing the risk of franchise failure, which has been a key problem in Britain (and
Britain’s franchises are already considerably larger, in general, than those elsewhere in
Europe). However, if reducing the size of franchises also increases the degree of franchise
overlap, then important economies of density may be lost in the process, so it is not a clear
policy conclusion. Turning the argument the other way round, larger franchises, that result in
reductions in franchise overlap and the exploitation of economies of density may reduce costs.
That said, Wheat and Smith (2014) develop a richer model, which takes account of service
heterogeneity (in particular, in terms of train speed and TOC type) in relation to returns to
scale and density. In that later paper it is found that the ability to exploit economies of density
may be constrained by service heterogeneity. Likewise, the losses of economies of density
from reducing franchise size might be smaller than indicated above. It is further found that
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 500 1000 1500 2000 2500
Train Hours per Day
Intercity Regional LSE Mixed
23
some franchises in Britain are operating at decreasing returns to scale, and may therefore be
too large.
What the above research suggests is that it is possible to shed new light on the structure of
costs of passenger train operations, and draw broad conclusions about the economies of scale
and density of those operations. The most recent work suggests that there could be cost
savings from reducing franchise size (because of scale diseconomies) and that losses in
economies of density might be reduced by service heterogeneity. Whilst we can draw these
general findings, we would however recommend more detailed, bottom-up modelling work be
carried out on a case by case basis if a decision is required on franchise mergers / de-mergers.
It may not be possible in an econometric to fully reflect the service and rolling stock
possibilities that result from such changes.
Findings on efficiency variation
The purpose of this section is to illustrate the potential of the methodologies with respect to
measuring efficiency of railway operators. There is an extensive literature analysing the
efficiency and productivity performance of vertically integrated railways around the world
(Oum et. al., 1999; Smith, 2006). More recently there has also been an interest in
understanding the impact of vertical separation on total industry costs, mainly focussed on
European evidence (Friebel, et. al., 2010; Asmild et. al., 2009; Growitsch and Wetzel, 2009;
Cantos et. al., 2010 and 2011; Mizutani and Uranishi, 2013; Nash et. al., forthcoming; van de
Velde et. al., 2012); although some studies considered evidence from North America
(e.g.Bitzan, 2003). Overall, the results seem inconclusive, costs suggesting that much depends
on the circumstances of the country concerned and the way in which the system is managed.
However, we consider the recent work by Nash et. al., forthcoming; van de Velde et. al., 2012
to offer interesting new insights on the circumstances in which vertical separation and the
holding company model might result in lower or higher costs. We review this work in more
detail in section 5 below.
There have also been a small number of studies focusing on the impact of competitive
tendering on one part of the rail industry, namely passenger train operations. In Germany and
Sweden the experience of competitive tendering has generally been positive, with the
evidence suggesting that savings in the region of 20-30 per cent can be achieved, alongside
increased patronage (see Brenck and Peter, 2007; Lalive and Schmutzler, 2008;
Alexandersson and Hulten, 2007; and Nash and Nilsson, 2009). Even here though, some
franchises have failed to achieve favourable results. Kain (2009) describes the major problems
that emerged in Melbourne, though the impact of the policy response is not described in any
detail. Long-term passenger (and also freight) rail franchises have also been signed in Latin
America, generally leading to radically improved performance, although in most cases renegotiation
has been required due to changed economic circumstances (in particular the
severe economic recession in the late 1990s; see Kogan, 2006).
Turning to studies of British TOCs, Affuso et. al. (2002; 2003) and (Cowie, 2002a, 2002b,
2005) study the early years after privatisation (prior to the major cost rises) and all find
improving productivity during this period. Only two studies cover the post-2000 period, after
which costs started to rise. Cowie (2009) finds declining productivity growth after 2000, with
the absolute productivity level falling post-2002. Smith and Wheat (2009) report productivity
24
levels falling as early as 2000 and not recovering over the remainder of the sample (to 2006).
Smith et. al. (2010) reviews this literature. Thus Britain's franchising experience appears to be
the outlier (at least within Europe), with costs rising rather than falling as in Germany and
Sweden.
Smith and Wheat (2012) investigates the impact of the response of the franchising authority in
Britain to franchise failure. Two approaches were adopted. First, most operators were placed
onto annually-negotiated management contracts (similar to cost-plus contracts). The second
saw some operators placed onto newly-negotiated short-term franchise arrangements. Figure 4
summarises the findings on the cost effect of different franchise contracts. This shows that the
franchising authority’s decision to place a large number of TOCs on management contracts
for an extended period led to a substantial deterioration in efficiency relative to other TOCs.
