Estimating technical and allocative efficiency using stochastic cost
frontier: an application to railway
[European Transport Conference 2013: Big data ]
*
Emmanuel BOUGNAa , Yves CROZETb
a
b
Laboratory of Transport Economics, University of Lyon (Phd student)
Laboratory of Transport Economics, University of Lyon (Professor )
*
Corresponding author: Laboratory of Transport Economics, 14 Avenue Berthelot F69363
Lyon Cedex 07, France +33(0) 608725375, [email protected]
Presenting author: Emmanuel BOUGNA , PhD student Laboratory of Economics of
Transport, University lyon2, France [email protected]
Abstract
By the end of the twentieth century, railroads were in dire straits, most national railway
companies were heavily subsidized but the shares of railroads in total (inter-modal)
transportation were, at best, stable. In many European countries, rail market shares
decreased throughout the 1990s. This paper examines economic efficiency of thirteen
European railways operators between 2000 and 2009. A stochastic cost frontier method
allowed us to measure the index of economic efficiency of these companies. A Tobit model
subsequently allowed us to identify the main determinants of the economic efficiency. This
study shows that there is a positive correlation between economic efficiency and factors such
as the degree of filling of passenger train (number of passengers per train), index of the use
of infrastructure by freight services (the number of train km freight per km of the line) and the
level of technology (the percentage of electrified lines). On the other hand there is a negative
correlation between economic efficiency index and the degree of filling of train freight. We
have shown that an undertaking, which has a very high density of train freight, does not
necessarily realise a good performance in passenger transport and vice versa. A horizontal
separation between freight services and passenger services can therefore lead to a reduction
in the cost of train km.
Keywords Stochastic Cost function, technical Efficiency, allocative efficiency
2 I. Introduction
In the early 1990s, European railway has experienced profound changes following
implementation of the European directives. These reforms aim the productivity and efficiency
of the European railways companies. They also seek to make rail more efficient from its
competitive potentials that are air transport and road transport.
The economic efficiency of the railways depends on several factors, which are: the
degree of State intervention, the level of the subsidies or taxation and efficiency
management of the company and the institutional and the regulatory setting within which the
railway operate. By the end of the twentieth century, railroads were in dire straits. Most
national railway companies were heavily subsidized (Crozet et al. 2000), but the shares of
railroads in total (inter-modal) transportation were, at best, stable. In many European
countries, rail market shares decreased throughout the 1990s (European Commission (EC)
2002). Moreover, surveys show low levels of customer satisfaction with railway services in
many countries (INRA 2000).
Productivity and economic efficiency measurement of railway companies was the
subject of several econometric studies. With different methods, these studies are able to
measure the productivity and economic efficiency of railway undertakings, but they also
identify the main factors, which have an impact on these quantities. Nash (1981) sought to
discover how much of the variation in the performance of Western European railways,
measured by market share, traffic trends and support (subsidy) requirements, may be
accounted for by government policies. He found that, in the passenger sector, the significant
factors determining both market share and support requirements were the prices charged
and the mix of services offered. These decisions regarding prices and services were almost
entirely determined by government policy. Cantos et al. (1999) analysed the impact of four
types of reforms (separation between infrastructure and operation, changes in the legal
constitution of companies, degree of regulation of prices, and degree of government
influence over investment) on different dimension of railway efficiency and found that vertical
separation appears to have the strongest impact. Friebel et al. (2005) looked at the impact of
European railway deregulation on the efficiency in passenger traffic. They found that reforms
have positively affected railway productivity and that higher reform intensity does not
necessarily increase productivity, rather it depends on the sequencing of reforms.
From a general point of view, the railway companies have two main activities, which are
respectively the passenger traffic and the traffic of goods. Measure the productivity of a
railway company returns either to build an indicator that best reflects these two activities or
failure to construct an indicator for each activity. There are two major indicators of
productivity: the available output measures (such as train-km, seat-km, of car-km and so on.)
and the revenue output measures (passenger-km, revenue ton-km and so on). The available
output measures indicate essentially the level of capacity supplied, while the revenue output
measures indicate the level of output consumed by users and the value they derive from
them.
