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Performance Measurement for RailwayTransport: Stochastic Distance Functions

with Inefficiency and Ineffectiveness Effects

Lawrence W. Lan and Erwin T. J. Lin

Address for correspondence: Lawrence W. Lan, Emeritus Professor, Institute of Traffic

and Transportation, National Chiao Tung University, 4F, 114 Sec. 1, Chung-Hsiao W.

Rd., Taipei, Taiwan 10012 ([email protected]). Erwin T. J. Lin is Deputy

Division Director, Bureau of High Speed Rail, Ministry of Transportation and

Communications, Taiwan. The authors wish to thank the constructive comments and

suggestions from two anonymous referees.

Abstract

To scrutinise the plausible sources of poor performance for non-storable transport services,

it is necessary to distinguish technical inefficiency from service ineffectiveness. This paper

attempts to measure the performance of railways that produce passenger and freight

services by two stochastic distance function approaches. A stochastic input distance

function with an inefficiency effect is defined to evaluate technical efficiency; whereas a

stochastic consumption distance function with an ineffectiveness effect is introduced to

assess service effectiveness. The empirical analysis examines 39 worldwide railway systems

over eight years (19952002) where inputs contain number of passenger cars, number of

freight cars, and number of employees, while outputs contain passenger train-kilometres

and freight train-kilometres, and consumptions contain passenger-kilometres and ton-

kilometres. The findings show that railways technical inefficiency and service

ineffectiveness are negatively influenced by gross national income per capita, percentage

of electrified lines, and line density. Overall, the railways in West Europe perform more

efficiently and effectively than those in East Europe and Non-European regions.

Strategies for ameliorating the operation of less-efficient and/or less-effective railways are

proposed.

Date of receipt of final manuscript: October 2005

383

Journal of Transport Economics and Policy, Volume 40, Part 3, September 2006, pp. 383408


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1.0 Introduction

Many railways in the world have been facing keen competition fromhighway carriers over past decades. Some railways have even suffered

from a major decline in the market share and failed to adopt effective

strategies to correct the situation. Taking freight transport as an example,

the market share (ton-km) for European Union (EU) rails has declined

from 32 per cent in 1970 to 12 per cent by 1999 (Lewis et al., 2001). As

Fleming (1999) pointed out, truckers can deliver furniture from Lyon,

France, to Milan, Italy, in eight hours, while railways need forty-eight

hours. The decline of the railway market could be attributed to the

relatively high level-of-service of other modes or to rails poor performance

in technical efficiency and/or service effectiveness. Without in-depthexamination, one cannot gain insights into the main causes for the decline

or the main sources of poor performance. In addition, enhancing technical

efficiency and service effectiveness should always be viewed as essential for

railway transport to remain sustainable in the market. If one could

scrutinise the sources of inefficiency and ineffectiveness by making a clear

distinction between efficiency and effectiveness, it would perhaps be

possible to propose more practical strategies to ameliorate the problems

of the operation of rail transport.

Many studies have dealt with railway transport performance evalua-

tion. They mainly focused on efficiency and productivity measurements.The methodologies were generally classified into four categories: index

number, least squares, data envelopment analysis (DEA) and stochastic

frontier analysis (SFA) (Coelli et al., 1998; Oum et al., 1999). For

example, Freeman et al. (1985) applied the index number method to

measuring and comparing the total factor productivity of Canadian

Pacific (CP) and Canadian National (CN) railways over the period of

195681. Tretheway et al. (1997) also employed the same method but

extended the data to 1991. They found that although CP and CN

sustained modest productivity growth throughout the period of 1956

91, their performance slipped over the next decade. Caves et al .(1981) adopted the least squares method to develop definitions of pro-

ductivity growth for more general structures of production. Friedlaender

et al. (1993) used the least squares method to estimate the short-run

variable cost function of US Class I railroads. They concluded that

the institutional barriers to capital adjustment might be substantial.

McGeehan (1993) also employed the least squares method to estimating

the cost functions of Irish railways and found that the CobbDouglas

functional form would not be appropriate in describing the production

structure.

Journal of Transport Economics and Policy Volume 40, Part 3

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Chapin and Schmidt (1999) used the DEA approach to measure the

efficiency of US Class I railroad companies since deregulation. By

regression analysis, they found that their efficiency had been improvedsince deregulation, but not because of mergers. Cowie (1999) also applied

the DEA method to compare the efficiency of Swiss public and private

railways by constructing technical and managerial efficiency frontiers and

then measuring both efficiencies. Private railways were found to have 13

per cent higher technical efficiency than the public ones (89 vs. 76 per

cent). Fa re and Grosskopf (2000) further introduced a network data

envelopment analysis (NDEA) for the multiple-stage production efficiency

measurement. Lan and Lin (2003b) employed different DEA approaches to

measure the technical efficiency and service effectiveness of worldwide

railways. Lan and Lin (2005) further developed a four-stage DEA approachto evaluate railway performance with the adjustment of environmental

effects, data noise, and slacks. Cantos and Maudos (2000) estimated

productivity, efficiency, and technical change for 15 European railways

by using the SFA approach. The results showed that the most efficient

companies were those with higher degrees of autonomy. Cantos and

Maudos (2001) also employed SFA to estimate both cost efficiency and

revenue efficiency for 16 European railways, concluding that the existence

of inefficiency could be explained by the strong policy of regulation and

intervention. Lan and Lin (2003a) compared the relative productive

efficiency of worldwide rail systems with DEA and SFA approaches.They found a translog production function more suitable than Cobb

Douglas for specifying the relation between inputs and outputs, and

variable returns to scale more relevant than constant returns to scale for

the rail transport industry.

When applying econometric approaches to estimate efficiency and/or

effectiveness, it is necessary to specify a suitable functional form. Produc-

tion function and cost function are the two conventional approaches

used in previous studies. However, when dealing with the multiple-output

nature of railway transport (passenger and freight services), the production

function has the disadvantage that only a single output can be appro-priately modelled. Although the cost function approach can overcome

this problem by allowing the modelling of a multiple-input and multiple-

output production technology, its drawback is that it requires data on

input prices and total cost, which are very difficult to collect in the

international context. Another model that can be utilised in dealing with

multiple-input and multiple-output production technology is the distance

function, which was initially introduced by Shephard (1970). However, it

was not used in measuring the efficiency of railways until Bosco (1996),

who developed an input distance function to estimate the excess-input

Performance Measurement for Railway Transport Lan and Lin

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expenditure for four European public railways over the period of 197187.