Furthermore, this effect was persistent and led to costs being considerably higher than other
TOCs for several years. However, the relative inefficiency was eliminated by competitive refranchising
for those TOCs that were subject to this process during the sample period. The
short-term franchise agreements which, once signed, retain incentives to reduce costs, saw a
more positive pattern, with costs remaining in line with other operators (those that remained
on their original franchise agreements throughout).
Figure 4. Findings for TOCs in Britain that were subject to short term management or
renegotiated contracts relative to other TOCs
* Some TOCs saw re-franchising during this period and came off their management contracts. Other TOCs
(dotted line in the above chart) continued on their management contracts to the end of the period.
Source: Reproduced from Smith and Wheat (2012).
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
CostfrontierlevelrelativetoOtherTOCs
Year
Other TOCs Management TOC Renegotiated TOC Management TOC Continuing
Management
andre-
negotiated
contractsstart
Lastyear of
management
contract*
25
The overall conclusion from this section is that whilst competitive tendering / franchising
appears to have reduced costs (or at least subsidies) in Germany and Sweden (Nash, Nilsson
and Link, ) costs have risen in Britain. Whilst the management contracts put in place
following numerous franchise failures explains part of the problem, Smith and Wheat (2012)
also report a general upward trend in train operating costs in Britain (affecting all operators).
It does appear that some British franchises may be inefficiently large.
However a major report on rail costs commissioned by the British Office of Rail Regulation
(ORR) and the Department for Transport in 2011 ( McNulty, 2011) concluded that a further
factor leading to cost increases in Britain was a misalignment of incentives between
infrastructure manager and train operating companies in the vertically separated structure of
railways in Britain. They advocated closer working arrangements, including a high level Rail
Delivery Group representing all parts of the industry, and alliances between the infrastructure
manager and train operating companies or even leasing of the infrastructure to franchisees at
the regional level. These issues are considered further at the European level in section 5.
4.3 Infrastructure costs
As noted above, infrastructure costs have risen even more than train operating costs. A major
reason for this was the expansion of maintenance and renewals activity following the fatal
accident at Hatfield in 2000 which was caused by a broken rail, but also the cost of the West
Coast Mainline renewal and upgrade programme rose to some £8b from an original estimate
of £2b. The result of these two events was that the privately owned infrastructure manager,
Railtrack, was placed in administration in 2001, and was ultimately succeeded in 2002 by
Network Rail, a company limited by guarantee, responsible to its members rather than
shareholders and with its debts guaranteed by the government. The Office of National
Statistics has recently ruled that, under current EU regulations, Network Rail is to be regarded
as a public sector organisation.
How did these events affect the efficiency of the British infrastructure manager over time, and
how does it compare with its European peers?
As noted above rail infrastructure costs rose substantially after the Hatfield accident. Whilst
part of this increase was driven by the need to increase maintenance and renewal activity in
the light of genuine concerns over the quality of the network, a wide range of evidence has
shown that Network Rail’s efficiency performance deteriorated sharply over that period.
Strong regulatory action has therefore resulted, with Network Rail being tasked with making
large efficiency gains in recent and the coming years.
Kennedy and Smith (2004) showed that Railtrack delivered substantial real unit cost
reductions in the early years after privatisation (6.4% to 6.8% for overall maintenance and
renewal activity between 1996 and 2002). However, these improvements were more than
offset by the post-Hatfield cost increases, which resulted in unit cost increases of 38% for
overall maintenance and renewal activity. Indeed, costs continued to rise after 2002 (see
Smith et. al. 2009). A further finding of Kennedy and Smith (2004) is that there was scope for
the infrastructure manager to reduce its costs by reduce intra-company performance
differences.
26
ORR carried out a review of Network Rail’s efficiency performance, in the light of the large
cost increases, and commissioned a wide range of studies (2003 Interim Review of the
company’s finances). A key weakness of the 2003 review though was that the ORR’s
efficiency determination was ultimately based on two bottom-up consultant reviews of
Network Rail’s business plan (LEK, TTCI and Halcrow, 2003 and Accenture, 2003). These
results were supplemented by internal benchmarking, which indicated the kind of savings that
could be achieved if Network Rail implemented its own best practice consistently across the
network.
Ultimately then, the 2003 Interim Review was unable to provide a clear, empirically based
assessment of Network Rail’s relative efficiency position based on hard data from external
sources. ORR nevertheless set a tough efficiency target of 31% over 5 years (2004-2009).
However, costs were starting from a very high base. Thus, although costs then started to fall
as Network Rail set about delivering its efficiency targets, by the time of the next periodic
review in 2008, the scene was set to take the benchmarking approach a step forward by
attempting international comparisons.
