2011-28
Does Vertical Separation Reduce Cost?
An Empirical Analysis of the Rail Industry
in OECD Countries
Fumitoshi Mizutani

Shuji Uranishi

Does Vertical Separation Reduce Cost?
An Empirical Analysis of the Rail Industry in OECD Countries*
byFumitoshi Mizutani (Kobe University)
Shuji Uranishi (Fukuyama Heisei University)

Correspondent Author: Fumitoshi Mizutani
Kobe University, Graduate School of Business Administration
2-1 Rokkodai, Nada-ku, Kobe 657-8501(Tel): +81-78-803-6905(Fax):+81-78-803-6977(E-mail): toshi@kobe-u.ac.jp[Abstract]: The main purpose of this study is to analyze structural separation policies, especiallyvertical (i.e. operation-infrastructure) separation and horizontal (i.e. passenger-freight service)separation. Using the total cost function of a railway organization, we evaluate whether or notvertical separation and/or horizontal separation can reduce costs.

For this analysis, we select 30

railway organizations from 23 OECD countries over 14 years, from 1994 to 2007.

Our findings

show that because the horizontal separation dummy has a negative sign with statistical significance,
horizontal separation can be seen to reduce the cost of a railway.

The effect of the verticalseparation changes according to the train density of a railway organization.

With lower train

density, vertical separation tends to reduce cost, while with higher train density vertical separation
increases cost.

[JEL Classification]: L23, L33, L51, L92, R48[Key Words]: Vertical Separation, Horizontal Separation, Total Cost Function, Railway*

An earlier version of this paper was presented at the 12th World Conference on Transport Research in Lisbon,
Portugal, July 11-15, 2010, an Economics Seminar at Osaka University, Graduate School of Economics, September
30, 2010, and an Applied Microeconomics Seminar at Kyoto University, Graduate School of Economics, January 27,
2011. For providing important information and valuable comments and suggestions we would like to thank thefollowing: Simon Fletcher (International Union of Railways: UIC), Motoshi Fukushige (Osaka University), Koichi
Futagami (Osaka University), Yuichi Fukuda (Osaka University), Se-il Mun (Kyoto University), Tatsuhiko Nariu(Kyoto University), Stephen Perkins (Joint Transport Research Centre of the OECD and the International Transport
Forum), Siebe Riedstra (Dutch Ministry of Infrastructure and Transport), Helge Sanner (Deutsche Bahn AG),
Katsuya Takii (Osaka University), Atsuo Utaka (Kyoto University), Vincent Vu (International Union of Railways:
UIC), Bastin Zibrandtsen (Danish Ministry of Transport) and anonymous referees.

1

Does Vertical Separation Reduce Cost?
An Empirical Analysis of the Rail Industry in OECD Countries
1 Introduction
Since the Japan National Railway (JNR) was privatized and subdivided into six
passenger JR companies and one nationwide freight JR company in 1987, privatization andregulation of railways have been effected in many countries, each according to its own railway
regulation

andcompetition

policies.

For

example,whileverticalseparation(i.e.

operation-infrastructure separation) is a common policy in the European Union, vertical integrationis still the structure of choice in the Japanese rail industry1.
there are many variations.

Among vertical separation options,

Possibilities include a functional accounting separation, an

organizational separation of rail operations and infrastructure, or organizational separation involving
a holding company. Massive horizontal (regional) separation of former state railways was adopted
in the UK and Japan, but in some countries the descendent organization of the former state railway
has a vital role in the market.

As for the ownership structure, a commercial organization withprivate ownership is common in the UK and Japan, in contrast to Denmark, where Danish Railway is
still a publicly owned organization.
Competition policy is a vitally important issue in regulatory reform.

Jensen (1998), by

using a model in an empirical study of the Swedish railway sector, finds that external competitive
pressure is strong in most supply segments.
different countries.

However, competition is handled in different ways in

For example, while direct competition, defined as “competitive

tendering/competition for the market” in regional passenger transport and “open access/competitionin the market” in freight transport and long distance passenger segments, is common in many
European countries, regulators in Japan, rather than allowing direct market competition to occur,
apply indirect competition schemes such as yardstick regulation (i.e. the benchmark competition
policy) to existing railway organizations (see, for example, Mizutani et al. (2009)).

There arevarious railway regulations and competition policies, with much empirical and descriptive researchhaving been carried out on individual countries’ railway regulations. Although some studies suchas Lodge (2002) explore the notion of regulatory failure in the railway domain by taking ananalytical and a comparative perspective, there are few studies analyzing regulatory and competition
policies across the international board. While some studies such as Oum and Yu (1994) and Lan
and Lin (2006) analyze a rail organization’s performance by using a cross-sectional data set, thesestudies do not focus on regulatory policy.

Oum and Yu (1994) undertake an international

comparison of economic efficiency among OECD countries’ railways.
1

Lan and Lin (2006) present

A series of regulatory reforms and regulation policies of each country is summarized, for example, by
the ECMT (1998, 2001, 2005).

2

an international comparison of performance measurements for railways by using stochastic distancefunctions.
This study focuses mainly on structural separation policy, the most controversial among
various regulatory policies in the rail industry, with our main purpose being to analyze how verticalseparation policy affects each individual rail operator’s performance.
measures, we pay special attention to cost structure changes.

Among performance

There already exist many empiricalstudies on vertical separation’s effect on cost, but their results vary, with some studies supporting theidea that vertical separation improves efficiency (e.g. Shires et al., Kim and Kim (2001)); somesuggesting the opposite (e.g. Cantos Sanchez (2001), Bitzan (2003), Jensen and Stelling (2007),
Ivaldi and McCullough (2008) and Growitsch and Wetzel (2009)); and one showing no effect (e.g.
Mizutani and Shoji (2004)).

Because studies have shown such differing, inconclusive results, theseparation issue needs further analysis.

In this study, we explain the effect of vertical separation

policy on cost, by considering the differences in the degree of train density in the empirical costmodel.
This paper consists of five sections after the introduction.

In the second section, wesummarize the previous literature, including both theoretical and empirical studies related to thevertical separation policy.

In the third section, we explain theoretical background by applying

Williamson’s transaction cost economics.
Preston (2002) and Hori (1996).
analysis.

For the conceptual argument here, we are indebted to

In the fourth section, we explain the empirical cost model for thisThe cost model is specified as translog total cost function.

In the cost model, bothvertical separation dummy and horizontal (passenger-freight) separation dummy variables areincluded.

The cost model is specified as to what extent vertical separation’s effects are changed by

the degree of train density of a rail organization.

Furthermore, in order to control the output

qualities, hedonic specification for output measures is used.

In the fifth section, the empiricalresults are shown, after and explanation of the sample selection and data.