Coelli and Perelman (1999) introduced both parametric and non-

parametric distance functions to estimate the efficiency of Europeanrailways. They suggested that a combination of technical efficiency scores

obtained by different methods could be used as the preferred set of

scores. Coelli and Perelman (2000) further estimated the technical efficiency

of European railways using a distance function approach. The results

indicated that the technical efficiencies of European railways differed

substantially from country to country. More recently, Kennedy and

Smith (2004) proposed an internal benchmarking approach to assess the

cost efficiency of Britains rail network based on seven geographical

zones within Railtrack. Their internal benchmarking approach was essen-

tially the input distance function proposed by Coelli and Perelman (1999).The models specified by Coelli and Perelman (1999, 2000) did not

consider random error terms, which were attributed to a deterministic

distance function approach. This paper attempts to evaluate railway trans-

port performance by employing stochastic distance function approaches

including consideration of the random error terms. Corresponding to a

certain level of output, a railway firm is presumed to minimise the input

factors (cost) and/or to maximise the sales (revenue). Therefore, we specify

the stochastic input distance function to measure technical efficiency,

whereas to estimate service effectiveness we specify the stochastic consump-

tion distance function. Moreover, in order to scrutinise the plausiblesources of less-efficient and/or less-ineffective firms, our stochastic distance

functions further incorporate inefficiency/ineffectiveness effects.

The paper is structured as follows. Section 2 elucidates the rationale for

the distinction of efficiency and effectiveness measurements for non-

storable commodities. Section 3 defines the stochastic input (consumption)

distance functions with inefficiency (ineffectiveness) effects. Section 4

conducts the empirical analysis and scrutinises the sources of inefficiency

and ineffectiveness. Section 5 addresses the policy implications and dis-

cusses the strategies for ameliorating problems in less-efficient and/or

less-effective firms.

2.0 Distinction of Efficiency andEffectiveness Measurements

We define technical efficiency as a transformation of outputs from inputs,

sale effectiveness as a transformation of consumptions from outputs, and

technical effectiveness as a transformation of consumptions from inputs.


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For ordinary commodities, measures of technical efficiency and technical

effectiveness are essentially the same because the commodities, once

produced, can be stockpiled for consumption. Nothing will be lost through-out the transformation from outputs to consumptions if one assumes that

all the stockpiles are eventually sold out (that is, conventional measures for

ordinary commodities assume perfect sale effectiveness). For non-storable

commodities, however, when commodities are produced and a portion of

them are not consumed straight away (that is, imperfect sale effectiveness),

the technical effectiveness, a combined effect of technical efficiency and sale

effectiveness, would be less than the technical efficiency.

Transport infrastructures and services are typical non-storable com-

modities because one can never store the surplus service capacity at low

demands (off-peak hours) for use at high demands (peak hours). Takingpassenger transport as an example, once the transport outputs (in terms

of seat-miles) are transformed from such inputs as vehicle, fuel and

labour, the seat-miles must be consumed immediately by the passengers,

otherwise they are exhausted and wasted. Both technical efficiency and

technical effectiveness for passenger transport services represent two

different measurements and thus should be evaluated separately consider-

ing the fact that not all the seat-miles are fully utilised in practice. Technical

effectiveness depends not only on how well the outputs (seat-miles) are

transformed from the inputs, but also on how well the consumptions

(passenger-miles) are transformed from the outputs. In summary, toassess the system performance for non-storable commodities, it would be

more informative if one could separate the efficiency measurement

(transforming the inputs into outputs) from the effectiveness measurement

(transforming the outputs into consumptions).

To explain this concept, Fielding et al. (1985) introduced three perfor-

mance measures for a transit system: cost efficiency, service effectiveness,

and cost effectiveness. They defined cost-efficiency as the ratio of outputs

to inputs, service-effectiveness as the ratio of consumptions to outputs,

and cost-effectiveness as the ratio of consumptions to inputs. It should be

noted that if the input factor prices are not known, one cannot measurecost efficiency or cost effectiveness. Nonetheless, one can still measure tech-

nical efficiency or technical effectiveness. Similarly, if sale prices are not

known, one cannot measure revenue-related effectiveness; but one can

measure service or technical effectiveness. Figure 1 uses rail transport as

an example to depict the concept of distinctive performance measurements

of technical effectiveness, technical efficiency, and service effectiveness for

non-storable commodities. This figure suggests that any poor performance

in transport services can be attributed to either poor technical efficiency or

poor service effectiveness or a combination of both. Without the separation


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of technical efficiency and service effectiveness measurements, it is difficult

to discover the sources of poor performance. Most previous studies related

to performance evaluation mainly focused on technical efficiency or techni-

cal effectiveness measures (Orea et al., 2004). To the best of the authors

knowledge, little has been devoted to service (or sale) effectiveness measures

for non-storable commodities.

3.0 Methodologies

3.1 Deterministic distance functions

To define a production technology, let x denote a non-negative input vectorand y denote a non-negative output vector. We use Px to represent alloutput sets y, which can be produced by using the input vector x. That is

Px y 2 RM : x can produce y

:

Following Fa re and Primont (1995), Px is assumed to satisfy:(1) 0 2 Px;(2) Non-zero output levels cannot be produced from a zero level of

inputs;

Figure 1Distinctive Performance Measurements for Non-Storable Commodities

(Rail Transport as an Example)

Inputs

Labour

Vehicle

Energy

Outputs

Passenger-train-km

Freight-train-km

Affiliated business

Consumptions

Passenger-km

Ton-km

Passenger-revenue

Freight-revenue

Affiliated-revenue

Technical

efficiency

measurement

Serviceeffectiveness

measurement

Technical

effectiveness

measurement


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(3) Px satisfies strong disposability of outputs; that is, if y 2 Px andy4y, then y

2P

x

;

(4) Px satisfies strong disposability of inputs; that is, if y can beproduced from x then y can be produced from any x5x;

(5) Px is closed;(6) Px is bounded;(7) Px is convex.The output distance function is then defined on the output set, Px, asdOx;y minfy: y=y 2 Pxg; where Px fy 2 RM : x can produce yg:Lovell et al. (1994) have pointed out that

(1) dOx;y is non-decreasing in y and non-increasing in x;(2) dOx;y is linearly homogeneous and convex in y;(3) dOx;y4 1; if y 2 Px;(4) dOx;y 1; if y 2 IsoqPx y:y 2 Px;o y =2 Px;o > 1f g.In summary, a firm is efficient if it lies on the frontier or isoquant. Conversely,

a firm is inefficient if it is located inside the frontier. From linear homo-

geneity, we can obtain dOx;o y o dOx;y, for any o > 0. One canarbitrarily choose one of the outputs (for example, the Mth output) and

set o 1=yM. Then dOx;y=yM dOx;y=yM. Thus, if we adopt thestandard flexible translog form, the deterministic output distance function

can be written as:

lndOi=yM a0 XM1m1

am lnymi

1

2

XM1m1

XM1n1

amn lnymi lny

ni

XKk1

bk ln xki 1

2

XKk1

XKl1

bkl ln xki ln xli

XK

k1 XM1

m1

rkm ln xki lnymi; i 1; 2; . . . ; N; 1

where ym ym=yM. LetlndOi=yMi TLxi;ymi=yMi;a;b;r; i 1; 2; . . . ; N:

Or,

lndOi lnyMi TLxi;ymi=yMi; a; b;r; i 1; 2; . . . ; N:Hence,

lnyMi TLxi;ymi=yMi;a;b;r lndOi; i 1; 2; . . . ; N: 2


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Similarly, the input distance function can be defined on the input set, Ly,as

dIx;y maxfl: x=l 2 Lyg; where Ly fx 2 RK: x can produce yg:Lovell et al. (1994) also point out that

(1) dIx;y is non-decreasing in x and non-increasing in y;(2) dIx;y is positively linearly homogeneous and concave in x;(3) dIx;y5 1, ifx 2 Ly;(4) dIx;y 1, ifx 2 IsoqLy x: x 2 Lyf g.From linear homogeneity, we obtain dIox;y odIx;y, for any o > 0.One can arbitrarily choose one of the inputs, say the Kth input, and set

o 1=xK, then dIx=xK;y dIx;y=xK. Thus, a translog form ofdeterministic input distance function becomes

lndIi=xKi a0 XMm1

am lnymi 1

2

XMm1

XMn1

amn lnymi lnyni

XK1k1

bk ln xki

1

2

XK1k1

XK1l1

bkl ln xki ln x

li

XK1

k1XMm1

rkm

ln xki

lnymi;

i

1;

2;

. . .;

N;

3

where xki xki=xKi. LetlndIi=xKi TLyi; xki=xKi; a; b;r; i 1; 2; . . . ; N:

Or,

lndIi lnxKi TLyi; xki=xKi; a; b;r; i 1; 2; . . . ; N:Hence,

lnxKi TLyi; xki=xKi;a;b;r lndIi; i 1; 2; . . . ; N: 4

In equation (2), lndOi can be viewed as residual. We can regress lnyMion TLJ by using the ordinary least squares (OLS) method and correcteach residual by adding the largest negative residual. To estimate the service

effectiveness of each firm, we simply find the exponent of each corrected

residual. Similarly, to estimate technical efficiency, we regress lnxKion TLJ in equation (4) and follow the same procedure as in effectivenessestimation.


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3.2 Stochastic distance functions

The output and input distance functions described in 3.1 are all deterministic

because they do not account for random errors. To account for statisticalnoise, Aigner, Lovell, and Schmidt (1977) proposed a composite error

model, called the stochastic production frontier model, defined as

yi fxi; b expvi expui fxi;b expvi TEi; 5where yi is the output ofith firm, vi is symmetric random error term. Aigner

et al. (1977) assumed that vi follows a normal distribution with zero mean

and constant variance, and ui is non-negative independently and identically

distributed (iid) random variable, which counts the technical inefficiency of

firms. The technical efficiency of firms (TEi) is defined as

TEi expui yi

fxi; b expvi; i 1; 2; . . . ; N: 6

In order to estimate ui, one has to impose a distribution form (for example,

half-normal, truncated-normal, gamma, and so on) on the model. Taking

half-normal distribution as an example, following Kumbhakar and

Lovell (2000), one can assume that

(1) vi $ iid N0;s2v;(2) ui

$iid N

0;s2u

;

(3) Both vi and ui are independently and identically distributed.

Because vi is independent of ui, the joint probability density function of uiand vi is

fe 2sffiffiffiffiffiffi

2pp exp 1 el

s

! exp e

2

2s2

2sf

e

s

el

s

; 7

where e v u, s s2u s2v1=2, l su=sv, f and are respec-tively the standard normal cumulative distribution function and probability

density function. The log likelihood function offe is

ln L const NlnsXNi1

ln

eil

s

1

2s2

XNi1

e2i: 8

One can estimate equation (8) by using maximum likelihood estimation

method. Jondrow et al. (1982) have derived

Ehuijeii mi s

fmi=s1 mi=s

! s

feil=s

1 eil=seil

s

!; 9


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where mi es2u=s2, s2 s2us2v=s2. The technical efficiency of firmsthen becomes

TEi expuui expEhuijeii: 10Battese and Coelli (1988) proposed another point estimator for TEi as

follows:

TEi Eexphuijeii

1 s mi=s1 mi=s

!expmi 12s2: 11

For any nonlinear function gx, Egx is not equal to gEx. In thiscase, Kumbhakar and Lovell (2000) indicate that equation (11) is preferred

to equation (10).

One can define stochastic output and input distance functions by simplyadding symmetric error term vi to the deterministic models as shown in

equations (2) and (4). The models become equations (12) and (13), respec-

tively. It should be noted that in equation (12) ui represents inefficiency due

to insufficient outputs, while in equation (13) ui stands for inefficiency due

to excess inputs.

lnyMi TLxi;ymi=yMi;a;b; r vi ui; i 1; 2; . . . ; N; 12lnxKi TLyi; xki=xKi;a;b;r vi ui; i 1; 2; . . . ; N: 13

3.3 Incorporation with inefficiency/ineffectiveness effects

To investigate further the factors causing the inefficiency of firms, a number

of researchers have developed models incorporating inefficiency effects into

stochastic production functions (Kumbhakar et al., 1991; Reifschneider

and Stevenson, 1991; Huang and Liu, 1994; and Battese and Coelli,

1995). For instance, Battese and Coelli (1995) proposed a model incorpor-

ating technical inefficiency effects into a stochastic frontier production

model. They assumed that the inefficiency effects were stochastic and

their model permitted the estimation of technical efficiency in the stochastic

frontier and the determinants of technical inefficiencies.

In this paper, we adopt the concept proposed by Battese and Coelli(1995) and define the stochastic consumption distance function with an

ineffectiveness effect as follows (hereinafter named the SCDF model):

lnyMit TLxkit;ymit=yMit;a; b;r vit uit;i 1; 2; . . . ; N; t 1; 2; . . . ; T:

14

We define uit as a vector of non-negative random variables associated with

service ineffectiveness, which are assumed to be independently distributed,

such that: uit is obtained by truncation (at zero) of the normal distribution


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with mean zitd and variance s2; zit is a vector of explanatory variables

associated with service ineffectiveness of firms over time; and d is a vector

of unknown coefficients to be estimated. Thus, the service ineffectivenesseffect, uit, in equation (14) can be specified as

uit zitd Wit; 15the random variable Wit is defined by the truncation of the normal distribu-

tion with zero mean and variance s2. Similarly, we define the stochastic

input distance function with an inefficiency effect as follows (hereinafter

named the SIDF model):

lnxKit TLyit; xit=xkit;a;b;r vit uit;i

1;

2;

. . .;

N;

t

1;

2;

. . .;

T:

16

The associated technical inefficiency effect could also be specified as in

equation (15).