Two approaches were adopted during the 2008 review. The first used a panel of thirteen
European infrastructure managers over an 11 year period. The data was provided from the
Lasting Infrastructure Cost Benchmarking (LICB) project undertaken by UIC. The dataset
included data on costs (adjusted based on PPP exchange rates), traffic volumes (by type),
network length, and a range of other variables characterising differences between the
companies (for example, extent of electrification, network density).
A structured inefficiency model (based on Cuesta, 2000; see section 3 above) was used that
permits inefficiency to vary by firm over time, but in a structured way that recognises the
panel nature of the dataset. The results are shown for Network Rail in Figure 5 (other
companies cannot be shown for confidentiality reasons); see Smith (2012). Results are shown
for maintenance only, and for maintenance and renewals, with the additional model variant to
allow for Network Rail’s renewals costs to be reduced downwards prior to modelling to allow
for the fact that the company was renewing at above steady state levels in terms of renewal
volumes. The overall message of Figure 5 is that Network Rail’s efficiency deteriorated
sharply after 2000, compared to its European comparators, leaving the company with an
efficiency gap of around 40% by the end of the period. The analysis was carried out by the
University of Leeds, with ORR and in conjunction with Network Rail and UIC.
In a separate, supporting study, ORR and University of Leeds, collected a new dataset
comprising five other rail infrastructure managers in Europe and North America. This
includes data on costs, outputs, and network characteristics at the regional level within each
country. Thus, although the number of companies included was smaller than in the LICB
dataset, the sample size was expanded via the use of regional data within companies (subcompany
data structure). The dataset also allowed ORR to study within-country variations in
inefficiency. The results broadly confirmed the results of the main study using LICB data (see
Smith et. al., 2010; Smith and Wheat, 2012).
27
Figure 5: Profile of Network Rail Efficiency Scores: Preferred Model
It is further worth noting that the ORR carried out a range of other studies, principally based
on bottom-up evidence. These confirmed the existence of a substantive gap, supported by
examples of best practice in other countries (see Table 3).
Table 3: Examples of European best practice
Asset inspection
and asset
management.
In general best practice European railways undertake fewer track inspections but
inspections are generally of higher quality. It is estimated that similar techniques
applied in Britain could reduce foot patrolling inspection costs by around 75% and
tamping expenditure by 20%
Recycling
components
This is common European practice. In Switzerland, for example, rail, point motors,
sleepers and signal heads are regularly refurbished then cascaded from higher to lower
category routes. Cascaded rail on lines re-laid with steel sleepers could lead to savings.
Additionally ballast cleaning (partial renewal) as opposed to traxcavation (complete
renewal) could reduce ballast renewal cost in Britain by 40%
High output rail
stressing
Stressing continuously welded rail by heating it rather than physically stretching it is a
process discontinued in Britain in the 1960s and 1970s. Some European networks
(using modern equipment) have re-introduced this method which doubles on-site
productivity and, if applied to the renewals re-railing workbank in CP4, could lead to
significant annual savings for Network Rail
Formation
rehabilitation
trains
Modern high output European plant is regularly used to undertake formation and also
ballast renewals. If applied to Network Rail’s CP4 category 7 and 12 track renewals
RailKonsult estimate that it could reduce unit costs for both activities by around 40%
Lightweight station
platforms
The use of modular construction polystyrene station platforms in the Netherlands could
provide opportunities in Britain, given the substantial CP4 platform extension
workbank. Analysis suggests a unit cost saving of around 25% in Britain
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Total cost
(steady-state
adjusted)
Total cost
(unadjusted)
Maintenance
costs
28
Efficient European
re-railing
techniques.
This particular study brought together many themes from the previous RailKonsult
work by focussing upon the Swiss re-railing method. Bespoke plant, high output
welding techniques and dedicated teams are applied routinely. Put together for basic rerailing
work alone this method is around 40% more efficient than current Network Rail
practice
Use of dedicated
teams
Contractors are widely used by most continental railways, as they are in Britain.
However there is generally a greater degree of specialisation by activity in Europe
(such as S&C renewal or tamping). This ensures a highly skilled and productive
workforce dedicated to particular tasks in contrast to the situation in Britain where
contractors are often not even dedicated to rail.
Source: Taken from Smith et al., 2010.
Although ORR carried out / commissioned a wide range of studies – all of which pointed in
the direction of a large efficiency gap – it was the output of the LICB-based econometric
model which was used to set Network Rail’s efficiency targets. ORR chose to compare
Network Rail against the upper quartile of the peer group, rather than the frontier, thus
meaning that the starting efficiency gap for its analysis – based on the preferred econometric
model from the analysis of the LICB data- was 37% rather than 40%. ORR also gave the
company ten years to close the gap, with only two thirds of the gap targeted to be closed
during the immediate control period (control period 4 (CP4); 2009-2014).
