＜論文＞

軌道改良が鉄道事業者の線路メンテナンス費用に与える長期的効果：
分布ラグモデルを用いた実証分析

Long-run Impact of Track Improvements on Railroad Track Maintenance Cost:
Empirical Analysis Using Distributed Lag Model
神戸大学大学院経済学研究科講師

北

村

友

宏

Lecturer, Graduate School of Economics, Kobe University, Japan
Tomohiro KITAMURA
ABSTRACT:
By adopting panel data of small and medium-sized regional passenger railroad companies in Japan, this study
clarifies the extent to which track maintenance cost can be reduced over the years by implementing track
improvements, such as replacing existing rails with heavier ones and replacing wooden sleepers with concrete
ones. We found that if the adoption rate of concrete sleepers increased by 1 percentage point every year, track
maintenance cost would be reduced by 0.714% in 18 years. On the other hand, no reduction in track maintenancecost was observed with regard to introducing heavy rails.
キーワード：鉄道、軌道改良、線路メンテナンス費用、長期弾力性
Keywords:

Railroad, Track improvement, Track maintenance cost, Long-run elasticity

1. Introduction

concrete ones. Based on the data in this study, more

Regional small and medium-sized passenger

than 70% of Japanese regional small and medium-

railroad companies in Japan have been facing difficult

sized passenger railroad companies have introduced

management situations. On one hand, the number

heavy rails or concrete sleepers in the 20 years fromof passengers has decreased due to a population

FY 1994 to FY 2013. Such track improvements notdecline along the railroad line and on the other hand,

only increase the strength of the track equipment

facilities maintenance costs have grown, making up

and improve safety, but also reduce the frequency

a larger percentage of the total cost. In the first halfof required track maintenance, which is expected toof 2017, train derailment accidents caused by ageing

reduce costs [Japan Railway Construction, Transport

wooden sleepers occurred one after another in the

and Technology Agency, 2008a, b]. However, track

three small and medium-sized passenger railroad

improvement is a large capital investment, and it iscompanies, and safety measures for these companies

difficult for railroad companies to implement it withhave become an important issue.

their own funds, so the national and local governments

Many regional small and medium-sized passenger

provide subsidies for track improvements.

railroad companies in Japan have implemented track

Here, a certain period of time (for example, 10

improvements such as replacing light rails withyears) is required before the track maintenance costheavier ones and replacing wooden sleepers with

reduction effect appears after the implementation― 54 ―

国際公共経済研究第31号

2 0 2 0 年

International Public Economy Studies Vol. 31 2020of track improvements because track maintenancemodel. These might be the reasons for the unevenworkers need to be skilled [Board of Audit of Japan,

conclusions of these previous studies.

2016]. It is important to determine exactly after how

Kitamura [2017, 2018] adopted Japanese small andmany years the cost reduction effect would occur

medium-sized passenger railroad companies’ data,and how much cost reduction can be expected, as

estimated distributed lag model, and found that an

it would help railroad companies and governments

increase in the adoption rate of concrete sleepers

gain clarity on the policy implications of track

every year might increase total factor productivity

improvements, and help them take well-informed(TFP) after more than 10 years, and found nodecisions.

significant correlation between the adoption rate ofRegarding the effect of track improvements onheavy rails and TFP. However, the study did not

track maintenance cost, many quantitative analyses

shed light on the effect on track maintenance costs.

have been made. For example, Johansson and Nilsson

Therefore, the current study aims to determine the[2004] conducted an empirical analysis of Swedish andperiod after which the effect of track improvements

Finnish railroads, Wheat and Smith [2008] analyzed

on track maintenance cost appears and the long-run

British railroads, and Odolinski and Smith [2016],

savings in track maintenance costs for regional small

and Odolinski and Nilsson [2017] analyzed Swedishand medium-sized passenger railroad companies inrailroads. However, these studies have produced