The use of a measure of productivity indicator depends on the issue of the study. If
there is no government control on railways it makes sense to use revenue output measures
for computing managerial efficiency. The use of available output measures may be justified
in measuring managerial efficiency when governments control the railways in terms of what
to supply (price, frequency of service, and so on). How ever, it is preferable to use the
revenue output measures when public policy analysis is the main purpose of the study. The
3 economic efficiency measured in revenue outputs reflects the combined effects of
managerial efficiency and the constraint imposed by the regulatory authority.
This paper uses econometric model proposed by Battese & Coelli (1995) To measure
the economic efficiency of thirteen European railway companies and to identify the main
determinants of this efficiency. The explanatory equation of efficiency was estimated
according to a Tobit model. As (Cantos Sanchez & Maudos Villarroya, 2000), (Bouf &
Péguy, 2001) and (Oum & Yu, 1994) we used train km (train km passenger and train km
freight) as an indicator of productivity measurement in our costs frontier.
This study is structured as follows. Section 2 describes the stochastic frontier
approach to the analysis of efficiency. Section 3 describes the sample and the variables used
in our model. Finally sections 4 and 5 will respectively present the results and the conclusion
of this study.
II. The stochastic frontier approach and inefficiency measurement
II.1 The model
The efficiency theory comes up in 1957, thanks to researcher Farrell’s work. According to
Farrell (1957), efficiency measures a company’s capacity to produce in large numbers, given
a whole production factors. In other words a company is efficient if, and only if, it requires a
little quantity of inputs to produce a given quantity of outputs (Atkinson and Cornwell, 1994).
There are lots of forms of efficiency, like for example technical efficiency, allocative efficiency
and economic efficiency.
-­‐ Technical efficiency links production inputs (physical measure of consumed
resources) to final results (outputs).
-­‐ Allocative efficiency measures the adjustment of inputs regarding the outputs, to
reflect the relative prices. In other words, allocative efficiency measures the needed
company’s capacity in production inputs in decent enough proportions to reach the
highest level of production.
-­‐ Economic efficiency takes into account both technical and allocative resources. When
those two efficiencies add up, the company is efficient economically.
Since the pioneering study by (1957), the measurement of inefficiency has been run parallel
to the estimation of frontier functions. Inefficiency is defined as the difference between the
real levels of the variable being studied (production, cost, benefit…) and the maximum level,
which is located at the frontier.).
The stochastic frontier approaches was introduced simultaneously by Aigner & al.
(1977) and Meeusen & Broeck (1977). These authors define the production frontier as the
geometrical point of the combination of input that maximizes the level of production of a firm.
In other words, a firm is located on the production frontier if, and only if, for a combination of
a given input factors, it reaches the maximum level of production. Any firm located on its
production frontier is considered as technically efficient, which means that with a determined
quantity of input factors, it gets the highest feasible output level (Lesueur & Plane, 1998). On
the contrary, any firm that deviated from the production frontier is considered as technically
inefficient one.
Due to the difficulty of estimating a production function when firm produce more than
one output, cost frontier approach have been preferentially used, in railway transport studies
(Cantos & Villarroya, 2000). The development of these models is credited to both Gathon &
4 Perelman (1992) and Filippini & Maggi (1993). Based on the minimization principle, the cost
frontier sets up, according to a given level of output, of input and of technology; the minimal
costs of a firm. This way, any firm located on its costs frontier is considered as economically
efficient (technical + allocative efficiencies). On the other hand, any firm that diverts from its
cost frontier is considered as economically inefficient.