In the next periodic review (PR13), ORR shifted the emphasis of its approach to bottom-up
methods. This was driven by a number of factors, but in part reflected increased doubts after
2008 about the quality of the LICB data and the commitment of the different companies to
providing accurate information. A re-run of the sub-company approach was also attempted,
but again it was considered that there was insufficient time to get enough certainty about the
quality and comparability of the data received. Therefore, although Network Rail
acknowledged the size of the efficiency gap resulting from the PR08 econometric modelling,
emphasis switched in the PR13 review to bottom-up analysis. Whilst new econometric
modelling with an updated LICB dataset was carried out and reported, in the process also
applying more advanced techniques (including the more recent methods set out in section 3),
the econometric modelling played a supporting role to the bottom-up analysis (thus reversing
the approach taken in PR08; see ORR (2013).
Perhaps one of the lessons that may be learned here is that international benchmarking is
inherently problematic because it takes considerable time and commitment from a group of
countries to make the analysis credible and usable. In PR08 ORR had the advantage of a
ready-to-go dataset, produced by UIC, and this enabled top down, econometric international
benchmarking to play a more significant role than it has in other regulated sectors. A further
factor at play in PR08 was the sheer size of the cost increases that had occurred and the scale
of the cost challenge, and given the lack of domestic comparators, there was a strong need
imperative to use this kind of approach. In PR13, with Network Rail acknowledging the size
of the gap, with the gap closing already, and with new uncertainties arising in the LICB
dataset, ORR has become much more cautious about top down international benchmarking,
and arguably the need to rely on it has become less. ORR also considers that its leading role in
29
collecting new data for the sub-company modelling approach is questionable – and that
perhaps this kind of work should be led and funded by companies rather than regulators.
One consideration going forward, however, is the extent to which ORR, and regulators in
general, can avoid the use of top-down benchmarking. Further, if international benchmarking
is to work, then it may require concerted efforts by regulators / governments across Europe
working together to establish a common benchmarking framework against which all
companies can be compared, thus also implying that data can be requested and audited by
regulators and policy makers. Finally, a further opportunity for benchmarking remains the
notion of internal benchmarking. Whilst not without its problems it remains a useful part of a
regulators toolkit as it establishes the savings that could be achieved if best practice (withincountry)
is consistently applied. The existence of disaggregation into units that have
managerial autonomy (at least to some degree) , as with Network Rail’s routes, is of course a
pre-requisite for such an approach, but these groupings / disaggregations do also exist in other
railways.
5. European rail systems
The previous section considered the impact of reforms on costs in Britain and attempts to
benchmark Network Rail (and to an extent the TOCs) with a view to challenging their costs
and improve efficiency. In this section we consider wider European experience. Most past
studies on the impact of reforms at the European level have applied data envelopment analysis
to physical data; our problems with that approach have been outlined above. Moreover they
have usually used the data published by the Union International des Chemins de Fer5
, data
which has been shown to contain inconsistencies (van de Velde et. al., 2012). Moreover this
source only contains data on UIC members, generally the incumbent but not new entrants, and
in some cases covers their activities in a number of countries rather than just their home
country. A rare example of the estimation of cost functions to study the impact of European
reforms is Asmild et al (2008); they also went to considerable efforts to clean up and
supplement the UIC data. They found that competitive tendering for passenger, open access
for freight services and accounting separation of infrastructure from operations all improved
efficiency, but could find no further effect of complete separation of infrastructure from
operations. However, their data series ended in 2001 before many reforms took place.
A recent example of the use of a translog cost function with panel data from a large number of
countries is Mizutani and Uranishi (2013). They used data for 30 railway companies from 23
OECD countries for the years 1994 to 2007, giving 420 observations. Whilst most of the
observations were from Europe, they included the vertically integrated passenger railways of
Japan, and also South Korea and Turkey. Where vertical separation had been implemented,
they added together the infrastructure manager and the train operating company to form a
5
Note this is published data as distinct from the confidential data from the LICB project described earlier.
30
single observation. The basic source of data was UIC, but this was supplemented as necessary
by data from company annual reports.
Two separate models were estimated, one using passenger kilometres and freight tonne
kilometres as outputs and the other total train kilometres, with the share of passenger revenue
to total revenue, passenger load factors and length of haul and freight number of cars per train
to reflect differences in the characteristics and therefore costs of the train kilometres. Factor
prices for labour, track, rolling stock and other materials were estimated. Finally route
kilometres, train kilometres per route kilometre and the percentage of line electrified were
included as descriptors of the network.