Rail operators andinfrastructure managers in OECD countries for the years from 1994 to 2007 are chosen. The main
data source is a compilation of railway statistics issued by the International Union of Railways (UIC).
The observations in the analysis cover, for example, JRs in Japan, SNCF in France, NS in Holland,
SJ in Sweden, KORAIL in South Korea, and so on.

By using empirical results, we evaluate

whether or not vertical separation and horizontal (passenger-freight) separation can reduce the costof railways. Last, we outline important points garnered from this analysis.
The main results of this study are as follows.
First, because the horizontal(passenger-freight) separation (i.e. passenger and freight service) dummy has a negative sign withstatistical significance, horizontal (passenger-freight) separation can be seen to reduce the cost of arailway.

Second, the effect of the vertical separation changes according to the train density of arailway organization.

With lower train density, vertical separation tends to reduce costs, while with3

higher train density, it would increase costs.

2 Previous Studies
There are many studies regarding structural separation in the rail industry, most aiming todiscuss the advantages and disadvantages of vertical separation based on both theory and empiricalevidence.

In this section, we will give an overview of studies regarding the theoretical effects ofvertical separation, such as Nash (1997), Hori (1996), Preston (2002), Ksoll (2004) and Drew (2009).
Other studies, such as Nash and Rivera-Trujillo (2004) and Di Pietrantonio and Pelkmans (2004),
summarize and discuss regulatory reforms, including vertical separation, in the EU railway industry.
Pittman (2003, 2005) discusses structural separation with a focus on developing countries.

There

are studies on the unbundling issue by Affuso and Newbery (2004) and infrastructure quality by
Buehler et al. (2004)2.
First, Nash (1997) cites the potential advantages of separation: (1) promotion of a varietyof operators; (2) clarification of intra-industry relationships; (3) specialization in both operation andinfrastructure.

On the other hand, he notes that separation has adverse effects on (1) pricing andperformance; (2) timetabling and slot allocation; (3) investment; (4) safety; and integrated
information and ticketing.

These advantages and disadvantages are summarized in order toformulate a practical policy for the rail industry.
Hori (1996) and Preston (2002) apply Oliver Williamson’s framework of transaction costeconomics to the railway industry.
example, model building.

These studies are not theoretical and do not involve, forHowever, they consider this issue as a trade-off between market

governance, which implies vertical separation, and bureaucratic internal governance, which implies
vertical integration.

For example, Preston (2002) evaluates the advantages and disadvantages ofthe operation-infrastructure separation. He mentions that the rail industry may well be thought ofas one in which there is site-specific transfer of intermediate product across successive stages andhence unified governance (i.e. vertical integration) might be preferred, but this would need to bevalidated by empirical results.

Although Hori (1996) mentions in his study that the degree of asset

specificity increases in urban rapid rail systems compared with local rail systems, he does not
explain why the degree of asset specification increases.
Like Nash (1997), Ksoll (2004) explores the arguments both in favor of and against
2

Affuso and Newbery (2004) investigate whether or not the investment pattern of the rail passenger
franchisees responds to structural and contractual characteristics using a unique panel data on privatizedrailways in Britain. Their results suggest that unbundling and competition for franchises combined withcommercial objectives can provide strong incentives for better performance, as is the case for investment
behavior. Buehler et al. (2004) investigate how various institutional settings affect a network provider’sincentives to invest in infrastructure quality. In their analysis, with suitable non-linear access prices,
investment incentives under separation become identical to those under integration.

4

vertical integration in railways.

There are eight advantages: (1) lower complexity of interfaces

simplifies operational co-ordination and conflict settlement; (2) comprehensive investment
incentives and avoidance of holdups strengthen capacity, quality, safety and innovation; (3) private
infrastructure provision within an integrated firm ensures higher productivity levels and market
driven allocation; (4) integration yields cost savings and synergies in shared facilities and services;(5) co-existence of integration and competition drives technological and product innovation; (6)encouragement of staff identification and responsibility increases quality and safety; (7) partial
avoidance of double marginalization increases consumer welfare; (8) strategic behavior of theintegrated firm can counteract excessive entry. On the other hand, there are four disadvantages ofvertical integration: (1) integration involves the risk of discriminatory behavior by the infrastructure
provider against downstream competition; (2) integration complicates regulation of the infrastructure
monopoly; (3) there is a conflict between public infrastructure obligations and private infrastructure
management; (4) integration may go along with lower and/or misguided performance incentives ininternal compared to fully external transactions.
Pittman (2003) evaluates the desirability of certain forms of restructuring in the rail
industry as well as in the electricity and telecommunication industries in transaction economies.
There are three potential forms of restructuring: a vertically integrated monopoly, vertical separation,and vertical integration with competition.

Pittman believes that one possible solution would be tocreate on-track competition between integrated and nonintegrated train operators, but that due toboth economies of density and intermodal competition, it seems unlikely the benefits of on-trackcompetition would be very great, except perhaps for the largest shippers.

Pittman concludes thatthe vertically integrated monopoly form might be the best model for creating competition andattracting private investment.
Kurosaki (2008, 2009) evaluates vertical separation policies that have been effected in theworld’s rail industries, classifying vertical separation options into fourgroups: (1) verticalseparation without within-rail competition (e.g. Vietnam, Indonesia and Tunisia), (2) verticalseparation with competition among operators (e.g. Sweden, U.K., Germany, France and Australia),(3) vertical separation for passenger or freight traffic (e.g. Japan (JR Freight), US (Amtrack)), (4)concession of long-run access to infrastructure.

He summarizes appropriate forms of verticalseparation policy according to differing market structures (e.g. with/without within-rail competition,or market share of passenger and freight service).

Kurosaki’s contribution is his recognition that

there is more than one feasible form of vertical separation.

However, the empirical evidence bywhich he reaches his conclusion remains weak.
Drew (2009) reviews and analyses the benefits for rail freight customers of the two
principal models for introducing competition in main line railway networks: (1) the verticalseparation of operations from infrastructure; and (2) the introduction of competition providing other5

operators with open access to the network.

He concludes that vertical separation benefits freightcustomers more than open access does alone.
Thus, there exists no definitive theoretical study of vertical separation in the railway
industry.

If we review existing literature from a theoretical point of view, we must say it is notclear whether or not a separation policy (i.e. vertical separation or vertical integration) is desirable.
As for empirical studies, there are many, but their results are not consistent.

Some studies

such as Shires et al. and Kim and Kim (2001) show that vertical separation is better than vertical
integration in terms of efficiency.
First, a study by Shires et al. shows that rail operating costs in Sweden are reduced byabout 10% after vertical separation, although this separation was also accompanied by the gradualintroduction of tendering (Preston, 2002, p.12).
Kim and Kim (2001) analyze the cost structure of Seoul’s subway systems by using thestochastic frontier cost function.