The cost boundary can be written this way:
LnCi =LnC(Yi,Pi,β )+ε i
(E1)
With
Ci: the observed cost of the firm I
Yi: the output vector
Pi: the vector of input prices
β: the vector of parameters to be estimated
LnC(Yi ,Pi,β ) : The logarithm of the predicted costs of the firm that minimizes production
costs
And ε i : the random error term.
In stochastic cost frontier approach, this error term consists in two components: ui, is the
economical inefficiency (technical inefficiency +allocative inefficiency) and Vi is the random
term. From this, we can draw the following relation:
ε i = ui + v i
(E2)
The cost frontier to estimate can then be written this way:
LnCi = LnC(Yi,Pi,β) + ui + v i
(Eq3)
The estimation of the equation (Eq3) requires to formulate some hypothesizes:
H1: vi is distributed as a normal with zero mean and variance σ v
2
H2: ui is distributed as a half-normal (ui is the absolute value of a variable that is distributed
as a normal with mean zero and variance σ u
H3: Ui and Vi are independently distributed.
These assumptions are made in order to separate the two components Ui and Vi. If the
inefficiency term is constrained to take positive values it is because we think that economic
inefficiency leads to an increase in the cost of production.
In order to identify the main determinants of economic inefficiency, we will estimate the
following system:
⎧
2
2 2
⎪ LnC = β + ∑ β LnY + 1 ∑ ∑ β LnY LnY
it
0
j
jit
jit
kit
2 j=1 k=1 jk
⎪
j=1
⎪
2 2
2
⎪
1 2 2
+ ∑ βlLnPlit + ∑ ∑ βlmLnPlitLnPmit + ∑ ∑ β jlLnYjitLnPlit
⎪
2 l=1 m=1
j=1 l=1
l=1
⎪
⎪
2
2
⎨
1
+ σ TT + σ 2TTT2 + ∑ σ jTTLnPjit + ∑ σ lTTLnYlit + Uit + Vit  (Eq4)
⎪
2
⎪
j=1
l=1
⎪
⎪
5
⎪
⎪
LnEF = α 0 + ∑ α iLnX + α t T + εi (Eq5)
⎪⎩
i=1
5 Equation (Eq4) is the expression of a trans log function with two outputs (Y1 and Y2) and two
inputs, whose prices are respectively P1 and P2. T=1, 2, …T. Note that a trend T has been
introduced in order to reflect the influence of technical progress. Equation (Eq5) draws up a
linear relation between the economic efficiency logarithm (LnEF) and its main determinants
(X).
II. 2.
Estimation technics.
To estimate the previous system, two-steps estimation held our attention.
Considering the hypothesis of independency of Uit and Vit, the first step of the method
consists in estimating the equation (Eq4) using maximum likelihood technique. At the end of
this estimation, we generated the economic efficiency index through the formula given by
Jondrow and al (1982). Under the hypothesis of a half-normal distribution, we adopt the
following expression for the efficiency:
EF = exp(−E ⎡⎣ui / (ui + v i ) ⎤⎦)
E ⎡⎣ui / (ui + v i ) ⎤⎦ =
Where
,
σλ ⎡ φ (ε i λ / σ ) ε i λ ⎤
−
⎢
⎥
(1+ λ )2 ⎣ Φ(−ε i λ / σ ) σ ⎦
and
are respectively the density and distribution function
of a random variable that is distributed as a normal.
Given the fact that the inefficiency term is marked out between 0 and 1, the Tobit model
enabled us to estimate the linear relation between economic efficiency and its main
determinants. So our second step is to estimate using maximum likelihood Tobit model in
which the dependent variable is the symmetry with respect to zero of the logarithm of the
efficiency index.
III. The data
For our analysis, we used a sample of 13 railways companies, over the period 2000 to 2009.