4.0 Empirical Analysis

4.1 Data

This study focuses on multi-product railways that provide both passenger

and freight services. The single-product railways providing only passengeror freight service are not considered in the empirical analysis. Since we also

conduct in-depth analysis on how external factors affect efficiency (effec-

tiveness) measures, those railways with incomplete data sets within the

eight-year study horizon are also excluded. Our complete data set, drawn

from International Railway Statistics published by the International

Union of Railways (UIC), contains 312 panel data composed of 39 railways

over the period of 19952002. In order to investigate whether efficiency and

effectiveness vary significantly among regions, we further classify the

samples into three regions: West Europe (WE), East Europe (EE) and

Non-Europe (NE).Previous studies used the number of employees, length of lines, and the

sum of freight wagons and coach cars as inputs (for example, Coelli and

Perelman, 1999; Cowie, 1999). For a multiple-output railway system that

provides passenger and freight services, it seems more reasonable to

separate those inputs for passenger and freight services. Thus, we separate

freight-car from passenger-car rolling stock in the input data set, and

separate freight-train-kilometres from passenger-train-kilometres in the

output data set. However, such factors as staff are not exactly divided

between both services; we directly use the total number of employees as


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another input. Because we measure the short-term performance of railways,

we discard length of lines as an input, which is in general attributed to a

fixed cost category. For simplicity, we do not account for such externalfactors as public/private ownership and regulatory differences across the

firms. Our panel data contain five data sets including two consumptions

(passenger-kilometres and ton-kilometres), two outputs (passenger train-

kilometres and freight train-kilometres), three inputs (number of passenger

cars, number of freight cars, and number of employees), two environmental

variables (per capita gross national income and population density), and

two variables characterising the railways (percentage of electrified line

and line density). Table 1 summarises the descriptive statistics of the

data. Note that the data in different regions are somewhat heterogeneous.

4.2 Estimation results

Previous studies may have used input-oriented comparison (measuring the

relative inputs under the same output level) or output-oriented comparison

(measuring the relative outputs under the same input level) in assessing

technical efficiency. Whether a company is output-oriented or input-

oriented is a question that depends on many factors. If companies have

restrictions on the inputs they use, the output distance function would be

the appropriate approach. If companies have restrictions on the quantities

of outputs, the input distance function would be appropriate. For the easeof comparison among different railways, we presume that firms minimise

the input factors (cost) and maximise the sales (revenue) associated with

a given level of output. Thus, when measuring the relative technical effi-

ciency we specify a stochastic input distance function (SIDF) model with

inefficiency effect as shown in equation (16); whereas to estimate relative

service effectiveness, we specify a stochastic consumption distance function

(SCDF) with an ineffectiveness effect as shown in equation (14). Note that

the estimated parameters of stochastic distance functions may violate the

monotonicity assumption. To avoid violation, some studies estimated the

parameters by imposing monotonic constraint on the specified functionalform (for example, ODonnell and Coelli, 2005; and Griffiths et al.,

2000). In order to maintain the flexibility of the specified distance functions,

we do not impose this restriction; instead, we check monotonicity after

estimation.

The FRONTIER 4.1 software, developed by Coelli (1996), is applied to

estimate both models. Table 2 reports the estimation results. We find that

most of the parameters (a;b;r) are statistically significant at the 5 percent significance level. s2v are significant in both models, supporting the

theory that stochastic distance functions, rather than deterministic ones,


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Table1

DescriptiveStatisticsoftheDecisionMakingUnits(39Railwaysover

8Years:19952002)

Consumptions

Outputs

Inputs

Environmental

variables

Characteristicsof

railways

Statistics

pax-km

(106)

ton-km

(106)

paxtrain-km

(103)

freighttrain-km

(103)

pax

cars

freight

cars

No.of

employees

GNI

PD

ELEC

(%)

LD

(km

/km

2)

WestEurope

Max.

74

,387

76

,815

739

,800

225

,500

21

,723

205

,431

294

,911

45

,060

389

.01

1.0

00

0.1

17

Min

.

268

357

5,6

47

920

146

146

1,4

38

10

,840

11

.45

0.0

00

0.0

06

Mean

17

,876

15

,310

136

,322

42

,599

4,9

17

29

,566

52

,938

26

,776

151

.78

0.6

00

0.0

54

Std

.dev.

22

,819

20

,831

182

,344

59

,229

6,0

95

45

,291

67

,438

9,2

02

105

.89

0.2

73

0.0

35

EastEurope

Max.

63

,752

195

,762

175

,696

110

,109

15

,781

266

,245

421

,010

10

,060

130

.42

1.0

00

0.1

20

Min

.

104

265

840

832

40

142

1,7

92

390

6.4

3

0.0

00

0.0

02

Mean

7,8

88

22

,587

47

,550

24

,592

2,9

93

41

,517

71

,326

3,5

54

88

.42

0.3

28

0.0

48

Std

.dev.

13

,461

42

,699

52

,771

29

,874

3,4

45

55

,740

99

,038

2,2

31

30

.84

0.2

05

0.0

30

Non-Europe

Max.

251

,723

40

,628

698

,160

85

,905

26

,150

30

,286

192

,456

35

,610

622

.13

0.6

11

0.0

53

Min

.

74

438

562

1,3

67

99

677

1,2

12

200

2.4

2

0.0

00

0.0

01

Mean

28

,865

8,7

87

87

,039

15

,734

3,4

49

9,2

00

32

,084

9,8

16

198

.54

0.2

61

0.0

19

Std

.dev.

72

,726

10

,314

206

,065

22

,945

7,5

05

6,7

20

47

,953

10

,901

206

.15

0.2

53

0.0

16

Total

Max.

251

,723

195

,762

739

,800

225

,500

26

,150

266

,245

421

,010

45

,060

622

.13

1.0

00

0.1

20

Min

.

74

265

562

832

40

142

1,2

12

200

2.4

2

0.0

00

0.0

01

Mean

16

,852

16

,436

89

,542

28

,785

3,8

01

28

,941

54

,663

13

,496

139

.40

0.4

09

0.0

43

Std

.dev.

40

,832

30

,160

158

,711

42

,972

5,7

31

45

,759

78

,739

12

,940

130

.84

0.2

83

0.0

32

Note:

GNIdenotespercapitagro

ssnationalincome(USdollar)and

PDdenotespopulationdensity(personspersquarekilometre)ofthecou

ntryto

whichtherailwaybelongs.ELEC

representsthepercentagesofelectrifiedlines.

LDdenoteslinedensity,

theratiooflengthoflinestotheareaofa

country.