Japan. To achieve this objective, this study estimatesinconsistent conclusions. Some of them found thatthe distributed lag model as Kitamura [2017, 2018]

costs can be reduced by track improvements, while

did. We regress the track maintenance cost on theothers did not. For example, in Swedish and Finnish

current and past adoption rates of heavy rails andrailroads, track maintenance cost is significantly

concrete sleepers and obtain the long-run impact oflower if the track quality (track weight, type of

installing heavy rails and concrete sleepers on track

sleepers, and welded rail usage) is high [Johansson

maintenance costs.

and Nilsson, 2004], while in British railroads, track

The remainder of this paper is structured as

maintenance cost is significantly higher if the trackfollows. Section 2 explains the background of thisquality (welded rail usage) is high [Wheat and Smith,study. Section 3 explains the empirical analysis

2008]. On the other hand, empirical studies bymethod, and Section 4 explains the data used for

Odolinski and Smith [2016] and Odolinski and Nilsson

the analysis. Section 5 presents the results of the[2017] found no significant correlation between track

analysis, and Section 6 discusses the results. Section

quality and maintenance costs in Swedish railways.

7 presents the conclusions of this study and the

All these previous studies, except Odolinski andremaining issues.

Nilsson [2017], estimated static models, which did
not take into consideration the time period required

2. Backgroundfor the cost reduction effect to appear after track1) Track Improvements in Japanese Railroad

improvements. Odolinski and Nilsson [2017] used

Companies

a dynamic panel model. However, estimating how

In Japan, track weight is measured in weight permuch the cost changes in a certain period andmeter. Some companies use rails of less than 30kg/m,

also estimating its precise standard errors for null

while others use rails of 60kg/m and over. Replacing

hypothesis testing is difficult with a dynamic panel

light rails with heavier ones not only increases the― 55 ―

strength and improves safety, but also reduces thecompanies, 23 companies increased both the adoption

maintenance cost of the track and labor costs forrate of 50kg/m and over rails and concrete sleepers,

maintenance [Japan Railway Construction, Transport

while 3 companies have increased only the adoption

and Technology Agency, 2008a]. Therefore, arate of 50kg/m and over rails, while the remaining 3

reduction in track maintenance cost is expected due

companies have increased only the adoption rate ofto the introduction of heavy rails.

concrete sleepers over the 20 years from FY 1994

There are several types of sleepers. Originally,

to FY 2013. The average adoption rate of 50kg/m

many railroad companies used wooden sleepers.

and over rails and concrete sleepers among the 32

However, an increasing number of companies arecompanies mentioned above has also increased overreplacing them with concrete sleepers. Concrete

the 20 years. Figure 1 shows the transition of thesleepers not only increase strength and durability of

average adoption rate of 50kg/m and over rails andthe tracks, but also reduce the frequency of track

concrete sleepers among 32 companies. According

maintenance [Japan Railway Construction, Transport

to this figure, the average adoption rate among 32

and Technology Agency, 2008b]. Therefore, there

companies has increased by about 21 percentage

is a possibility that the track maintenance cost canpoints for 50kg/m and over rails, and by about 8

be reduced by installing concrete sleepers. Trackpercentage points for concrete sleepers over the 20

improvements, such as introducing heavy rails andyears, respectively.

concrete sleepers, have been on the rise, especially in2) Derailment Accidents Due to Track Deterioration

regional small and medium-sized passenger railroad

In the first half of 2017, three train derailment

companies in Japan. Based on the data in this study,

accidents occurred in Japanese small and medium-out of 32 companies that existed consistently fromsized passenger railroad companies. First, a train

FY 1994 to FY 2013, 29 companies (91%) exhibit

derailed on January 22, 2017 at Kishu Railway,

an increased adoption rate of 50kg/m and overfollowed by February 22 at Kumamotodentetsu,

rails or concrete sleepers in the 20 years. Of the 29

and on May 22 at Watase Keikoku Railway. These

Changes in Average Adoption Rates of Improved Tracks of the 32 Railroad Companies in This Study
0.55

Average adoption rate

0.50
0.45
0.40
0.35

9
19 4
9
19 5
9
19 6
9
19 7
9
19 8
99
20
0
20 0
01
20
0
20 2
0
20 3
0
20 4
05
20
0
20 6
07
20
0
20 8
09
20
1
20 0
11
20
1
20 2
13

0.30

19

Figure 1

Fiscal year
50kg/m and over rails
Source: Author’s diagram using annual rail statistics data.