Their calculation results show that the total cost of the verticallyseparated system was about 3.6% lower than that of the vertically integrated system in 1998.
Although their study does not focus only on structural reforms, Friebel et al. (2010) apply
a production frontier model for railways in EU countries over a period of 20 years in order toanalyze the effect of regulatory reforms such as vertical separation, the introduction of third-party
access, and the creation of independent regulatory institutions.

Although this study does not clearly

uncover the effects of vertical separation policy alone, the authors find that regulatory reforms
increase efficiency.
On the other hand, some studies such as Cantos Sánchez (2001), Bitzan (2003), Jensen and
Stelling (2007), Ivaldi and McCullough (2008) and Growitsch and Wetzel (2009) show that verticalseparation is inferior to vertical integration.
Cantos Sánchez (2001) analyzes the vertical relationship by applying translog total costfunction for a data set of 12 European state railways for the period 1973 – 1990.

He obtains theresult that there are complementary effects between costs deriving from freight transport andinfrastructure, while the effects are substitutable between costs deriving from passenger transport
and infrastructure.

Sanchez concludes that infrastructure and operations must be coordinated bothin order to maintain the coordination effect and to avoid possible inefficiencies.
Bitzan (2003) examines the cost implications of competition over existing US freight raillines by testing for the condition of cost subadditivity.

He finds that there are economies associatedwith vertically integrated roadway maintenance and transport.

This result suggests that verticalseparation of infrastructure from operations increases costs.
Jensen and Stelling (2007), by using data from the railway industry in Sweden, explore
how deregulation has affected cost efficiency.

In their cost estimation, they evaluate the effect ofvertical separation and conclude that it increases costs.
6

Ivaldi and McCullough (2001) apply the cost function to Class I U.S. railways andevaluate the effects of vertical separation.

They find modest cost complementarities between

general freight operations and infrastructure maintenance, but anti-complementarities between bulk
and infrastructure and between intermodal and infrastructure maintenance.

However, in more

recent empirical results by Ivaldi and McCullough (2008) for U.S. freight railways for the period
1978-2001, they find both vertical and horizontal economies of scope.

According to the authors,

there would be a 20 to 40% loss of technical efficiency if railway freight operations were separated
from infrastructure and an additional 70% loss of operational efficiency if on-rail operations wereseparated.
Growitsch and Wetzel (2009) investigate the performance of European railways with aparticular focus on economies of vertical integration. They apply data envelopment analysis (DEA)
to a data set of 54 railway companies from 27 European countries over 5 years from 2000 to 2004.
From their analysis, they conclude that for a majority of European railways, there exist economies ofscope.
One study shows no difference in efficiency.

Mizutani and Shoji (2004) apply thetranslog cost function to maintenance activities in the Japanese rail industry and evaluate whether or
not the vertical separation of operation and infrastructure activities would reduce cost.

The results

indicate that vertically separated systems might not be significantly different from verticallyintegrated ones.
Thus, previous empirical analysis has produced inconsistent results.

It remains unclear

whether vertical separation yields efficiency or inefficiency with regard to cost.

3 Theoretical Background of Vertical Separation/Integration in the Rail Industry
In this section, we explain the rationale for the vertical separation/integration policy in therail industry.

Our plausible conclusion is that the vertical separation/integration depends on thelevel of train density.

These theoretical arguments on vertical separation/integration can be

explained by both the framework of transaction cost economics by Williamson (1985) and theapplication to the rail industry by Hori (1996) and Preston (2002).

Although we use the frameworkof transaction cost economics, we also explain the effects of vertical separation by looking at train
density rather than asset specificity, and by assuming that the degree of asset specificity is related totrain density.
Based on Hori (1996) and Preston (2002), the application of Williamson’s transaction costeconomics to the rail industry is as follows.

The key concept is the trade-off between the costassociated with market governance, which implies vertical separation, and internal governance,
which implies vertical integration.

We define ΔPC as the difference between the production costs
7

of internal governance (PCB(k)) and the production costs of market governance (PCM(k)).
Williamson (1985) assumes that the production costs of market governance, PCM(k) are always
lower than the production costs of internal governance, PCB(k).

However, as the potential for scaleeconomies across firms is reduced as the degree of asset specificity, k, increases, the production costdifference becomes smaller.

After all, when the degree of asset specificity is too high, theproduction cost of market governance becomes larger than that of internal governance. Therefore,
the production cost difference, ΔPC, declines as the degree of asset specificity increases.
Furthermore, governance costs, ΔGC, are defined as the difference between internal
governance costs (GCB(k)) and market governance costs (GCM(k)).

If the degree of asset

specificity is very low, the railway organization can purchase infrastructure management services
from anybody in the market.
governance costs.

Therefore, internal governance costs are much higher than market

On the other hand, if the degree of asset specificity is very high, market

governance costs become larger than internal governance costs because the railway company cannot
find a safe infrastructure management company.
When we consider the total cost, ΔC, which is the sum of ΔPC and ΔGC, we can see thecrossover point at k**.
ΔGC) are positive.

To the left of point k**, the market will be cost effective because ΔC (=ΔPC+

This means that vertical separation could be reasonable.

On the other hand, tothe right of point k**, internal organization will be cost effective. Therefore, vertical integration
could be reasonable.

****************
Figure 1****************
Finally, we will explain how the degree of asset specificity of the rail infrastructure isrelated to the train density of a rail organization. This train density variable is considered a proxyvariable for asset specificity.

We do not mean to imply that focusing on train density necessarily

leads to perfect decision making about whether to self-supply infrastructure maintenance and train
control activities,3 but we can use train density to understand more easily how vertical separation
can affect the production and governance costs of train operation and track maintenance activities.
First, as for production costs, maintenance activity of rail infrastructure is divided into
two components, one related to track length and the other to train density.
3

As the maintenance

U.S. freight railways often rely on independent firms to supply important traffic related maintenanceactivities such as tamping and grinding services. In Japan, some private railways use outside
independent firms for track maintenance.

8

activities of the first component are fixed regardless of the degree of train density, we can expect arailway to make use of resources available on the market.

However, with regard to the second

component of maintenance activities (e.g. rail and electric wire inspection, signal system
maintenance), the situation is different. When a railway’s train density is very low and its schedule
relatively simple, it would be more efficient for that railway to use maintenance offered on themarket than to hold its own staff and machinery.

However, when train density is very high andtrain operations much more complex, daily maintenance activities become more frequent anddemanding. For high-density organizations, internal ownership of maintenance staff and machineryis preferable because it reduces the difference in production costs between internal governance andmarket use. The production cost difference decreases as train density increases.
A more important point is governance cost.
train density increases.

Cost differences decrease more rapidly as

Governance costs by market governance include labor costs related to thecoordination of divisions between two organizations, material costs such as those associated with
documents related to maintenance activity plans, legal costs, and insurance costs.

When train

density is very low, market governance costs would be low because a simple maintenance activity
contract would suffice.

However, such costs would clearly be formidable under conditions ofheavy train density because of the necessity to conduct safe train operations.