These data were obtained from the International Union of Railways (UIC) and some from
annual reports of the companies. Table 1 gives a summary of the principal statistics of the
variables for the as a whole. Although for some of the companies’ complete information was
not available for all year. Note that companies were chosen according to the availability of
the data
è Output vector
In the railway transport field, lots of indicators can be used to measure the production level of
a railway company. It concerns mainly measures like: the number of ton-km or the number of
train-km for freight activity, and the number of passenger-km or train-km of passenger for
passenger transport activity. Such as Cantos & Villarroya (2000), Bouf & Péguy, (2001), we
kept the combination of train-km passenger (TKMP) for a train-km freight (TKMF) as indicator
of productivity measure. The use of this indicator enables us to estimate the degree of
management of the railway companies.
6 è Inputs prices
As price of inputs, we used labor price and the purchase price and the external expenses,
which includes the price of energy and consumed material. These prices were expressed in
constant euro of 2009 by means of the Purchasing Power parity (PPP). We defined then our
variables as follows:
-­‐ The labor price (P1): we took the labor costs divided by the total number of worker.
Labor costs are the sum of expense from wages, plus pensions and social charges.
-­‐ The price of the consumed material (P2): it is the ratio material and energy price over
the total train-km supplied by each company.
Those variables are the same as the ones used by Sanchez and Villarroya (2000) and Couto
and Graham (2008). Ideally materials and energy would be constructed as two distinct
variables but the disaggregate data on both input are not available.
è Production cost
Like Sanchez and Villarroya (2000), we used the operating cost (CE) as depended variable
to our frontier cost. Those operating costs include labor cost, energy and consumed material
costs, purchases and external services and other costs.
è The determinants of economic efficiency
As potential determinants of economic efficiency we selected:
-­‐ The number of passenger per train (PT) and the number of tons of freight per train
(TT) as indices of the utilization of trains. These variables are expected to be
correlated negatively with the efficiency level when train-km are used as indicator of
output.
-­‐ The number of passenger trains-km per km of line (TKMPL) and the number of freight
train-km per km of line (TKMFL). Those variables measure the utilization of
infrastructure index. It is expected that a more intense use of infrastructure could lead
to the reduction of cost of train-km.
A detailed analysis of table 1 allows us to identify the following facts:
•
From a point of view of passenger services, DB has an average of 73177 million
passengers km, it ranks as first in our sample. It is followed by FNM, which has an
average of 46107-million passenger km. SNCF ranks fifth with an average of 3631
million-passenger km. The last row is occupied by CFL, which has an average of 292
million-passenger km. For the rate of use of infrastructure by passenger service, the
first rank is assigned to DB with an average of 706-million train km. It is followed by
SNCF, which has an average of 398-million train km. At the bottom of the ranking we
have CFL with an average of 5.6 million-train km.
•
With regard to freight activity, DB also takes first place with an average strength
of 80793 million tonnes km for 200-million train km. It is followed by the SNCF, which
has an average strength of 39693 million tonnes km for 101-million train km freight. At
the bottom of the ranking we have FNM, which has an average strength of 20 million
tonnes km for 67 thousand-train km
•
The ratio of passenger km/ton km allows us to see that in our sample, SNCB,
RENFE and CP companies achieves more train passenger km than freight trains
because they have a higher ratio has a. This ratio is estimated at 0.91 for DB. It
shows that productivity freight is almost identical to that of the transport of
7 passengers. . For the SNCF, it is estimated at 0.091.Unlike DB, we can say that
SNCF realised more tonne km than passenger km. This result also applies to
companies such as BLS (0.5) CD (0.45) CFL (0.55) SZ (0.25) and VR (0.35).
•
Ratio of passenger train km / freight km train. It represents the rate of use of
infrastructure services freight or passenger services. This ratio shows that in our
sample, infrastructure is more used for passenger service than freight service
because this ratio is greater than one in the whole of the sample.
•
The number of employees also makes a distinction between those companies. In
terms of workforce, DB is in the first position with an average staffs of 226488
employees. It is followed by the SNCF, which has an average staff of 164430
employees. At the bottom of the scale we have FNM, which has a staff of 2599.