― 56 ―

Concrete sleepers

国際公共経済研究第31号

2 0 2 0 年

International Public Economy Studies Vol. 31 2020

derailment accidents were all caused by ageing

logarithmic. We define θ

HR

and θ

CS

as follows:

wooden sleepers and rail fastening devices [Japan(2)

Transport Safety Board, 2018a, b].
In response to these incidents, the Japan(3)

Transport Safety Board submitted “Opinion
Regarding Prevention of Train Derailment

θ is the long-run elasticity of track maintenanceAccidents due to Track Gauge Spread” to thecost with respect to the adoption rate of heavy rails.

Minister of Land, Infrastructure, Transport andThis indicates that the track maintenance cost will

Tourism, the regulatory minister, on June 28, 2018.

increase by θ % after S years if the adoption rate

In that document, the Board urged the Ministerof heavy rails increases by 1 percentage point every

to instruct each railroad company to promote

year. Similarly, θ is the long-run elasticity of track

measures to prevent derailment accidents such as

maintenance cost with respect to the adoption rate

introducing concrete sleepers [Japan Transportof concrete sleepers. This indicates that the track

Safety Board, 2018a]. The Minister acted upon thismaintenance cost will increase after S years if therecommendation by instructing the director of the

adoption rate of concrete sleepers increases by 1

railroad department of each regional transportation

percentage point every year. The long-run elasticity

bureau to review the management of sleepers andθtake necessary measures.

study.

HR

HR

CS

HR

As a res ult, trac k improvement s, such a s

and θ are the parameters of interest in thisCS

Substituting (2) and (3) into (1), we obtain

introducing concrete sleepers, came to be viewed as
an important and urgent issue.

(4)

3. Methodology

By estimating this form of equation, it becomesThis study assumes the following distributed lag

possible to obtain the standard error of long-model in order to measure the long-run impact of

run elasticity θ

track improvements, such as introducing heavy rails

multicollinearity of the lagging explanatory variables

and concrete sleepers, on track maintenance cost.

in (1) [Wooldridge, 2013]. Therefore, this study
(1)

HR

and θ

CS

while relaxing theestimates (4). For details on the distributed lag
model, see Wooldridge [2013].

where TMC it is the track maintenance cost forcompany i in year t , HRit is the adoption rate of

4. Dataheavy rails (for example, 50kg/m and over rails),

In this study, we use annual panel data for regional

CSit is the adoption rate of concrete sleepers, Qit issmall and medium-sized passenger railroad companies

the transport volume, Nit is the network size, andin Japan. The data was obtained from annual railu it is the disturbance term. Because HR i,t-s is notstatistics (each year edition) published by the Ministry

logarithmic, the coefficient of it, δ , indicates thatof Land, Infrastructure, Transport, and Tourism. The

the track maintenance cost in year t will increase by

period for analysis was 20 years from FY 1994 toδ % if the adoption rate of heavy rails at year t － s

FY 2013. The companies to be analyzed are thoseincreases by 1 percentage point. Similarly, CSi,t-s is notthat use only electric cars among private and third

HR
S

HR
S

― 57 ―

sector companies. In Japan, third sector companies

the passenger kilometers and operating kilometers,

are companies that have both private and public

respectively. The passenger kilometers index

stakeholders. Companies that use diesel cars may havebecomes 1 unit if a passenger travels 1km. Tablea different cost structure from those that use only