Further increasing

costs of high-density organizations is the need for adequate insurance and legal documentation incase of accidents.

Also increasing governance costs would be the minutely detailed contracts

necessary to prevent outside service-supplying companies from engaging in opportunistic behavior.
Of course, with internal governance, these costs are to some degree necessary but coordination andlegal costs become much smaller because the top manager can make decisions about priorities andmanagement power hierarchy among different internal divisions.

Therefore, as train density

becomes larger, the degree of the asset specificity becomes larger, increasing the governance costs ofhigh-density railway organizations.
Therefore, the plausible conclusion is that vertical integration is more cost effective thanvertical separation, if the rail organization’s train density is very heavy.

On the other hand, verticalseparation is more cost effective than vertical integration under low train density.

This is true

because the degree of the asset specificity in the rail infrastructure is highly related to the train
density of the rail organization.

Although there is systematic empirical evidence, in particular, theexperience of JR Freight relative to JR passenger companies after the privatization of JNR shows
support for our argument (see for example, Mizutani and Nakamura (2004)).

Moreover, in Japan,

some small railway companies with low train density operating in rural areas have delegatedmaintenance of their privately held rail tracks to extra-mural, mostly public organizations.
Issues remain.
policy.

The current vertical separation policy is based on a belief in competition

As the rail industry in general tends to have strong economies of scale, the government
9

seeks to stimulate competition by separating rail infrastructure from operations. However, if the
train industry’s economies of scale are too strong, the result of vertical separation may be twomonopolies instead of one, as Pittman (2003) and Thomas (2003) point out.

In fact, Ivaldi andMcCullough (2001) note that even if railways are separated into operations and infrastructure, thefirms still experience operational returns to density and enjoy large market share, so that an open
access regime would not necessarily lead to competitive outcomes.
While this may be true, our main interest is in whether vertical separation can reduce total
railway costs.

There is also the fact that the separation policy creates at least two separated

companies (i.e. an operations and an infrastructure company), and that governance costs will becreated to coordinate the two companies.

The framework of Williamson’s transaction costeconomics clarifies separation/integration issues.

We will investigate these issues from anempirical point of view.

4 Empirical Cost Model
Based on our arguments in the previous section, we investigate the vertical separation
issues related to total cost.

Our hypothesis is that cost reduction associated with vertical separation

changes with the degree of train density.

At low train density, vertical separation works to reduce

costs, but as train density increases, vertical separation increases costs.

To investigate thishypothesis, the most important characteristic of our cost model is specified such that the effect ofvertical separation varies by train density.
In this study we employ a translog total cost function,4 in which we include two kinds ofinstitutional variables: a vertical separation dummy (DVS) and a horizontal (passenger-freight)
separation dummy (DHS).

The cost model is specified such that the effect of vertical separation on

the cost varies by the degree of train density.

The output measure is specified as a hedonic functionof output characteristics in order to control the differences in output conditions.
The translog cost model used here is shown as follows:2

lnTC =0 +Y lnY + jjlnwj + NlnN + T T + (1/2)YY (lnY) + jYj (lnY)(lnwj) +YN (lnY)(lnN) + YT (lnY)(T) + (1/2) kjjk (lnwj) (lnwk) +jjN (lnwj) (lnN) + jjT (lnwj) (T) + (1/2) NN (lnN)2+ NT (lnN)(T) +2(1/2)TT T + (VS1 + VS2lnV)DVS + HSDHS
lnY = lnQ + f f ln Hf,

(1)
(2)

4

Several studies (e.g. Savage (1997), Mizutani (2004), Mizutani and Uranishi (2007)) use the variable
cost function. However, as the main purpose of this study is to evaluate the effect of infrastructure
management on cost, we use the total cost function.

10

where

TC: total cost
Y: output measure
Q: quantity of output
Hf: characteristics of output ( f = PR (passenger revenue share),
LF (load factor of passenger service), PTL (passenger travel length), FRC(number of freight cars per train))
wj: input factor price 5 (j (or k) = L (labor), M (material), K (capital)),
N: total route length,
T: technology 6 (T: percentage of electrified length),
V: train density,
DVS: vertical separation dummy (vertical separation =1, otherwise = 0),
DHS: horizontal (passenger-freight) separation dummy (horizontal separation = 1,otherwise = 0).

In this model, we impose the restriction on input factor prices such that jj = 1, kjk = 0,jjN = 0, jjT = 0, jYj = 0, jk = kj, jN = Nj, jT = Tj.
Lemma to the total cost function.

Furthermore, we apply Shephard’s

Then we can obtain the input share equations as follows:

Sj = j + Yj (lnY) + kjk (lnwk) + jN (lnN) + jT (T),
where

(3)

Sj: input j’s share of total cost.

As for the estimation technique, we apply the seemingly unrelated regression (SUR)
method by the total cost function and the input share equations.

For the estimation, we will divide

all observations of each variable by the sample mean, except for time trend.
In this study, we apply Shephard’s Lemma to the cost function.
that the rail company minimizes its costs.

This implicitly assumes

Most railway companies used in this study are publicorganizations, and there might be skepticism about whether such public organizations actually
minimize costs, but if the cost-minimizing assumption is not held, there is the possibility that the5

We estimate the cost function with three input factor prices (labor, material and capital). However,some train companies do not separate the information of material and capital expenditures. Therefore,
we also estimate the case of the cost function with two input factor prices in order to check the estimationbias.
6
In this study, as for technology variable (T), we take the natural logarithm for percentage of electrified
length (i.e. ln T). We also estimate the cost function by using time trend for T. However, the overall
results by time trend are inferior to these by percentage of electrified length. Therefore, we chose thisvariable.

11

estimation results of the input share equations could be faulty.

This approach allows us to checkour results.

5 Empirical Analysis
5.1 Sample Selection
The main purpose of this study is to examine how differences in structural reform affectcost structure; that is, we evaluate how differences in unbundling methods, such as verticalseparation and horizontal (passenger-freight) separation, affect cost difference.

In order to evaluate

the structural factor only, we selected railway organizations with relatively similar conditions.

As asample selection, we chose railway organizations from OECD countries, excluding those of OECD
railway organizations in the US, Canada and Australia, however, because their network conditions
are generally different (e.g. long line hauls).

In Japan, we count each JR company separately inorder to avoid the estimation bias that would result from combining the JRs into one huge railorganization.

And while there exist cost studies, for example that of Smith (2006), which do use

data from the UK rail industry, we unfortunately have to forgo including the UK because of theoverall lack of data.

As Table 1 shows, we collected data on 30 railway organizations from 23

OECD countries for the 14 years from 1994 to 2007, giving us 420 observations (i.e. 30 railways
times 14 years).
We follow the definition of structural reform 7 of the UIC, which classifies railway
organizations into five categories: (1) integrated company, (2) railway undertaking, (3) passenger
operator, (4) freight operator, and (5) infrastructure manager.