This descriptive analysis shows that our sample is as diverse as varied because it includes
companies with high or low performance in passenger transport, companies with high or low
performance in freight transport, large or small companies. This multidimensional analysis
does not allow us to distinguish between the most efficient and less efficient companies. To
move from multidimensional analysis to an univariate analysis we will use frontier model. IV. The results
In the first part of this section, we will present the estimated coefficients of the stochastic cost
frontier. More precisely we will take an interest in indicators enabling to judge the validity of
the model and its main variables, which have an influence on the cost b frontier. In the
second part, we will present the main determinants of economic efficiency and we will
compare them with those studied throughout the literature.
è Parameters of stochastic frontier cost.
Table 2 in Annex, presents the results of the estimation of the stochastic frontier cost. Let’s
recall that in this estimation, our dependent variable was the companies’ operating costs
logarithm. The P-value associated to the Wald test (global significance test), shows that
among the variables to explain, there is at least one factor that influences the operating cost.
The Student’s test (individual significance test) shows that all the variables introduced in the
model enable the explanation of the costs frontier, except the variable LY1 (logarithm the
number of passengers train-km), which has a t of Student lower than 1.96 in absolute value.
Just like we observe than signs associated to coefficients are practically identical to those
studied in the literature. The price elasticity, which is the logarithm of labor price, shows that
a rise of 1% in the price of the labor price leads to a rise of 1.865% in the operating costs.
This result shows the theoretical specificities of the cost are valid.
è The levels of economic efficiency
It is important to recall that the economic efficiency index is the result of a formula proposed
by Jondrow and al (1982). Table 3 in Annex, gives us the average of the efficiency index for
each company, the minimum, the maximum and the standard deviation, on the period
studied. The average economic efficiency index of the sample is estimated to be 0.85. This
index shows us that, in average, efficiency enables the company to reduce its costs by 17%.
Within our sample the four companies, which have a very high economic efficiency index,
8 are, respectively, FNM, CP, CD and BLS. The companies, which have a low economic
efficiency level, are, respectively, SNCB, ÖBB and CFL. Like Cantos & Villarroya (2000), our
analysis shows that companies such as SNCB and ÖBB, which know a high public
intervention in their management, are the ones having a low economic efficiency index. We
can also observe that in most of the situations, the economic efficiency index depends on the
status of the company (private or public) and the degree of State intervention. The ideal
situation would be to construct indicators that allow us to measure the degree of autonomy in
the management of the company and the level of state intervention. But our data do not allow
us to realize this.
è The determinants of economic efficiency
To identify the main determinants of economic efficiency, we estimated a Tobit model in
which our variable to explain is the symmetry bearing on zero, of the logarithm of the
economic efficiency index. This transformation enables our variable to have a zero as lower
bound. The efficiency index is obtained after the estimation of the cost boundary, thanks to a
formula made by Jondrow and al (1982). The results of the Tobit’s model estimation are
presented in Table 4 in Annex. This table respectively includes the estimated coefficient, the
standard deviation, the Student’s test and the P-value, associated to each parameter. The
Student test (individual significance test) allows us to identify as determinants of efficiency
variables LPTL, LTTL, LTKMF and LEL. The signs, associated to those variables, match up
with those got by Oum and Yu (1994) and Gathon and Pestieau (1995). Thus an increase of
1% in the density of passenger’s trains generates an increase of 0.047% in the efficiency
level while a rise of 1% in the density of freight trains leads to a reduction of 0.095% in the
efficiency index. This result is similar to the Oum and Yu’s one (1994). Thus the cost per train
km increases with the filling freight trains and decreases with the filling rate of passenger
trains. The coefficient associated to the TKMFL variable is statistically different from zero,
and we can then conclude that a rise of 1% in the utilization of infrastructures rate by the
freight activity leads to an economic efficiency gain of 0.1%, and thereby reduces the cost of
the train km. This result is similar to the ones from Sanchez & Villarroya (2000) and Oum and
Yu (1994). The LEL variable (percentage of electrified lines) enables us to observe that the
percentage of electrified lines leads to an improvement of the efficiency index and as a result
a reduction in the cost. This result confirms the idea that a rise in electrified lines leads to a
reduction in the labor cost and consumed energy costs. This result is similar as Gathon and
Perelman’s one (1992). The TKMPL is not significant. All things being equal, we think that a
company with a high density of freight trains doesn’t necessarily make a high performance in
passenger’s transportation and vice versa.