1 shows the descriptive statistics for each variable

electric cars, and if they are included in our data, theyused in the empirical analysis in this study. From

may affect the analysis results. For similar reasons,this table, it can be seen that there are companies

third-sector companies with routes that are along high-that do not adopt 50kg/m and over rails at all in a

speed lines and were operated by private operators

year, while there are companies in which all tracks

before the opening of the high-speed lines were also

are installed with 50kg/m and over rails in a year.

excluded from the sample. As a result, the number

Regarding the adoption rate of concrete sleepers,of companies in the sample was 45. However, somethere are companies that do not adopt them all in acompanies entered or exited during the 20 years, while

year, while there are companies where the adoption

32 companies existed throughout the 20-year period.

rate of concrete sleepers is 97% in a year.

The total number of observations was 785.
In this study, large railroad companies and urban

5. Empirical Results

railroad companies were excluded from the sample.

We estimated the distributed lag model (4),This is because these companies had almost 100%

described in Section 3, beginning from maximum lag

adoption rate of heavy rails and concrete sleepers as

S＝0 order and then progressively increased valueof FY 1994.

of S by one (S＝1, S＝2, and so forth). If S is 18 orAmong the variables in the model in the previous

less, we can estimate the models. Table 2 shows thesection, the track maintenance cost is a monetary

estimation results from “the model taking up to 10

variable, so it is transformed into a real variable by

years lag (S＝10)” to “the model taking up to 18 years

dividing it by the domestic corporate price index

lag (S＝18).” (1) The number of observations is not(gross average) published by the Bank of Japan. In

necessarily “20 minus the lag length” multiplied bythis study, a heavy rail is defined as a rail weighing

the number of companies because some companies

50kg/m or more, and its adoption rate variable isentered or dropped during the sample period—

created by dividing the distance of its main track by

20 years. In addition, for almost all companies,

the main track length. The adoption rate variable

the operating kilometers, one of the explanatoryof concrete sleepers was created by dividing thevariables of the model, is constant over time, so we

distance along which concrete sleepers were adopted

did not assume a fixed effect model.(2)by the total distance along which the sleepers were

The coefficients of adoption rate of concrete sleepers

laid. The transport volume and network size areindicate the long-run elasticity of track maintenance

Table 1
Variables’ nameTrack maintenance cost (thousand JPY)
Adoption rate of 50kg/m and over rails
Adoption rate of concrete sleepers
Passenger kilometers(thousand people times kilometers)
Operating kilometers (kilometers)

Descriptive Statistics

Mean
133,843.42
0.43
0.44

Median87,379.30
0.34
0.45

Minimum
7,140.45
0.00
0.00

Maximum
1,436,267.08
1.00
0.97

61,574.96

32,040.00

1,287.00

746,895.00

94,791.08

28.36

20.60

4.20

100.5021.31

Note: The number of observations was 785.

― 58 ―

Standard Deviation
137,845.25
0.37
0.33

Table 2― 59 ―

0.097 ***
0.139 *
0.634 ***

0.626
0.293
4.086
1.58
1.74
0.834
35
132

国際公共経済研究第31号

Notes: ***, **, and * indicate statistical significance at the 1%, 5%, and 10% significance levels, respectively. Standard errors are robust for company-level clustering structure.

0.618
0.275
4.191
1.48
1.58
0.818
36
168

0.094 ***
0.134 *
0.667 ***

0.633
0.254
4.127
1.42
1.47
0.803
36
204

0.241 *** －0.777
1.637 ** －5.058
2.339 **
6.507
1.466
0.228
2.625
4.782
1.863
－1.741
2.503
2.828
1.417
－7.040
0.949
2.527
0.856
－0.7360.808 *** －2.709
2.379－1.2692.074－4.220
1.905
2.311
5.213
11.1933.790 －12.188
4.382－0.688－4.013
6.296
1.850
0.709
0.754
－3.373－0.4390.882－0.328－3.166－1.462－2.944
2.039
2.959
0.180