The rail reform variables were dummies reflecting complete vertical separation (the holding
company model being regarded as integrated) and horizontal separation of passenger and
freight operations. It was found that whilst horizontal separation unequivocally reduces costs,
vertical integration only reduced costs for densely trafficked railways; for most European
railways it increased them. Given that there are no separate variables representing the degree
to which competition is permitted or actually takes place, it must be assumed that these
impacts are the net effect of any additional costs directly caused by vertical separation and of
the impact of competition which in most of Europe must presumably be sufficient to outweigh
these costs. The explanation given for the impact on costs varying with density is that given
above, that the transactions costs caused by vertical separation will be much greater in densely
trafficked networks than in less densely trafficked ones.
Van de Velde et al (2012) takes this work further by updating and improving the data set and
introducing separate dummy variables for holding companies and complete vertical separation
(this work also later published in the academic literature, see Nash et. al. forthcoming and
Mizutani et. al, 2014). They also added in Britain, the country in which the most radical
reforms had taken place, but which had been excluded from most previous studies due to lack
of data. Finally, they introduce dummy variables representing passenger and freight market
competition.
They confirm the previous finding that, compared with complete vertical integration, vertical
separation reduces costs at low levels of density but increases them at high; at mean European
density levels costs are not affected by the change. This effect is not likely to be one of pure
transactions costs (negotiating and enforcing contracts), which have been shown to be a
relatively small proportion of total systems costs (Merkert et al, 2012) but is more likely a
problem of misalignment of incentives leading to poor integration of infrastructure and
operations in circumstances (dense traffic) when this is particularly important. They find weak
evidence (significant at 10% only) that the holding company model reduces costs compared
with vertical integration, but this does not vary with density, so the holding company would
be preferred to vertical separation at high levels of density but not at low.
Within the range of the data, the introduction of competition seems to have had no effect on
costs. Horizontal separation of freight and passenger undertakings seems to have sharply
reduced costs (perhaps because this has typically been associated with preparation of the
freight undertaking for privatization), whilst a high proportion of revenue coming from freight
rather than passenger tends to increase the costs of vertical separation (perhaps because
planning freight services efficiently requires closer day to day working than passenger, since
31
freight services vary from day to day whereas passenger services are generally fixed for the
duration of the timetable). The paper also provides qualitative evidence on the issue of how
misalignment of incentives may raise costs and show how, whilst efficiently set track access
charges and performance regimes are important, they do not provide incentives for railway
undertakings to assist infrastructure managers in seeking the minimum cost solution to
infrastructure provision. Only a complete sharing of changes in costs and revenues, as
provided for in some of the alliances now being negotiated in Britain, will achieve that.
The conclusion of the studies in this section is that there is no one size fits all policy for
European railways. Based on a mixture of qualitative and quantitative research the evidence
suggests that vertical separation may perform less well than the Holding company model for
intensely used networks, whilst being the structure of choice for less dense networks. Whilst
this is in part intuitive, it is not totally clear why separation reduces costs for lightly used
networks, particularly if there is little competition. It is further disconcerting that it has not
been possible to find clear competition effects in the data. To date no research has yet been
published to consider the impact of regulation on costs, though research is ongoing at
University of Leeds in this respect. A final note must be that although we consider the cost
function approach to be the best, and with the van de Velde et. al. (2012) study incorporating
new data from CER members to supplement published data, there nevertheless remains work
to be done on the data side to improve its comparability.
6. Conclusions
There are various measures of efficiency available, and all have their uses. Partial productivity
measures may have their value in shedding light on utilisation of particular resources, but they
are inadequate as measures of overall efficiency, such as are needed in econometric studies of
the influences of alternative policies on efficiency of the rail industry as a whole. For this
there are a number of possibilities, including total factor productivity measures and Data
Envelopment Analysis, but for various practical reasons we prefer the econometric estimation
of cost functions.
Detailed studies of Britain suggest that the reforms in Britain did not achieve lasting
improvements in cost efficiency. In the case of the infrastructure manager, the events
surrounding the placing of Railtrack into administration brought about a major reduction in
efficiency from which the current infrastructure manager, Network Rail, is only gradually
recovering. Surprisingly, competitive tendering did not achieve a reduction of train operating
cost, which has risen substantially. There appear to be various reasons for that, but the use of
management contracts to deal with cases of financial failure, the use of too large areas as the
basis for franchising (from a cost and risk of failure point of view) and the loss of economies
of density through overlapping franchises all seem to be factors in this (though it must be
noted that splitting franchises to reduce their size increases the prospect of franchise
overlaps). Most continental franchises are smaller and subject to less overlap of homogenous
32
services, and they appear to be more successful. However, it must still be noted there that the
studies carried out other than in Britain are based on data on subsidies and not cost, and it may
be that costs have been reallocated elsewhere in the system.