For example, as for

operation-infrastructure management, DSB in Denmark was separated from its infrastructureorganization (BDK) in 1997, so that DSB is classified as having had vertical separation since 1997.
However, the freight service of DSB, which became Railion DK, was separated in 2001, so that DSB
is also classified as having had horizontal (passenger-freight) separation since 2001. KORAIL in
Korea was neither vertically nor horizontally separated between 1994 and 2007, so that KORAIL isclassified as an integrated system.

Therefore, vertical separation here means that the activities ofrail operations and infrastructure management are provided by completely separate organizations.
Two different organizations under the same holding company are not separated bodies.
There are potential problems related to data.

First, most railway companies belong to the

public sector, with infrastructure possibly supported by the government.

We know that eachcountry’s accounting system is different and that all infrastructure investment might not be recordedin the UIC data, but due to a lack of other data sources, we are compelled to use what might beincomplete information.
7

There are some studies on classifications of structural reforms (e.g. ECMT (1998, 2001) and Kurosaki(2008, 2009). In this study, we focus on the effect of organizational separation. The standard data are
well organized in the UIC data set. Therefore, we follow the definition of the UIC.

12

****************
Table 1****************

5.2 Main Data Source and Definition of Variables
The main data source for this study is International Railway Statistics, issued annually by
the UIC.

In this source, however, some railway organizations’ data are incomplete, and to fill inthese information gaps, we have used data from several other sources. Table 2 shows our main data
sources.

****************
Table 2****************
Before we explain the definition of variables, we must explain the treatment of total cost in
the structurally separated organization.
cost structure.

In this study, we analyze the structural separation effect on

In the case of integrated rail systems, we can use the reported total cost itself.

However, in the case of structurally separated companies, we combine these organizations, as Table
3 shows.

It is worth noting that input factors such as labor and rolling stock are also combined incases where organizations are combined.

In general, the separated rail company’s infrastructure

costs are included as service costs, which are paid as infrastructure fees.

****************
Table 3****************

Table 4 shows the definition of all variables used for the estimation of total cost function.
First, total costs (TC) in this study are defined as the sum of labor, energy, material costs and capitalcosts including tax expenditures.

In rail operation companies with vertically separated systems,

13

service costs for infrastructure service are included in the total costs. In the integrated rail system,
infrastructure costs are included as depreciation and maintenance activity costs for infrastructure.
As for output measure, we use the total number of train kilometers (Q) for both passenger
services and freight services.

In order to avoid estimation bias based on different kinds of output,

we also include four kinds of variables of output characteristics: passenger revenue share (HPR), loadfactor of passenger service (HLF), passenger travel length (HPTL) and number of freight cars per train(HFRC).

First, passenger revenue share is defined as the ratio of passenger service revenue to totalrail service revenues.

Second, passenger load factor is defined as the ratio of the number ofpassengers per train to the designated capacity of a passenger vehicle.

The designated capacity of apassenger vehicle is calculated by multiplying the number of vehicles per train by the number ofseats per passenger vehicle.

The number of passengers per train is obtained by dividing revenue

passenger kilometers by passenger train kilometers.

Third, passenger travel length is measured as

the ratio of revenue passenger kilometers to the total number of passengers.

Last, number of freightcars per train is obtained by dividing gross-ton-km of freight service by train-km of freight service.
We assume that the weight of a freight car is 50 tons per vehicle. As we explained before, these
output measures and output characteristics measures are specified as a hedonic function.

****************
Table 4****************

There are three kinds of input factor prices.

First, labor price (wL) is obtained by dividing

labor costs by the total number of employees.

Material price (wM) is obtained by dividing service

and material expenditures by rolling stock.

Capital costs are considered mostly as a portion of

expenditures and financial expenditures.

In this study, we allocated 75% of depreciation

expenditures as capital cost for integrated rail organizations.
capital cost per route length.

Capital price (wM) is defined as

In order to check for estimation bias, we also estimate the costfunction by two input factor prices models.

In this case, material and capital costs are combined.

Material and capital price (wM&K) is obtained by dividing material and capital costs by the composite
material index.

The composite material index is the weighted share of rolling stock and route

length.

In this study, we assume that the rolling stock’s weight is 24% and the route length’s weightis 76%.

We should note that due to a lack of data we are unable to include energy prices.

are included in the price of material and capital.

14

These

As for the network variable, we include the total route length (N). As for the technology(T) variable, there are two possibilities. First, there are two possible proxy variables that would
show technological progress, such as the percentage of ATS (Automatic Train Stop) or ATC(Automatic Train Control), control systems for maintaining safe train operation, and electrified line
length.

In this study, we define technology as the percentage of electrified lines (T).

Although we

considered using the ratio of ATS or ATC as variables, we were forced to forgo their use due to alack of data availability. Alternatively, technology is used as a measure of time trends.

In thisspecification, all railway organizations can progress technologically in a linear fashion and canobtain technology on an equal basis.

Although we estimate the cost function by using time trend,

the results of the percentage of electrified lines are better.

Therefore, we report the case of thepercentage of electrified lines only.
Train density (V) is obtained by dividing the number of train-km by the total route length ofa railway. This variable is measured as per-day so that it is divided by 365.

This variable is usedwith the vertical separation dummy in order to measure the multiple effects of vertical separation andtrain density, as explained above.
Finally, two kinds of structural dummy variables are defined.

First, the vertical separation

dummy (DVS) is defined as a binary measure, in which the vertically separated railway company isequal to one but is otherwise zero.

The horizontal (passenger-freight) separation dummy (DHS) is

also defined as a binary measure.

If a railway company’s passenger and freight services are

separated, this measure is equal to one but is otherwise zero.

5.3 Empirical Results
We estimate the total cost function shown in equation-(1) and (2) with equation-(3).

Forour estimation, we use the seemingly unrelated regression (SUR) method by the total cost function
and input share equations. The estimation results of the total cost function are summarized in Table5.

We show four cases in Table 5: two kinds of input factor prices model (i.e. two input factor(combined material and capital price) or three input factor (separated material and capital price) andwhether train density is considered in the vertical separation dummy (i.e. with/without the cross-termof train density and vertical separation dummy).
The goodness-of-fit in the regressions is acceptably high for these models because pseudo R2
is very high.

As for the required properties in the cost function, first, symmetry and homogeneity

conditions in input factor prices are satisfied, because we imposed restrictions on the cost model.
Second, as for monotonicity conditions, it is necessary that the cost function be a non-monotone
decreasing function in both output and input factor prices.

Whether or not the monotonicity

conditions are satisfied was evaluated by checking that the partial derivative of the cost function
with respect to output and input factor prices is not negative (i.e. lnC/lnY > 0 , lnC/lnwj > 0).
15

Around the sample mean, these conditions are satisfied.