0.244 **
1.749
2.073 **
1.348
1.877
2.459 *
0.819 **
1.078
0.907
0.929
1.086 **
1.680
1.813
2.084
2.271 *

－0.627－0.9265.045－0.1201.251－4.7981.739－0.7390.350
0.164－2.923－1.315－2.007－0.103
4.356

17 lags
18 lags
Coef. Std. Err.
Coef. Std. Err.
0.568
0.230 **
0.456
0.273
－0.971
0.925
0.293
2.046
0.430
2.785
－13.318
3.536 ***
0.208
4.329
10.8956.336 *
2.475
4.590
11.1109.456－2.5734.959－12.836
7.797
2.293
4.256
7.487
3.506 **
－1.374
3.533
0.704
7.775
－6.4133.168 *
－6.7085.005－0.9991.532－2.3462.677
4.209
1.630 ** －0.079
2.236－1.661
1.692
2.459
2.042
4.825
3.306
5.716
5.553
－0.740
4.146
3.771
9.760
－4.8603.254－7.253
9.702
3.467
3.856
－5.944
3.682
2.730
3.311
9.715
3.595 **
－1.7192.125－7.319
6.950
4.409
4.366
0.253 *** －0.884
0.323 ** －0.714
0.386 *
2.167 **
3.148
4.236
2.414
5.397
3.187 **
2.007
3.438
－1.169
4.500
1.903
1.647
2.198
－4.874
4.583
3.408
6.835
4.500
18.924 10.288 *
2.582
2.314
2.670
－7.205 12.350
2.152－4.684
4.254
4.100
7.330
2.984 **
2.671
4.101
－9.0945.944
1.516－5.541
3.984
7.911
5.479
1.252
0.718
1.483
－8.0663.643 **
1.301 ** －3.722
1.602 ** －0.708
2.398
2.643
－2.4852.881－7.8422.660 ***
3.139
－3.215
3.569
1.642
1.917
2.627
4.761
4.536
－0.892
9.252
5.617 *
15.7889.264 *
20.994 13.199
5.727 ** －5.946
8.232
1.929 12.980
3.597－13.289
6.370 ** －9.811
6.631
5.507
4.284
－20.850
7.604 **
13.9874.572 ***
0.099 ***
0.603
0.093 ***
0.639
0.102 ***
0.150 *
0.277
0.150 *
0.188
0.153
0.626 ***
4.332
0.596 ***
4.282
0.940 ***
1.90
2.57
2.20
2.91
0.842
0.878
33
32
97
64

15 lags
16 lags
Coef. Std. Err.
Coef. Std. Err.
0.480
0.224 **
0.481
0.214 **
－1.511
1.134
0.461
0.936
2.362
1.051 ** －1.049
2.200－0.034
1.190
2.832
2.794
1.641
1.169
0.896
3.046
－1.4591.402－0.627
3.365－3.3962.534－0.6992.455－0.0472.023－2.4502.755－1.542
1.183－3.9952.044 *
－1.1680.591 * －0.001
1.242
3.539
0.928 *** 2.991
1.191 **
－0.1541.007－0.773
1.450
2.326
2.315
3.732
2.797
0.985
2.136
0.415
3.315
－3.437
1.786 * －1.912
2.701
1.727
1.457
－0.050
3.145
0.939
1.997

14 lags
Coef. Std. Err.
0.419
0.229 *
－1.5141.004
2.699
1.581 *
－0.297
1.757
2.177
1.850
－4.5752.256 *
－0.823
1.104
0.299
1.115
－1.2370.900－0.8280.725
2.959
1.088 **
0.017
1.293
0.675
1.890
0.124
2.027
0.306
1.886

