example of technical articel
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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
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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.
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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
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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.
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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.
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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
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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
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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
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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
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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
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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
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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
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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
Performance Measurement for Railway Transport Lan and Lin
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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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