Determining whether or not the Hessian

matrix holds negative semi-definite can test for the concavity condition in input factor prices.

In

our test results, two-input-factor-price models show very high: about 90% of observations satisfy the
concavity condition.

However, three-input-factor-price models produce a moderate result: about

51% satisfy the concavity condition.

Furthermore, the goodness-of-fit in the regressions is

acceptably high for the input share equations so that the assumption of cost minimization can be
accepted.
Among these cases, Case 2 is the best based on the log likelihood statistics.
the three-input-factor-price model, Case 4 is better than Case 3.

If we consider

Therefore, we conclude that thesecases are all acceptable but Case 2 is the best and Case-4 is an alternative for thethree-input-factor-price model.

****************
Table 5****************

We evaluate the effects of structural reform based on empirical results.

First, because thecoefficients of the horizontal (passenger-freight) separation dummy (DFS) in any case of our analysis
show the negative sign with a statistical significance of 1%, it seems clear that companies can reduce
cost when they functionally separate passenger and freight services. In fact, Kim (1987) finds that
there are diseconomies of scope between passenger and freight service.

If this is true, a horizontal(passenger-freight) separation policy is advisable.
Second, as for vertical separation, in general, vertical separation tends to reduce the costs ofrailways, as the coefficient of the vertical separation dummy (DVS) shows only the negative sign.
These have a statistical significance of 1%.

However, the cross-tem with train density (lnV・DVS)

shows the positive sign with a significance of 1%. This can hold in both Case 2 and Case 4,
regardless of whether the two-input-factor-price or three-input-factor-price model is used.

From

these results, it can be seen that vertical separation effects with lower train density tend to reduce thetotal costs of a railway organization.

But as train density increases, vertical separation causes anincrease in a railway’s total costs.
Our results could explain why previous studies have produced differing results.

In the caseof lower train density, our result supports that vertical separation contributes to cost reduction in therailway industry, which is consistent with studies by Shires et al. and Kim and Kim (2001).
However, in the case of higher train density, our result shows that the vertical separation causes an
16

increase in costs, which is consistent with studies such as Cantos Sanchez (2001), Bitzan (2003),
Jensen and Stelling (2007), and Growitsch and Wetzel (2009).
What accounts for this result?

As explained in the previous section, the framework of

Williamson (1985) and Preston (2002) is helpful. In the case of lower train density, as trains areoperated on tracks, the coordination cost is low between the operating company and theinfrastructure company.

Therefore, production costs can be saved by specializing in activities (i.e.

train operation and infrastructure management).

On the other hand, in the case of higher train

density, coordination between the train operating company and the infrastructure managementcompany is expensive because there are necessarily a lot of costs for such things as meetings formaintenance scheduling, maintaining safety under a busy train operation schedule, and so on.
Therefore, any costs saved by vertical separation specialization would be canceled out by highcoordination costs between two different organizations.
If we consider the component of vertical separation only (i.e. (VS1 + VS2lnV )DVS in
Equation (1)), the effect on cost can be seen clearly.

Figure 2 shows how cost reduction changes

according to the degree of train density based on the estimation results of Case 2 and Case 4. The
cost reduction rate due to vertical separation decreases as train density increases, when otherconditions are fixed.

If train density reaches about 2 times the sample mean, vertical separation

begins to increase costs, as Figure 2 shows.
The train density level of each railway company in 2007 is shown in Table 6.

Among ourobservations in 2007, railway organizations with higher train density are BLS (Switzerland), SBB
CFF FFS (Switzerland), JR East, JR Central and JR West (Japan), KOREAIL (South Korea) and NS(Netherlands). 8

Except for NS, a vertical integration policy has been taken in these railorganizations.
These empirical results show that the European Commission’s policy to apply the verticalseparation policy to all organizations is not appropriate in terms of costs, but may be appropriate
only for the railway organizations with less train density.

For railway organizations with higher

train density, vertical separation is more costly than integration.
****************
Figure 2********************************
Table 6****************
8

The railway organization with the higher train density is a railway organization whose value of train
density (V) is 1.5 times the value of the sample mean.

17

6 Conclusion
Regulatory reforms, including privatization and deregulation in the rail industry, havebeen carried out in many countries, each with its own regulation and competition policies.
Especially noticeable is that while vertical separation is common in Western Europe and is being
undertaken in Eastern Europe as well, vertical integration is still standard practice in East Asia,
especially in Japan.

The main purpose of this study has been to analyze structural separation policy,

especially vertical (i.e. operation-infrastructure) separation and horizontal (i.e. passenger-freight
service) separation. By using the total cost function of a railway organization, we evaluate whether
or not vertical separation and/or horizontal (passenger-freight) separation could reduce costs. We
selected 30 railway organizations from 23 OECD countries for the 14 years between 1994 and 2007.
Our main findings are as follows.

First, because the coefficients of the horizontal(passenger-freight) separation dummy in any case of our analysis show the negative sign with astatistical significance of 1%, horizontal (passenger-freight) separation appears to lower a railway’s
costs. Because of diseconomies of scope between passenger service and freight service, horizontal(passenger-freight) separation is a better policy than the alternative.

Second, as for verticalseparation, in general, vertical separation tends to reduce the costs of railways, as the coefficient of
the vertical separation dummy shows only the negative sign.

However, the cross-term with train

density (lnV・DVS) shows the positive sign with significance of 1%.

From these results, the overall

vertical separation effects with lower train density tend to reduce the total cost of a railway
organization. But as train density increases, vertical separation causes total costs to increase.
In conclusion, our results regarding vertical separation show that the effects on cost
reduction depend on the magnitude of train density. If a rail organization has lower train density,
the vertical separation policy might be reasonable.

However, a rail organization with higher train

density should take a vertical integration policy. Therefore, the European Commission’s policy
applying universal vertical separation policy is not appropriate in terms of costs.

Evidence suggeststhat vertical separation is more costly than the vertical integration for the railway organizations withhigher train density.

[2011.5.13 1045]

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21

Cost Difference (ΔC = CIntegration – Cseparation)

ΔC : Total Cost Difference (= ΔGC + ΔPC)
ΔGC : Governance Cost Difference

ΔC = ΔGC + ΔPC

ΔPC : Production Cost Difference

ΔPC

ΔGC

k
Vertical separation is desirable.

**

Train density(Asset Specificity (k))
Vertical integration is desirable.

Figure 1 The Relationship between Cost Difference and Train Density:
Application for Concept of Production and Governance Costs and Asset Specificity% of cost reduction
by vertical separation

Vertical separationis cost effective.

Degree oftrain density

Vertical integrationis cost effective.

Figure 2 Cost Reduction Rate by The Degree of Train Density

22

Table 1 Railway Operators Included in Our StudyNo.