Estimation Results of Distributed Lag Models

10 lags
11 lags
12 lags
13 lags
Coef. Std. Err.
Coef. Std. Err.
Coef. Std. Err.
Coef. Std. Err.
50kg/m and over rails ratio
0.262
0.218
0.287
0.228
0.322
0.228
0.366
0.223
50kg/m and over rails ratio(t-1)-50kg/m and over rails ratio(t) －1.374
1.198－1.8401.338－1.1161.052－1.6700.959 *
50kg/m and over rails ratio(t-2)-50kg/m and over rails ratio(t)
0.940
0.702
0.849
1.261
1.376
1.416
2.391
1.140 **
50kg/m and over rails ratio(t-3)-50kg/m and over rails ratio(t)
0.069
0.736
0.065
0.811
－0.910
1.355
0.302
0.993
50kg/m and over rails ratio(t-4)-50kg/m and over rails ratio(t)
0.162
0.849
0.143
0.925
－0.7470.660－1.3331.406
50kg/m and over rails ratio(t-5)-50kg/m and over rails ratio(t) －0.677
0.796－0.9410.741－0.1510.959－1.6060.779 **
50kg/m and over rails ratio(t-6)-50kg/m and over rails ratio(t)
0.824
0.758
0.707
0.681
－0.1260.739－0.3350.954
50kg/m and over rails ratio(t-7)-50kg/m and over rails ratio(t)
0.129
1.160
0.252
1.400
0.588
1.192
0.493
1.068
50kg/m and over rails ratio(t-8)-50kg/m and over rails ratio(t) －0.959
0.611－0.5600.821－0.6370.949－0.8000.860
50kg/m and over rails ratio(t-9)-50kg/m and over rails ratio(t) －0.499
0.762－0.7070.807－0.3810.716－0.7960.686
50kg/m and over rails ratio(t-10)-50kg/m and over rails ratio(t)
1.558
1.016
1.010
0.839
0.980
0.630
2.656
0.838 ***
50kg/m and over rails ratio(t-11)-50kg/m and over rails ratio(t)
0.613
1.000
－0.3791.130－0.5510.966
50kg/m and over rails ratio(t-12)-50kg/m and over rails ratio(t)
1.165
1.091
0.197
2.142
50kg/m and over rails ratio(t-13)-50kg/m and over rails ratio(t)
0.770
1.640
50kg/m and over rails ratio(t-14)-50kg/m and over rails ratio(t)50kg/m and over rails ratio(t-15)-50kg/m and over rails ratio(t)50kg/m and over rails ratio(t-16)-50kg/m and over rails ratio(t)50kg/m and over rails ratio(t-17)-50kg/m and over rails ratio(t)50kg/m and over rails ratio(t-18)-50kg/m and over rails ratio(t)Concrete sleepers ratio－0.3300.202－0.3700.209 * －0.453
0.215 ** －0.537
0.224 **
Concrete sleepers ratio(t-1)-Concrete sleepers ratio(t)－0.146
0.960
1.372
1.580
0.967
1.719
－0.102
1.732
Concrete sleepers ratio(t-2)-Concrete sleepers ratio(t)
0.341
0.791
－1.135
1.704
3.168
1.988
5.270
2.826 *
Concrete sleepers ratio(t-3)-Concrete sleepers ratio(t)－0.148
0.872
0.002
0.842
－4.3302.025 ** －1.508
1.646
Concrete sleepers ratio(t-4)-Concrete sleepers ratio(t)－0.7620.919－0.855
1.104
0.649
0.496
－4.0092.253 *
Concrete sleepers ratio(t-5)-Concrete sleepers ratio(t)
0.721
0.644
0.901
0.768
－0.441
1.038
1.201
0.810
Concrete sleepers ratio(t-6)-Concrete sleepers ratio(t)
0.524
0.718
0.656
0.717
1.356
0.871
0.959
0.679
Concrete sleepers ratio(t-7)-Concrete sleepers ratio(t)－1.1111.349－0.7841.373－0.9941.177－0.8991.181
Concrete sleepers ratio(t-8)-Concrete sleepers ratio(t)
0.368
0.670
－0.284
0.746
0.021
0.880
0.130
0.715
Concrete sleepers ratio(t-9)-Concrete sleepers ratio(t)－0.027
0.713
0.348
0.669
－0.078
0.798
0.377
0.802
Concrete sleepers ratio(t-10)-Concrete sleepers ratio(t)－0.251
1.179－1.8980.801 ** －1.715
0.675 ** －3.123
0.869 ***
Concrete sleepers ratio(t-11)-Concrete sleepers ratio(t)
1.382
0.953
－1.3751.293－0.5201.515
Concrete sleepers ratio(t-12)-Concrete sleepers ratio(t)2.581
1.443 * －2.519
2.172
Concrete sleepers ratio(t-13)-Concrete sleepers ratio(t)4.628
1.470 ***
Concrete sleepers ratio(t-14)-Concrete sleepers ratio(t)Concrete sleepers ratio(t-15)-Concrete sleepers ratio(t)Concrete sleepers ratio(t-16)-Concrete sleepers ratio(t)Concrete sleepers ratio(t-17)-Concrete sleepers ratio(t)Concrete sleepers ratio(t-18)-Concrete sleepers ratio(t)Log of passenger kilometers
0.642
0.094 *** 0.640
0.094 *** 0.637
0.090 *** 0.633
0.089 ***
Log of operating kilometers
0.199
0.131
0.195
0.129
0.201
0.124
0.233
0.127 *
Constant term
4.165
0.703 *** 4.202
0.721 *** 4.235
0.694 *** 4.182
0.649 ***
Variance inflation factor of 50kg/m and over rails ratio
1.30
1.31
1.34
1.38
Variance inflation factor of concrete sleepers ratio
1.21
1.23
1.30
1.36
Adjusted R-squared
0.777
0.776
0.785
0.796
Number of companies
39
38
37
36
Number of observations
354
315
277
240