395


14/26

Table2

EstimationResultsofSCDFandSIDFModels

Effectiveness(SCDF)model

Efficiency(SIDF)model

parameters

variables

coefficient

t-ratio

parameters

variables

coefficient

t-ratio

a0

Constant

3

.7260

25

.4717

a0

Constant

3

.3368

4.7

839

a1

lny1

0.7

982

6.2

850

a1

lny1

0

.2835

1.8

907

a2

lny2

0.2

018

a2

lny2

0

.5557

2.5

532

a11

lny1

=y2

2

0.0

090

0.1

430

a11

lny

2 1

0

.1772

3.0

103

b1

lnx1

1

.0286

6

.2938

a22

lny

2 2

0

.0803

1.2

738

b2

lnx2

0

.5366

3

.2983

a12

lny1

lny2

0.1

224

2.1

669

b11

lnx

2 1

0

.1230

1

.0963

b1

lnx1

0.4

616

4.2

160

b12

lnx1

lnx2

0

.4012

3

.7785

b2

lnx2

0.1

291

2.9

608

b22

lnx

2 2

0.2

995

2.7

411

b3

lnx3

0.4

093

r11

lnx1

lny1

=y2

0.0

409

0.4

837

b11

lnx1

=x32

0.0

258

2.9

605

r21

lnx2

lny1

=y2

0

.1630

2

.0547

b22

lnx2

=x32

0.0

008

0.2

530

b12

lnx1

=x3lnx2

=x3

0.0

094

3.0

675

r11

lny1

lnx1=x3

0.0

050

0.1

963

r12

lny1

lnx2=x3

0

.0229

1.9

627

r21

lny2

lnx1=x3

0

.0043

0.1

621

r22

lny2

lnx2=x3

0.0

313

2.4

080

d0

Constant

1.7

768

10

.2252

d0

Constant

0.5

452

3.6

497

d1

ln(GNI/1000)

0

.1599

5

.6655

d1

ln(GNI/1000)

0

.4615

19

.1562

d2

ln(PD)

0

.0248

0

.6474

d2

ln(PD)

0

.1199

1.5

629

d3

ELEC

0

.6574

4

.8052

d3

ELEC

0

.1275

4.2

635

d4

LD

15

.7592

6

.3563

d4

LD

2

.7882

3.8

158

D1

Region

0

.7769

4

.6472

D1

Region

0

.3108

4.3

392

D2

Region

0

.0026

0

.0342

D2

Region

0.0

414

0.8

329

s2 v

Variance

0.1

323

7.3

704

s2 v

Variance

0.0

420

9.2

617

g

Varianceratio

0.9

602

71

.0177

g

Varianceratio

0.8

508

14

.1537

Note:

denotessignificanceatthe5percentsignificantlevel(twotailed

).a2

andb

3arecalculatedbyhomogeneityconditions.Twodummyvaria

blesare

introduced:D

1

1forWestEurope,D

1

0forelsewhere;D

2

1forEastEurope,D

2

0forelsewher

e.


396


15/26

are appropriate. Moreover, g are significant in both models indicating the

importance of ineffectiveness and inefficiency effects for the performance

measurements.To scrutinise the plausible sources of inefficiency and ineffectiveness,

Table 2 further provides useful information as we can express the service

ineffectiveness and technical inefficiency effects by the following two

models, respectively.

uineffectivenessit 1:777 0:160z1 0:025z2 0:657z3 15:759z4 0:777D1 0:003D2 Wit;

uinefficiencyit 0:545 0:462z1 0:120z2 0:128z3 2:788z4

0:311D1 0:041D2 Wit;where z1 is ln(GNI/1000), z2 is ln(PD), z3 is ELEC, z4 is LD, and D1 and D2are two dummy variables of region. The estimated coefficients in these two

models are of particular interest to this study. Note that, except for z2 and

D2, the coefficients z1, z3 and z4 of both the ineffectiveness and inefficiency

models are all negative and significant. This indicates that a higher gross

national income per capita, a higher percentage of electrified lines, and a

higher line density will significantly lead to less ineffectiveness and less

inefficiency in railway transport services. Moreover, the negative coefficient

of D1

indicates that the service effectiveness and technical efficiency of

railways in West Europe are significantly greater than the other two

regions. However, D2 is not statistically significant in both models, suggest-

ing that inefficiency and ineffectiveness have no significant difference

between East Europe and Non-Europe regions.

The technical efficiency and service effectiveness scores for each DMU

over eight years are reported in Appendices 1 and 2, respectively. The

distributions of both efficiency and effectiveness scores are summarised in

Table 3. The mean efficiency and effectiveness scores are 0.637 and 0.640,

respectively, indicating that there is considerable technical inefficiency

and service ineffectiveness in the railway transport industry. Both appen-

dices also show that, in general, the levels of railways technical effectiveness

and service efficiency are either stable over time or present smooth changes,

as anticipated. The only exceptions appear in less developed countries (such

as Mozambique) or in transition economies (such as Hungary).

4.3 Statistical testing

In the following, we conduct some statistical tests, including testing for

inefficiency and ineffectiveness effects, checking for the monotonicity of

the distance functions, testing for the shifts of efficiency and effectiveness


397


16/26

frontiers over time, and testing for the differences of inefficiency and ineffec-

tiveness among regions.

4.3.1 Testing for inefficiency/ineffectiveness effects

Since we estimate parameters and efficiency/effectiveness by using maximumlikelihood estimation, we conduct a one-sided generalised likelihood-ratio

test for the null hypothesis H0: s2u 0. For the SCDF model, it is found

that

LR 2flnLH0 lnLH1g 2137:56 43:03 189:06;which is greater than the 5 per cent critical chi-square value of 14.853; hence

we reject H0. That is, s2u 6 0, indicating that significant service ineffective-

ness exists. Similarly, for the SIDF model,

LR

2

94:32

108:07

404:78;

which is also greater than 14.853, indicating that technical inefficiency exists

significantly. These test results concur with the significant results for g in

Table 2. Thus we conclude that both inefficiency and ineffectiveness effects

are significant in the railway transport industry over the period of 1995

2002.

4.3.2 Checking for monotonicity

The stochastic consumption distance function is non-decreasing in y and

non-increasing in x. Non-decreasing in y means that partial derivatives of

Table 3

Distributions of Effectiveness and Efficiency Scores

(Total Number of DMUs 312)No. of DMUs (per cent)

Score Effectiveness Efficiency

Greater or equal to 0.900 85 (27.2%) 62 (19.9%)

0.8000.899 57 (18.3%) 50 (16.0%)

0.7000.799 17 (5.4%) 32 (10.3%)

0.6000.699 15 (4.8%) 28 (9.0%)

0.5000.599 22 (7.1%) 39 (12.5%)

0.4000.499 23 (7.4%) 37 (11.9%)

Less than 0.400 93 (29.8%) 64 (20.5%)

Min. 0.087 0.144Max. 0.977 0.981

Mean 0.639 0.637

St. dev. 0.281 0.243


398


17/26

the dO with respect to y must be greater than or equal to zero. For a Cobb

Douglas specification, bi5 0 ensures global monotonicity. However, for atranslog specification, it is more complicated and we may only check local

monotonicity: @dO=@ym @ln dO=@lnym dO=ym5 0, or equivalently@ln dO=@lnym5 0 and @ln dO=@ln xk4 0. Based on the estimated resultsin Table 2, the SCDF is

lny2 3:726 0:798lny 12 0:009lny2 1:029 ln x1 0:537 ln x2 12 0:123ln x12 0:3ln x22 0:401 ln x1 ln x2

0:041 ln x1 lny

0:163 ln x2 lny

vit

uit;

where y y1=y2 and uit are defined in equation (15). The first derivativesof the SCDF with respect to y1 and y2 should be greater than or equal to

zero, and the first derivatives of the SCDF with respect to x1 and x2should be less than or equal to zero. By substituting observation data

into the above first derivatives, we obtain the elasticity of each variable

for the SCDF model (Table 4).