9 V.
Conclusion
This paper uses Battese and Coelli (1995) model’s to identify the main determinants of
economic efficiency (technical efficiency plus allocative efficiency) of the European railway
companies. This model consists in two equations that are the stochastic cost frontier and the
equation linking economic efficiency index to its main determinants. A trans logarithmic
function has been used to estimate the cost function while a Tobit model enabled us to
identify the causality relation between economic efficiency and its main determinants. The
advantage of this modelling is that the economic efficiency index includes both allocative and
technical efficiencies. As an estimation technique, we use maximum likelihood technique
This study shows that there is a positive correlation between economic efficiency and
factors such as the degree of filling of passenger train (number of passengers per train),
index of the use of infrastructure by freight services (the number of train km freight per km of
the line) and the level of technology (the percentage of electrified lines). On the other hand
there is a negative correlation between economic efficiency index and the degree of filling of
train freight. We have shown that an undertaking, which has a very high density of train
freight, does not necessarily realise a good performance in passenger transport and vice
versa. A horizontal separation between freight services and passenger services can therefore
lead to a reduction in the cost of train km. As the main result, we show that companies (BLS,
CD, CP and FNM) having a very high economic efficiency index are the ones having a high
autonomy degree. Just like Sanchez and Villarroya (2000), we have shown that companies
(ÖBB, SNCB and CFL) with a low index of economic efficiency are one that certainly knows
a strong state intervention in the management of the company.
As economic efficiency determinants, we found: the loading rate of passengers trains,
the loading rate of freight trains, the utilization of infrastructures intensity and the percentage
of electrified lines. These determinants are practically the same as those found by Oum and
Yu (1994) and Gathon and Pestieau (1995).
This paper enables then to show the positive influence of economic efficiency on the
reduction of production cost. Thus, a perfect autonomy in the company’s management can
be considered as a lever of reduction in production costs.
10 Table 1. Principal Statistics of the sample (Average for the period analysed)
PKM (in
Million)
TKM (in
Million)
TKMP (in
Thousand)
TKMF (In
Thousand)
CE
P1
P2
BLS
562.5
1215
9235.333
3103.333
4.17e+08
82122.31
1.993096
CD
6770
14929.1
111764.5
34661.1
1.86e+09
12788.24
5.166004
CFL
292
529.1429
5840.429
1392.286
4.49e+08
61709.74
3.524402
CP
3550.714
2362.429
30162.71
7620.429
4.23e+08
31758.86
.3789086
DB AG
73177.5
80793.9
706003.4
200341.5
2.87e+10
41907
3.852235
FGC
752.7778
36.55556