Studies of European-wide reforms suffer even more data problems than studies in a single
country, but a recent study which sought to overcome these was Van de Velde et al (2012)
using part published data and new data provided by CER members. They found that complete
vertical separation only reduces cost in low density countries; at higher densities it raises cost.
The reason for this is likely to lie in the misalignment of incentives, a factor considered
important in Britain by the McNulty report (McNulty, 2011). The level of competition in both
freight and passenger markets appears to be an insignificant factor in determining costs.
It is clear from all these studies that much still needs to be done to understand the
determinants of rail cost efficiency. The most fundamental requirement, whether within or
across countries, is for good quality consistent data on the variables we are seeking to
measure (in cost analysis, a key area here is the costs of depreciation and interest). Better
measures of policy variables are needed, including in particular the quality of regulation and
the degree of competition. At the same time, the measurement of service quality is an
important factor – as noted above, no sensible operator minimises costs wholly at the expense
of service quality.
The data challenges are unlikely to be overcome based on published data. Experience
suggests that some progress can be achieved by working with companies, however this takes
time and commitment, and sometimes companies may start involvement in a benchmarking
project, only to withdraw later. Long-term commitment to developing a framework and data
collection exercise is required. Ultimately it may be that data issues cannot be fully addressed
without concerted, European-wide effort by multiple policy makers and regulators to require
data to be collected to a common set of definitions, with appropriate audits in place to achieve
comparability.
Whilst the data will never be perfect and there will never be data on every possible variable
that may drive differences between companies, methodological advances mean that, with
enough data points (and with panel data), there are ways of disentangling inefficiency from
unobserved factors that cause costs to vary between railways. Thus we consider that it is both
possible and sensible to continue to develop our understanding of railway costs and efficiency
performance using existing datasets, improved where possible, and applying state of the art
methods.
Finally we note that the challenges facing policy makers seeking to compare performance are
further hampered by the increased need for railways to improve the quality of what they
deliver, whilst expanding capacity, reducing carbon, and also responding to the increased
challenges posed by climate change. All of these raise new data and methodological
challenges which researchers and policy makers will need to grapple with in the coming
years.
33
References
Accenture, 2003. Review of Network Rail’s Supply Chain. London.
Affuso, L., A. Angeriz, and M.G. Pollitt (2003): ‘Measuring the Efficiency of Britain’s Privatised
Train Operating Companies’, mimeo (unpublished version provided by the authors).
Alexandersson, G. and S. Hulten (2007): ‘Competitive tendering of regional and interregional rail
services in Sweden’, in European Conference of Ministers of Transport Competitive Tendering
for Rail Services, Paris.
Arrow, K. J., H. B. Chenery, B. S. Minhas, and R. M. Solow (1961),"Capital-Labor Substitution and
Economic Efficiency," Review of Economics and Statistics, August, pp. 225—250.
Asmild, M., T. Holvad, J.L., Hougaard, D. Kronborg, D. (2009), ‘Railway reforms: Do they influence
operating efficiency?’, Transportation, 36 (5), 617-638.
Battese, G. E. and Coelli, T. J. (1995). “A Model for Technical Inefficiency Effects in a Stochastic
Frontier Production Function for Panel Data,” Empirical Economics 20, 325-332.
Beattie and Taylor (1985)
Brown, M. (1962), "The Constant Elasticity of Substitution Beattie, B.R. and Taylor, C.R. (1985), The
Economics of Production, New York, Wiley.
Berechman, J. (1993), Public transit economics and deregulation policy. Amsterdam: North Holland.
Bitzan, J (2003) Railroad costs and competition. Journal of Transport Economics and Policy. 37 ( 2)
201-225
Bitzan, J. D. And Wilson , W.W. (2008). ‘A hedonic Cost Function Approach to Estimating Railroad
Costs’. Research in Transportation Economics, 20. 69-95.
Brenck, H. and Peter, M. (2007), Experience with Competitive Tendering in Germany, In European
Conference of Ministers of Transport (2007) Competitive tendering for rail services, ECMT,
Paris.
Cantos P., J.M. Pastor and L. Serrano (2010), ‘Vertical and horizontal separation in the European
railway sector and its effects on productivity’, Journal of Transport Economics and Policy, 44
(2) 139-160.
Cantos P., J.M. Pastor and L. Serrano (2011), ‘Evaluating European railway deregulation using
different approaches’, Paper given at the workshop on Competition and Regulation in Railways,
FEDEA, Madrid, March 12.
34
Christensen, L., Jorgenson, D., and. Lau, L. (1971), Conjugate Duality and the Transcendental
Logarithmic Production Function, Econometrica, 39, pp 255-256.