Similarly, we can calculate the elasticity of each variable for the SIDF

model (also reported in Table 4). An increase in each consumption variable

or a decrease in each output variable, on average, will level up the service

effectiveness. The results are consistent with what we anticipated because

we define the consumption distance function as the direct measure for

service effectiveness. In contrast, a decrease in each input variable or an

increase in each output variable will raise technical efficiency. The results

also agree with what we expected as we define the reciprocal of input

distance function as the measure for technical efficiency.

4.3.3 Testing for changes in efficiency and effectiveness frontiers

Our panel data cover the years from 1995 to 2002, so it is necessary to

test whether there are frontier shifts during this period. We adopt a

Table 4

Elasticities of SCDF and SIDF Models

Elasticities of variables Effectiveness (SCDF) model Efficiency (SIDF) model

passenger-km 0.5247

ton-km 0.4753

passenger-train-km 0.7161 0.5590freight-train-km 0.4516 0.3550no. of passenger cars 0.1405

no. of freight cars 0.2331

no. of employees 0.6264


399


18/26

KruskalWallis rank test (Sueyoshi and Aoki, 2001) with the following

statistic:

H 12NN 1

Xj

T2j

nj

" # 3N 1;

where Tj is the sum of ranks for group j, nj is the number of group jand Nis

total number of samples (Hays, 1973). In our case, nj is 39, j is 8, and N is

312. We estimate both efficiency and effectiveness by using equations (16)

and (14) associated with equation (15). All the efficiency (effectiveness)

scores are ranked in a single series, and by eliminating the effect of ties

the efficiency and effectiveness statistics (H) are 5.13 and 0.062, respectively,

both less than the critical value of w2 (

14.07, with d.o.f.

7 and

Pr 0.05). The null hypotheses that both efficiency and effectivenessfrontiers do not shift during the observed period cannot be rejected; thus,

changes in technical efficiency and service effectiveness frontiers do not

occur during the period 19952002. This finding is particularly important

to justify the pooling of eight-year sampling data in the same model.

4.3.4 Testing for differences of efficiency/effectiveness among regions

A KruskalWallis rank test can also be used to examine whether scores vary

among regions or not. Our samples are divided into three regions: West

Europe, East Europe and Non-Europe. After eliminating the effect of ties,we obtain Heffi 126:57 and Heffe 126:39, both significantly greaterthan the critical value ofw2 ( 5.99, with d.o.f. 2 and Pr 0.05). There-fore, we reject the null hypothesis that the efficiency (effectiveness) scores

do not vary across regions. The testing results are consistent with the

dummy variables D1 in both the SCDF and SIDF models being negative

and significant, indicating that railways in West Europe are less inefficient

and ineffective than those in other regions. Table 5 reports the details of

the efficiency and effectiveness scores in the three regions. On average,

Table 5

Comparison of Effectiveness and Efficiency Scores among Regions

Effectiveness score Efficiency score

Statistics West Europe East Europe Non-Europe West Europe East Europe Non-Europe

Max. 0.966 0.936 0.889 0.961 0.825 0.961

Min. 0.586 0.210 0.172 0.604 0.180 0.196

Mean 0.875 0.572 0.412 0.828 0.497 0.586

St. dev. 0.103 0.259 0.254 0.109 0.165 0.285


400


19/26

railways in West Europe are more efficient and effective than those in the

other two regions. It could be due to greater technological sophistication

in West Europe compared with the other two regions. Higher gross nationalincome per capita, higher percentages of electrified lines, and higher line

density in West European countries could also explain the results.

5.0 Policy Implications and Discussion

Based on the results of two stochastic distance functions, a performance

matrix is established in Figure 2, in which each firms efficiency and effec-

tiveness scores are indicated. Since we adopt input and consumptiondistance functions to measure railways technical efficiency and service

effectiveness respectively, the results should be explained as input savings

and consumption augments for each DMU in order to attain the efficient

and effective frontiers. Those firms in the upper-left matrix with relatively

low efficiency but high effectiveness, such as DMU16 (Croatia, HZ),

DMU17 (Czech, CD), DMU20 (Hungary, MAVRt), DMU23 (Poland,

PKP) and DMU25 (Slovakia, ZSSK) should focus on curtailing excess

Figure 2

Performance Matrix for 39 Railways

Efficiency

0.0 .2 .4 .6 .8 1.0

Effe

ctiveness

1.0

.8

.6

.4

.2

0.0

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

1716

15

14

13

1211

10

98

7

6

5

4

3

21


401


20/26

inputs; whereas those in the lower-right matrix with relatively high effi-

ciency but low effectiveness, such as DMU19 (Hungary, GySEV),

DMU30 (Israel, IsR), DMU35 (South Korea, KORAIL) and DMU39(Australia, QR) should put more emphasis on attracting more passengers

and/or freight. Those firms in the lower-left matrix with relatively low

efficiency and low effectiveness, in particular DMU27 (Moldova,

CFM(E)), DMU33 (Mozambique, CFM), DMU28 (Ukraine, UZ), and

DMU38 (Turkmenistan, TRK), should consider both directions to

improve poor performance. In general, introducing innovative production

and marketing techniques are always important for any rail firm to enhance

efficiency and effectiveness so as to remain sustainable in competitive

transport markets.

In Table 4, the elasticity of the input distance function with respect tothe number of employees ( 0.6264) is greater than that with respect tothe other two inputs (freight-car 0.2331 and passenger-car 0.1405),implying that overstaffing is critical in the railway transport industry.

Thus, reducing the number of employees should be viewed as the impera-

tive strategy to enhance technical efficiency. This strategy can be explained

as the result of restructuring of some DMUs. For instance, DMU14

(Switzerland, CFF) and DMU6 (Ireland, CIE), both companies have

enhanced technical efficiency due to a considerable reduction of the

number of employees after 1997 and 1998, respectively. Table 2 shows

that the percentage of electrified lines and line density are two internalfactors significantly affecting efficiency. The policy implications of this

suggest that railway firms should increase the percentage of electrified

lines as well as enlarge the network to improve technical efficiency. The

elasticity of the consumption distance function in Table 4 with respect to

passenger service ( 0.5247) is only slightly greater than that with respectto freight service ( 0.4753), suggesting that the provision of passenger aswell as freight services could be equally important for a railway company

to enhance its service effectiveness. Table 2 also shows that gross national

income per capita is an important external factor affecting railways effec-

tiveness and efficiency. On the one hand, higher gross national income percapita generally leads to intensive transport demands for passenger and

freight services due to strong socio-economic activities. On the other

hand, higher income countries normally possess more innovative technolo-

gies and advanced management knowledge.

Railway operators cannot control such external factors as gross

national income per capita and population density to improve effectiveness.