8632.333
125.4444
1.13e+08
50188.82
.1626399
FNM
46107.33
19.66667
7877.333
67
2.58e+08
49293.08
13.86868
RENFE
13980.29
10487.43
143494
33795.14
2.58e+09
45989.87
1.465732
SNCB
81910
7634.2
79679.2
13410.4
3.95e+09
167003.4
2.984447
SNCF
3630.571
39693.71
398872.6
101079.4
1.75e+10
49612.47
11.44681
SZ
784.5556
3111.667
11693.22
7714
3.07e+08
20870.81
6.030656
VR
3541.9
10062.9
31808.1
17107.1
1.25e+09
54255.55
11.23965
ÔBB
1813
19802.5
90820.75
50506
5.06e+09
48876.46
12.69303
11 Table 2. Coefficients of frontier model
Coefficients
Se
T-statistic
P-value
LY1
-0.054
0.145
-0.370
0.711
LY2
-2.268***
0.128
-17.731
0.000
LP1
1.865***
0.075
24.816
0.000
LP2
-0.358***
0.038
-9.440
0.000
A1
-0.018
0.020
-0.905
0.366
A2
-0.042***
0.003
-13.893
0.000
A3
0.058***
0.004
13.349
0.000
A4
0.123***
0.006
21.417
0.000
Y1Y2
0.161***
0.010
16.831
0.000
Y1P1
-0.186***
0.011
-16.824
0.000
Y1P2
0.073***
0.003
26.126
0.000
Y2P1
0.058***
0.010
5.990
0.000
Y2P2
-0.053***
0.001
-53.836
0.000
LP1t
0.038***
0.002
17.328
0.000
LP2t
0.004***
0.001
6.935
0.000
LY1t
0.030***
0.002
18.662
0.000
LY2t
-0.019***
0.001
-17.227
0.000
t
-0.549***
0.033
-16.497
0.000
A5
-0.009***
0.001
-11.013
0.000
Sigma-u
0.781***
0.2458
3.18
0.001
Lambda
1240.662***
0.2458
5048.56
0.000
12 Table 3. Efficiency level
Mean
Std.Dev.
Min
Max
BLSa
0.9073808
0.0826703
0.7836854
0.9988134
CD
0.949978
0.0586889
0.8500131
0.9987486
CFLb
0.6564021
0.0336215
0.627539
0.7257438
CPc
0.9746401
0.0191708
0.9484656
0.9982437
DB AG
0.8181137
0.0912782
0.6416845
0.9987389
FGCd
0.9472437
0.0666728
0.8296832
0.9986871
FNMe
0.9924181
0.0098925
0.9809984
0.9983624
RENFEf
0.8186599
0.1351756
0.6767408
0.9985859
SNCBg
0.4753567
0.2958882
0.2834809
0.9983599
SNCFh
0.87166
0.0737105
0.7884629
0.9987444
SZ
0.8959395
0.1125521
0.7204575
0.9988238
VR
0.8878884
0.1115569
0.6970689
0.9989469
ÔBBi
0.6494659
0.0372764
0.5960425
0.6791295
AVERAGE
0.8488742
0.1622366
0.2834809
0.9989469
a
Except years 2004, 2005 and 2006
Except years 2008 and 2009
c
Except years 2000, 2001 and 2009
d
Except the year 2000
e
Only years 2002, 2003 and 2006
f
Except years 2000 and 2001
g
Except years 2000 and 2004
h
Except years 2000 and 2002
a
Except years 2005 and 2008
b
13 Tableau 4. Determinants of efficiency
Coefficients
SDV
T-statistic
P-value
LPTL
0.047**
0.015
3.124
0.002
LTTL
-0.095***
0.023
-4.155
0.000
TKMPL
0.021
0.043
0.478
0.634
TKMFL
0.102***
0.026
3.860
0.000
LEL
0.459***
0.081
5.679
0.000
t
-0.000
0.008
-0.022
0.983
cons
-0.657
0.517
-1.270
0.207
sigma
0.193***
13.614
0.000
Appendix 1: Railways firms
BLS
CD
CFL
CP
DB
FGC
FNM
RENFE
SNCB
SNCF
ÖBB
SZ
VR
Swiss railway
Czech Railways
Luxembourg Railways
Portuguese Railways
German Railways
Catalonian Government Railways
Ferrovie Nord Milano
Spanish National Railways
Belgian National Railways
French National Railways
Austrian Federal Railways
Slovenian Railways
Finland railways
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