Christensen, L. R., Jorgenson, D.W. and Lau, L.J. (1973), ‘Transcendental Logarithmic Production
Frontiers’, Review of Economics and Statistics, vol. 55, pp. 28-45.
Coelli, T., Perelman, S. & Romano, E. 1999. Accounting for environmental influences in stochastic
frontier models: With application to international airlines. Journal of Productivity Analysis, 11,
pp. 251-273.
Colombi, R., Kumbhakar, S.C., Martini, G. and Vittadini, G. (2104), ‘Closed-skew normality in
stochastic frontiers with individual effects and long/short-run efficiency’, Journal of
Productivity Analysis, 42, pp. 123-136.
Cornwell, Snmidt and Sickles (1990)
Cowie, J. (2002a). ‘Subsidy and Productivity in the Privatised British Passenger Railway’, Economic
Issues 7 (1), 25-37 38.
Cowie, J. (2002b). ‘The Production Economics of a Vertically Separated Railway – The Case of the
British Train Operating Companies’, Trasporti Europei, August 2002, 96-103.
Cowie, J. (2005). ‘Technical Efficiency versus Technical Change – The British Passenger Train
Operators’. In Hensher, D. A. Ed (2005). Competition and ownership in land passenger
transport: selected refereed papers from the 8th International Conference (Thredbo 8) Rio de
Janeiro, September 2003. Amsterdam ; London : Elsevier, 2005.
Cowie, J. (2009). ‘The British Passenger Rail Privatisation: Conclusions on Subsidy and Efficiency
from the First Round of Franchises’, Journal of Transport Economics and Policy, 43(1), 85-
104.
Cuesta, R. A. (2000). ‘A production model with firm-specific temporal variation in technical
inefficiency: with Application to Spanish Dairy Farms.’, Journal of Productivity Analysis. 13
(2), 139-152.
Diewert, W. (1971): ‘‘An Application of Shephard Duality Theorem: A Generalised Leontief
Production Function,’’ Journal of Political Economy, 79, 481–507.
Farsi, M., Filippini, M. and Kuenzle, M. 2005. Unobserved heterogeneity in stochastic cost frontier
models: an application to Swiss nursing homes. Applied Economics, 37(18): 2127-2141.
Friebel, G., M. Ivaldi, and C. Vibes (2010): ‘Railway (De) regulation: a European efficiency
comparison’, Economica, 77, 77-91.
Greene, W. (2005), ‘Reconsidering heterogeneity in panel data estimators of the stochastic frontier
model’, Journal of Econometrics, vol. 126, pp. 269-303.
Growitsch, C. and Wetzel, H., 2009. Testing for economies of scope in European Railways: an
efficiency analysis. Journal of Transport Economics and Policy, 43 (1) 1-24.
35
Kennedy, J. and Smith, A.S.J (2004), ‘Assessing the Efficient Cost of Sustaining Britain’s Rail
Network: Perspectives Based on Zonal Comparisons’, Journal of Transport Economics and
Policy, vol. 38 (2), pp. 157-190.
Kogan, J. (2006): ‘Latin America: Competition for Concessions’, in Jose Gomez-Ibanez and Gines de
Rus (eds.) Competition in the railway industry: an international comparative analysis, Edward
Elgar, Cheltenham.
Kumbhakar , S.C. and Lovell, C.A.K (2000). Stochastic Frontier Analysis, Cambridge University
Press, Cambridge UK.
Lalive, R. and Schmutzler, A. (2008). Entry in Liberalized Railway Markets: The GermanExperience.
Review of Network Economics, Vol. 7, no. 1, pp. 37-52
LEK, TTCI, Halcrow, 2003. Bottom-up review of Network Rail’s business plan: 2003/04-2005/06.
Report to ORR. London.
McNulty, Sir R (2011) Realising the potential of GB Rail: final independent report of the Rail Value
for Money study. Department for Transport and Office of Rail Regulation, London.
Merkert, R. Smith, A.S.J. and Nash, C.A. (2009). ‘Benchmarking of train operating firms - A
transaction cost efficiency analysis’, Journal of Transportation Planning and Technology.
Merkert, R., Smith, A.S.J. and Nash, C.A. (2012), ‘The measurement of transaction costs – evidence
from European railways’, Journal of Transport Economics and Policy, 46 (3), 349-365.
Mizutani, F. and S. Uranishi, (2013), ‘Does vertical separation reduce cost? An empirical analysis of
the rail industry in OECD countries’, Journal of Regulatory Economics. 48 (1), 31-59.
Mizutani, F. Smith, A.S.J., Nash, C.A. and Uranishi, S. (2014). Comparing the Costs of Vertical
Separation, Integration, and Intermediate Organisational Structures in European and East Asian
OECD Railways, mimeo (available from the authors on request).