Nor can they impose any restriction on the use of private vehicles. How-

ever, operators can concentrate on enhancing service quality, such as

raising the punctuality rate, introducing more high-speed rails, replacing


402


21/26

over-aged assets (tracks and rolling stock), and reducing total loading

and unloading time at stations (particularly for freight), to attract more

passengers from private cars and/or more freight from trucks. More impor-tantly, because the demands for transport are derived and transport

services are non-storable, rescheduling trains so as optimally to match

the demands for passenger and freight services should be considered.

Certainly, improving the booking system, developing the prepaid ticketing

system, and providing discounts to loyal customers, frequent users, or

group travellers, are also potential good strategies for promoting railway

effectiveness.

It is worth noting that rail is the most important mode in long-distance

land haul, particularly for low-value bulk commodities including raw

materials, intermediate, and final products. Rail freight transport is verylabour-intensive and time-consuming, especially at the terminals where

loading and unloading take place. Hence, expediting the processing of

freight at terminals by introducing fast loading and unloading facilities in

association with the intelligent transport technologies might make a rail

service more compatible with a trucking service. Intercity passenger

trains or high-speed trains can also consider providing line-haul service

for high-value compact goods, if the logistics can be well integrated with

local pickup and delivery services.

Note that distance function approaches are parametric methods.

Efficiency and/or effectiveness measures can also be evaluated by non-parametric methods (such as data envelopment analysis). A comparison

of technical efficiency and service effectiveness for rail transport between

parametric and non-parametric methods deserves further exploration. In

this study, we did not account for such external factors as public/private

ownership and regulatory differences across the firms. As pointed out by

Pittman (2004), countries throughout the world are in the process of

abandoning the centralised, monopolistic, and state-owned model of rail

in favour of models that create competition. For example, with the

privatisation of British Rail (BR) between 1994 and 1997, the British gov-

ernment intended to transfer to the private sector the main responsibility ofoperating and funding rail transport. A structural reform, with vertical and

horizontal separation of track and trains, was therefore introduced. The

ownership and operation of the entire track network was transferred to a

private infrastructure company (Railtrack), while passenger rail services

were horizontally separated into 25 operations consisting of a bundle of

services over various train-paths under an open access competition

franchise mechanism. Once the operator had been assigned a franchise,

access to the track for the provision of the service in the assigned area

was obtained from Railtrack at a regulated price. However, this open


403


22/26

access project was suspended as the British government felt necessary to

move towards more integration rather than pursuing further separation

(Affuso, 2003).A similar vertical separation of rail infrastructure from service opera-

tion was also established in Italy in 2002. The train paths were allocated

by means of an auction mechanism. The potential operators participating

in the auction were required to specify the paths they demanded including

details of the services they intended to run. The outcome of the competition

was then based on the quality of the service offered rather than the price

(which was regulated). The bidders could decide the type of services to

offer given the price that was automatically supplied by the infrastructure

manager for each potential bid (see http://www.rfi.it).

More recently, a multinational intermodal PolCorridor project wasannounced in 2002 to create a new trans-European freight supply network.

The northern part of the corridor will consist of sea-land connections from

Sweden, Finland, and Norway to an intermodal hub in Poland. From

there, the corridor will be connected via a regularly scheduled block train

(Blue Shuttle Train) to an intermodal terminal in Vienna. The southern

part of the corridor will involve the utilisation of existing land connections

to destinations in most of central and southeastern Europe. Through

collaboration with various transport and logistics organisations, a com-

prehensive feeder network will be established to supply cargo by truck,

train, and ferry to one of the PolCorridor logistical centres. From there,cargo will be redistributed to the Blue Shuttle Train, which will carry it

faster, cheaper, and more securely than current transport alternatives (see

http://www.toi.no).

The outcome and effectiveness of the above-mentioned recent changes

in the rail sector (vertical and horizontal separation, different mechanisms

to introduce more competition such as auction systems, and multinational

intermodal integration) will be of great interest. Such changes may invite

more competition and introduce important modifications in the perfor-

mance of the rail sector, but the results have yet to be empirically tested.

It would be interesting to examine differences in technical efficiency andservice effectiveness resulting from these institutional and restructuring

changes in the rail sector in a future study.

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Appendix 1

The Service Effectiveness Scores Measured by SCDF Model(Ranked by Average Score within Each Region)

Region

Average

score

DMU

no. Country Railways 1995 1996 1997 1998 1999 2000 2001 2002

West- 0.966 5 Germany DBAG 0.977 0.975 0.960 0.958 0.968 0.969 0.956 0.968

Europe 0.952 8 Luxembourg CFL 0.961 0.960 0.967 0.968 0.969 0.939 0.896 0.960

0.946 1 Austria OBB 0.943 0.897 0.954 0.969 0.973 0.963 0.942 0.927

0.931 9 Netherlands NSNV 0.961 0.945 0.938 0.924 0.942 0.937 0.904 0.893

0.931 11 Spain RENFE 0.956 0.945 0.959 0.923 0.946 0.935 0.894 0.888

0.925 14 Switzerland CFF 0.944 0.959 0.932 0.910 0.897 0.882 0.923 0.952

0.911 2 Belgium SNCB 0.893 0.898 0.931 0.910 0.944 0.932 0.893 0.884

0.906 4 France SNCF 0.936 0.837 0.928 0.910 0.917 0.898 0.907 0.912

0.897 12 Norway NSB 0.932 0.940 0.943 0.945 0.861 0.864 0.848 0.844

0.856 7 Italy FS Spa 0.863 0.881 0.900 0.885 0.868 0.844 0.786 0.821

0.842 13 Switzerland BLS 0.860 0.836 0.894 0.918 0.818 0.875 0.828 0.708

0.803 6 Ireland CIE 0.713 0.849 0.839 0.850 0.802 0.786 0.847 0.738

0.803 10 Portugal CP 0.672 0.739 0.885 0.936 0.771 0.872 0.787 0.763

0.586 3 Finland VR 0.566 0.568 0.571 0.585 0.583 0.580 0.604 0.630

East- 0.936 16 Croatia HZ 0.920 0.955 0.968 0.968 0.963 0.869 0.957 0.886

Europe 0.932 17 Czech Rep. CD 0.923 0.910 0.910 0.939 0.952 0.945 0.929 0.950

0.923 20 Hungary MAVRt 0.945 0.938 0.912 0.902 0.949 0.923 0.915 0.904

0.885 26 Slovenia SZ 0.905 0.925 0.913 0.882 0.903 0.872 0.861 0.821

0.738 25 Slovakia ZSSK 0.660 0.699 0.763 0.742 0.794 0.746 0.756 0.746

0.653 23 Poland PKP 0.622 0.631 0.629 0.646 0.657 0.648 0.722 0.6690.574 24 Romania CFR 0.506 0.506 0.556 0.582 0.597 0.570 0.592 0.683