Railway Operator

Country

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

ÖBB (Österreichische Bundesbahnen)
SNCB/NMBS (Société Nationale des Chemins de fer Belges)
BLS (BLS AG)SBB CFF FFS (Schweizerische Bundesbahnen)
CD (České Dráhy)
DB AG (Deutsche Bahn AG)
DSB (Danske Statsbaner)
RENFE (Red Nacional de los Ferrocarriles Españoles)
VR (VR-Group Ltd)SNCF (Société Nationale des Chemins de fer Français)OSE (Hellenic Railway Organization)
GySEV/RÖEE (Györ-Sopron-Ebenfurti Vasút Részvénytarsasag)
MAV (Magyar Államvasutak Rt.)
CIE (Coras Iompair Éireann)FS (Ferrovie dello Stato SpA)JR Hokkaido
JR East
JR Central
JR WestJR Shikoku
JR Kyushu
KOREAIL (Korean National Railroad)
CFL (Société Nationale des Chemins de fer Luxembourgeois)
NS (N. V. Nederlandse Spoorwegen)
NSB (Norges Statsbaner AS)
PKP (Polskie Koleje Państwowe S. A.)
CP (Caminhos de Ferro Portugueses, E. P)
SJ (Statens Jämvägar AB)
ZSSK (Slovak Rail)TCDD (Türkiye Cumhuriyeti Deviet Demiryollari Isletmesi)

Austria
Belgium
Switzerland
Switzerland
Czech Rep.
Germany
Denmark
Spain
FinlandFranceGreeceHungary
Hungary
Ireland
Italy
Japan
Japan
Japan
Japan
Japan
Japan
South Korea
Luxembourg
Netherlands
NorwayPolandPortugal
SwedenSlovakia
Turkey23

Vertical
Separation
1997~
2005~
1995~
1997~
2007~
1998~
1996~
1997~
1988~
2002~
-

Horizontal
Separation
2003~
2003~
2001~
2006~
1987~
1987~
1987~
1987~
1987~
1987~
2007~
2000~
2002~
2002~
2005~
-

Table 2 Major Data Sources for Our Study
Items
Costs, Output measures, Wage,
Number of employees, Rollingstock, Route length etc.

Exchange rate
GDP deflator

Source(1) International Railway Statistics by the UIC(2) Jane’s World Railways(3) Annual reports by each individual railway organization(4) Danish Ministry of Transport for missing data of DSB and
BDK(5) Annual Railway Statistics for JR
Eurostat(1) World Development Indicators by the World Bank
(2) Economic Outlook 83 Database by OECD

Table 3 Total Costs in Structurally Separated Organizations
Structure
Vertical structure

Typeofrailwayorganization
Vertical integration
Vertical separation

Horizontal(passenger-freight)
structure

Horizontal integration
Horizontal separation

Definition of total costs
Vertically integrated company’s total
cost
Operation company’s total cost +Infrastructure company’s total cost
Horizontally integrated company’s
total cost
Passenger company’s total cost +Freight company’s total cost

(Note):(1) DVS : vertical separation dummy, DHS : horizontal separation dummy

24

Structural dummy
variable
DVS =0
DVS =1
DHS =0
DHS =1

Table 4 Definition of Variables Used for the Estimation of Cost Function
Variable

Definition

Unit

Mean

Standard
Minimum Maximum
DeviationTC
Sum of labor, energy
million
4,063
5,841
80
32,524(Total cost)energy and capital costeuro
Q
thousand
Total train-km(1)137,887 178,241
1,648
936,714(Output)
km
wL
Labor costs per employee
euro40,59522,751
4,203
107,479(Wage)(2)
wM
Material costs per rollingeuro
115,616
117,683
5,749
580,032(Material price)
stock
wK
Capital costs(3) per route length
euro180,651 321,904
292
2,322,617(Capital price)wM&K
Material and capital costs per
euro
312,455 402,805
14,889 2,655,127(Material and capital price) composite material index(4)N
Total route km
km
7,172
8,607
220
41,718(Total route length)
T
Percentage of electrified line
%
52.45
26.93
0.01
100.00(Technology index)
HPRS
Share of passenger revenue to0.78370.11520.43340.9875
total revenue(5)(Passenger revenue share)
HLF
Passenger per train
0.37300.13710.12640.9355(Load factor of passenger)
to capacity(6)HPTL
Revenue passenger-km per
km
52.03
30.09
14.64
190.21(Passenger travel length)
passenger
HFRC
Number of freight car per train
car
17.30
4.31
5.37
30.74
(Average freight car)V
Train-km per route length per
Train/day
61.44
36.17
12.26
165.12day(Train density)(7)
DVS
Vertical separation dummy
0.24050.42790.00001.0000(Vertical separation)(Vertical separation = 1)
DFS
Horizontal separation dummy
0.29290.45560.00001.0000(Horizontal separation = 1)
(Horizontal separation)SL
Share of labor
0.38860.12330.10580.6850(Share of labor)
input expenditureSM
Share of material expenditure
0.37390.10210.13260.7359(Share of material)
SK
Share of capital expenditure
0.23750.14380.00290.6743(Share of capital)
SM&K
Share of material and
0.61140.12320.31480.8942
capital expenditure(Share of material & capital)(Note):(1) Total train-km (Q) = Passenger train-km + Freight train-km(2) Material costs = Purchases of material and external services + 0.25 * Depreciation(3) Capital costs = Tax + Other operating expenses + 0.75 * Depreciation + Financial expenses+ Total costs of Infrastructure Manager(4) Composite material index (M) = 0.24 * Rolling stock + 0.76* Total route lengths(5) Passenger revenue share(HPRS) = Passenger service turnover / Passenger and freight service turnover(6) Load factor of passenger (HLF) = Passengers per train / Capacity
Where Capacity = Number of wagons per train * Number of seats per passenger wagon
Number of wagons per train = Passenger gross hauled ton-km / Passenger train-km / 50 ton *1000
Passengers per train = Revenue passenger-km / Passenger train-km * 1000
(7) Train density (V) = Train-km/Route-km/365