Nash C A and Nilsson J E (2009) Competitive tendering of rail services – a comparison of Britain and
Sweden Paper presented at the Thredbo 11 conference, Delft.
Nash, C A, Nilsson JE and Link H (2013), ‘Comparing three models for introduction of competition
into railways’, Journal of Transport Economics and Policy, 47, Part 2, May 2013, 191–206.
Nash, C.A., A. S. J. Smith, D. van de Velde, F. Mizutani and S. Uranishi (forthcoming): Structural
reforms in the railways: incentive misalignment and cost implications, Research in
Transportation Economics.
Nash, C.A. and Smith, A.S.J. (2007), ‘Modelling Performance: Rail’, in Hensher, D.A. and Button,
K.J. eds., Handbook of Transport Modelling, Second Edition, Elsevier.
ORR (2013).
Oum T.H. and Yu, C. (1994), ‘Economic Efficiency of Railways and Implications for Public Policy: A
Comparative Study of the OECD Countries’ Railways’, Journal of Transport Economics and
Policy, vol. 28, pp. 121-138.
36
Oum, T.H., Waters, W.G. (II) and Yu, C. (1999). ‘A Survey of Productivity and Efficiency
Measurement in Rail Transport’, Journal of Transport Economics and Policy, 33 (I), 9-42.
Oum, T. H. and Zhang, Y. (1997). ‘A Note on Scale Economies in Transport’. Journal of Transport
Economics and Policy, 309-315.
Pitt and Lee (1981), Preston (2008).
Schmidt, P. and Sickles, R.C. (1984), ‘Production Frontiers and Panel Data’, Journal of Business &
Economic Statistics, vol. 2 (4), pp 367-374.
Shephard, R. W. (1953). Cost and Production Functions. Princeton: Princeton University Press.
Smith, A.S.J. (2004),’ Essays on Rail Regulation: Analysis of the British Privatisation Experience,
Doctoral Thesis, University of Cambridge.
Smith, A.S.J. (2006). ‘Are Britain’s Railways Costing Too Much? Perspectives Based on TFP
Comparisons with British Rail; 1963-2002’, Journal of Transport Economics and Policy, 40 (1),
1-45.
Smith, A.S.J. (2012). ‘The application of stochastic frontier panel models in economic regulation:
Experience from the European rail sector’, Transportation Research Part E, 48, 503–515.
Smith, A.S.J., and P.E. Wheat (2009): ‘The Effect of Franchising on Cost Efficiency: Evidence from
the Passenger Rail Sector in Britain’, 11th
Conference on Competition and Ownership in Land
Passenger Transport, Delft University of Technology, The Netherlands, 20-25 September 2009
Smith, A.S.J. and Wheat, P.E. (2012), ‘Estimation of Cost Inefficiency in Panel Data Models with
Firm Specific and Sub-Company Specific Effects, Journal of Productivity Analysis, vol. 37, pp.
27-40.
Smith, A.S.J, Nash, C. and Wheat, P. (2009). ‘Passenger Rail Franchising in Britain – has it been a
success?’ International Journal of Transport Economics, 36 (1), 33-62.
Smith, A.S.J., Wheat, P. and Nash, C.A. (2010). ‘Exploring the Effects of Passenger Rail Franchising
in Britain: Evidence from the First Two Rounds of Franchising (1997-2008)’, Research in
Transportation Economics, 29 (1) 72-79.
Smith, A.S.J., Wheat, P.E. and Smith, G. (2010), ‘The role of international benchmarking in
developing rail infrastructure efficiency estimates’, Utilities Policy, vol. 18, 86-93.
Spady, R. H. and Friedlaender, A. F. (1978). ‘Hedonic cost functions for the regulated trucking
industry’. The Bell Journal of Economics, 9 (1), 159–179.
van de Velde, D., C. Nash, A. Smith, F. Mizutani, S. Uranishi, M. Lijesen and F. Zschoche
(2012),"EVES-Rail - Economic effects of Vertical Separation in the railway sector", Report for
CER - Community of European Railway and Infrastructure Companies, by inno-V (Amsterdam)
in cooperation with University of Leeds – ITS, Kobe University, VU Amsterdam University and
Civity management consultants, Amsterdam/Brussels, 188 pp.
37
Wheat, P.E. and Smith, A.S.J. (2014), Do the usual results of railway economies of scale and density
hold in the case of heterogeneity in outputs: A hedonic cost function approach, Journal of
Transport Economics and Policy (online first, January 2014).
Zellner, A. (1962), ‘An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests
for Aggregation Bias, Journal of American Statistical Association, 57, pp. 348-368.