0.564 15 Bulgaria BDZ 0.341 0.536 0.507 0.523 0.619 0.570 0.681 0.733

0.466 29 Turkey TCDD 0.462 0.489 0.472 0.459 0.455 0.483 0.458 0.453

0.391 22 Lithuania LG 0.386 0.406 0.399 0.403 0.378 0.402 0.392 0.359

0.375 18 Estonia EVR 0.404 0.418 0.435 0.432 0.367 0.364 0.317 0.265

0.346 21 Latvia LDZ 0.355 0.353 0.353 0.350 0.340 0.373 0.341 0.303

0.331 19 Hungary GySEV 0.339 0.234 0.222 0.292 0.235 0.436 0.378 0.511

0.257 27 Moldova CFM(E) 0.247 0.253 0.205 0.221 0.318 0.284 0.274 0.251

0.210 28 Ukraine UZ 0.214 0.215 0.214 0.212 0.212 0.204 0.206 0.204

Non- 0.889 37 Taiwan TRA 0.817 0.857 0.883 0.877 0.876 0.898 0.945 0.963

Europe 0.830 36 Japan JR 0.837 0.814 0.824 0.844 0.841 0.814 0.836 0.827

0.487 35 South Korea KORAIL 0.419 0.432 0.460 0.484 0.534 0.526 0.500 0.5430.409 34 Azerbaijan AZ 0.381 0.462 0.478 0.419 0.393 0.399 0.391 0.346

0.314 39 Australia QR 0.304 0.326 0.342 0.332 0.329 0.311 0.280 0.286

0.299 32 Syria CFS 0.347 0.306 0.327 0.302 0.279 0.334 0.245 0.256

0.257 30 Israel IsR 0.230 0.240 0.236 0.241 0.273 0.258 0.272 0.304

0.237 33 Mozambique CFM 0.097 0.087 0.131 0.288 0.310 0.382 0.378 0.227

0.222 31 Morocco ONCFM 0.241 0.224 0.212 0.221 0.220 0.220 0.220 0.218

0.172 38 Turkmenistan TRK 0.156 0.144 0.202 0.198 0.213 0.166 0.150 0.151

Mean 0.640 0.621 0.630 0.645 0.650 0.648 0.648 0.641 0.635


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Appendix 2

The Technical Efficiency Scores Measured by SIDF Model(Ranked by Average Score within Each Region)

Region

Average

score

DMU

no. Country Railways 1995 1996 1997 1998 1999 2000 2001 2002

West- 0.961 12 Norway NSB 0.954 0.978 0.979 0.981 0.944 0.961 0.946 0.944

Europe 0.939 3 Finland VR 0.909 0.916 0.943 0.950 0.948 0.948 0.948 0.954

0.924 8 Luxembourg CFL 0.933 0.928 0.911 0.929 0.941 0.928 0.916 0.907

0.902 13 Switzerland BLS 0.832 0.771 0.907 0.942 0.963 0.907 0.920 0.972

0.899 11 Spain RENFE 0.824 0.831 0.902 0.904 0.916 0.913 0.954 0.952

0.878 5 Germany DBAG 0.858 0.890 0.891 0.886 0.861 0.853 0.868 0.913

0.868 9 Netherlands NSNV 0.921 0.850 0.885 0.880 0.846 0.877 0.853 0.833

0.845 1 Austria OBB 0.752 0.778 0.811 0.861 0.864 0.878 0.909 0.904

0.812 14 Switzerland CFF 0.667 0.745 0.765 0.910 0.825 0.862 0.846 0.877

0.794 6 Ireland CIE 0.661 0.711 0.717 0.710 0.952 0.841 0.926 0.832

0.774 4 France SNCF 0.635 0.787 0.805 0.715 0.741 0.761 0.861 0.886

0.765 10 Portugal CP 0.687 0.677 0.831 0.815 0.613 0.686 0.902 0.907

0.624 2 Belgium SNCB 0.617 0.629 0.619 0.625 0.628 0.620 0.625 0.628

0.604 7 Italy FS Spa 0.552 0.592 0.619 0.603 0.583 0.605 0.613 0.663

East- 0.825 26 Slovenia SZ 0.775 0.783 0.810 0.817 0.838 0.859 0.855 0.861

Europe 0.756 19 Hungary GySEV 0.718 0.623 0.651 0.715 0.754 0.887 0.792 0.906

0.614 18 Estonia EVR 0.405 0.404 0.541 0.572 0.718 0.755 0.670 0.848

0.542 21 Latvia LDZ 0.393 0.464 0.528 0.507 0.609 0.663 0.576 0.594

0.533 20 Hungary MAVRt 0.470 0.491 0.527 0.533 0.565 0.557 0.586 0.534

0.529 16 Croatia HZ 0.444 0.471 0.496 0.503 0.534 0.573 0.572 0.6350.505 17 Czech Rep. CD 0.493 0.512 0.485 0.466 0.473 0.515 0.546 0.554

0.504 29 Turkey TCDD 0.483 0.505 0.533 0.516 0.501 0.507 0.494 0.494

0.497 23 Poland PKP 0.487 0.455 0.469 0.491 0.516 0.526 0.514 0.518

0.489 25 Slovakia ZSSK 0.473 0.458 0.485 0.472 0.471 0.473 0.536 0.539

0.484 22 Lithuania LG 0.457 0.487 0.492 0.476 0.461 0.494 0.482 0.527

0.381 15 Bulgaria BDZ 0.390 0.382 0.390 0.346 0.356 0.351 0.402 0.428

0.321 24 Romania CFR 0.377 0.342 0.333 0.318 0.233 0.310 0.313 0.346

0.290 28 Ukraine UZ 0.269 0.265 0.294 0.293 0.291 0.297 0.291 0.318

0.180 27 Moldova CFM(E) 0.207 0.202 0.188 0.180 0.156 0.150 0.169 0.190

Non- 0.961 39 Australia QR 0.926 0.941 0.965 0.967 0.969 0.971 0.974 0.976

Europe 0.931 36 Japan JR 0.894 0.934 0.945 0.905 0.944 0.937 0.948 0.943

0.849 30 Israel IsR 0.927 0.838 0.849 0.834 0.763 0.861 0.880 0.8410.767 37 Taiwan TRA 0.860 0.821 0.758 0.721 0.714 0.749 0.752 0.757

0.735 35 South Korea KORAIL 0.690 0.714 0.704 0.672 0.733 0.743 0.874 0.747

0.493 31 Morocco ONCFM 0.383 0.441 0.448 0.493 0.508 0.513 0.565 0.592

0.338 38 Turkmenistan TRK 0.365 0.335 0.344 0.311 0.338 0.321 0.342 0.347

0.328 32 Syria CFS 0.390 0.327 0.321 0.290 0.287 0.312 0.314 0.381

0.212 33 Mozambique CFM 0.170 0.183 0.224 0.186 0.190 0.221 0.220 0.306

0.196 34 Azerbaijan AZ 0.144 0.162 0.167 0.185 0.214 0.220 0.236 0.240

Mean 0.637 0.600 0.606 0.629 0.628 0.635 0.651 0.666 0.682


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