25

Table 5 Estimation Results of the Total Cost Function
Variable
Case 1Case 2
Case 3
Case 4
Variable
Case 1Case 2
Case 3
Case 4
Y
0.6187*** 0.5588*** 0.7629*** 0.6981*** Y･wM
0.0327*** 0.0419***(0.0351) (0.0388) (0.0366) (0.0400)(0.0102) (0.0107)
HPRS-1.3293*** -1.5508*** -1.2888*** -1.7110*** Y･wK
-0.1417*** -0.1550***(0.1603) (0.1718) (0.1472) (0.1556)(0.0144) (0.0150)
HLF-0.2000*** -0.2816*** -0.0795 -0.1616*** Y･wM&K -0.1147*** -0.1137***(0.0640) (0.0714) (0.0528) (0.0569)(0.0100) (0.0103)
Y･N
HPTL
0.1220*** 0.1352*** 0.1675*** 0.1787***
0.5094*** 0.5304*** 0.4468*** 0.5033***(0.0441) (0.0453) (0.0417) (0.0421)(0.1112) (0.1116) (0.1029) (0.1042)
Y･T
HFRC
0.2871*** 0.2062** 0.3568*** 0.2006**
0.1785*** 0.1604*** 0.1646*** 0.1219***(0.0853) (0.0886) (0.0780) (0.0789)(0.0409) (0.0421) (0.0381) (0.0398)
wL･N -0.1288*** -0.1283*** -0.1133*** -0.1169***wL
0.3312*** 0.3305*** 0.3085*** 0.3061***(0.0050) (0.0051) (0.0051) (0.0052)(0.0103) (0.0106) (0.0099) (0.0102)
wL･T -0.0293*** -0.0293*** -0.0296*** -0.0311***wM
0.3805*** 0.3789***(0.0052) (0.0053)(0.0040) (0.0041) (0.0038) (0.0039)
wK
0.3111*** 0.3150*** wM･N
-0.0202** -0.0260**(0.0102) (0.0106)(0.0068) (0.0068)
wM･T
wM&K
0.6688*** 0.6695***
0.0004-0.0029(0.0050) (0.0051)(0.0041) (0.0042)
wK･N
N
0.3638*** 0.4148*** 0.2331*** 0.2779***
0.1334*** 0.1429***(0.0386) (0.0416) (0.0403) (0.0430)(0.0141) (0.0146)
T-0.3029*** -0.2721*** -0.3523*** -0.3123*** wK･T
0.0292*** 0.0340***(0.0378) (0.0390) (0.0375) (0.0381)(0.0058) (0.0059)
Y･Y-0.4208*** -0.4355*** -0.2508** -0.2718*** wM&K･N 0.1288*** 0.1283***(0.1094) (0.1102) (0.1008) (0.1045)(0.0103) (0.0106)
N･N-0.6951*** -0.7296*** -0.7350*** -0.8390*** wM&K･T 0.0293*** 0.0293***(0.1282) (0.1279) (0.1229) (0.1223)(0.0040) (0.0041)
N･T
wL･wL 0.1632*** 0.1612*** 0.1543*** 0.1543***-0.4698*** -0.4513*** -0.5249*** -0.4866***(0.0073) (0.0075) (0.0062) (0.0062)(0.0543) (0.0558) (0.0515) (0.0529)
T･T
wL･wM
-0.0661*** -0.0651***-0.0317*** -0.0217** -0.0238** -0.0037(0.0047) (0.0048)(0.0104) (0.0107) (0.0100) (0.0105)
wL･wK-0.0882*** -0.0892***
DVS-0.1946*** -0.1711*** -0.2005*** -0.1717***(0.0044) (0.0045)(0.0264) (0.0279) (0.0264) (0.0273)
V･DVS
wL･wM&K -0.1632*** -0.1612***0.2218***0.1713***(0.0073) (0.0075)(0.0449)(0.0431)
wM･wM
0.1060*** 0.1078***
DHS-0.3117*** -0.3093*** -0.3831*** -0.3621***(0.0052) (0.0052)(0.0266) (0.0258) (0.0267) (0.0252)
wM･wK-0.0399*** -0.0427*** Constant 8.7276*** 8.7449*** 8.7861*** 8.8028***(0.0045) (0.0046)(0.0220) (0.0215) (0.0216) (0.0207)
wK･wK
0.1282*** 0.1318*** Log of
63.6081 73.7701 21.2133 34.7842(0.0064) (0.0065) likelihood
wM&K･ 0.1632*** 0.1612***
Pseudo R2 0.9751
0.97620.97000.9717wM&K(0.0073) (0.0075)
Y･wL
0.1147*** 0.1137*** 0.1091*** 0.1132*** Satisfied
90.48%
51.67%
51.19%(0.0100) (0.0103) (0.0099) (0.0103) concavity 89.52%
condition(Note):(1) *** Significant at 1 percent, ** 5 percent, * 10 percent.
(2) Number of observations: 420(3) R2 of the Cost Share Function
Case 1 (Labor: 0.6001), Case 2 (Labor 0.5974),
Case 3 (Labor: 0.6363, Material: 0.6538), Case 4 (Labor: 0.6343, Material: 0.6478)

26

Table 6 Train Density Level in 2007
No.

Railway Operator

Country1ÖBB (Österreichische Bundesbahnen)
Austria2
SNCB/NMBS (Société Nationale des Chemins de fer Belges)
Belgium3
BLS (BLS AG)
Switzerland
4
SBB CFF FFS (Schweizerische Bundesbahnen)
Switzerland
5
CD (České Dráhy)
Czech Rep.
6
DB AG (Deutsche Bahn AG)
Germany7
DSB (Danske Statsbaner)
Denmark
8
RENFE (Red Nacional de los Ferrocarriles Españoles)
Spain
9
VR (VR-Group Ltd)
Finland
10
SNCF (Société Nationale des Chemins de fer Français)France11
OSE (Hellenic Railway Organization)
Greece12
GySEV/RÖEE (Györ-Sopron-Ebenfurti Vasút Részvénytarsasag) Hungary
13
MAV (Magyar Államvasutak Rt.)
Hungary
14
CIE (Coras Iompair Éireann)Ireland15
FS (Ferrovie dello Stato SpA)
Italy
16
JR Hokkaido
Japan
17
JR EastJapan
18
JR Central
Japan
19
JR WestJapan
20
JR Shikoku
Japan
21
JR Kyushu
Japan
22
KOREAIL (Korean National Railroad)
South Korea
23
CFL (Société Nationale des Chemins de fer Luxembourgeois)
Luxembourg24
NS (N. V. Nederlandse Spoorwegen)
Netherlands
25
NSB (Norges Statsbaner AS)
Norway26
PKP (Polskie Koleje Państwowe S. A.)
Poland27
CP (Caminhos de Ferro Portugueses, E. P)
Portugal
28
SJ (Statens Jämvägar AB)
Sweden29
ZSSK (Slovak Rail)
Slovakia
30
TCDD (Türkiye Cumhuriyeti Deviet Demiryollari Isletmesi)
Turkey(Note)(1) “Train density” is defined as train-km per route length per day.
(2) “Ratio” means that each company’s train density to the sample mean of train density.

27

Train
Density
66.6
77.1
132.2
142.7
43.6
72.7
80.4
36.4
24.4
44.9
21.4
48.7
37.0
26.9
55.9
46.0
93.3
165.1
118.4
68.7
88.8
94.7
72.0
116.6
22.7
27.2
37.6
22.1
35.1
12.6

Ratio
1.08
1.26
2.15
2.32
0.71
1.18
1.31
0.59
0.40
0.73
0.35
0.79
0.60
0.44
0.91
0.75
1.52
2.69
1.93
1.12
1.45
1.54
1.17
1.90
0.37
0.44
0.61
0.36
0.57
0.20