International Public Economy Studies Vol. 31 2020

2 0 2 0 年

cost with respect to concrete sleepers ratio, theinsignificant estimates of δS

estimates of θ in the equations (3) and (4). For all

applies to θ .

CSHRfor all s. The sameCSmodels shown in Table 2, the sign of the coefficients of

The variance inflation factor of 50kg/m andadoption rate of concrete sleepers are negative. The

over rails ratio, HR it in the equation (4), and thatcoefficients of concrete sleepers’ adoption rate showof the concrete sleepers ratio, CSit in the model (4),statistical significance at the 10% significance level inrange from 1.21 to 2.91 and do not exceed 10 for all

the 11-year and 18-year lag models, 5% significancemodels shown in Table 2. This indicates that therelevel in the 12-year, 13-year, 14-year, and 17-year lag

is no evidence that the coefficients of these twomodels, and 1% significance level in the 15-year andvariables suffer from multicollinearity. There is thus

16-year lag models, respectively.

the possibility that the standard errors of long-run

Furthermore, the coefficients of the adoption

elasticity θ and θ are estimated precisely.
HRCS

rate of 50kg/m and over rails indicate the long-run

In addition, for all models shown in Table 2, theelasticity of track maintenance cost with respect

coefficient of passenger kilometers representing theto 50kg/m and over rails ratio, the estimates ofamount of traffic is statistically significant at theθ in the equations (2) and (4). Unlike the coefficientssignificance levels of 1%, and the sign is positive. Thisof concrete sleepers’ adoption rates, the sign ofresult is consistent with the results of Johansson andthe coefficients of the adoption rate of 50kg/m

Nilsson [2004], Wheat and Smith [2008], Odolinski andand over rails are positive for all models shown inSmith [2016], and Odolinski and Nilsson [2017].

HR

Table 2. The coefficients of 50kg/m and over rails’

Furthermore, the coefficients of operating

adoption rate show statistical significance at the 10%

kilometers representing the size of the network show

significance level in the 14-year lag model, and 5%

a positive sign. They show statistical significance atsignificance level in the 15-year, 16-year, and 17-year

the 10% significance levels in the 13-year, 14-year, 15-

lag models, respectively.

year, 16-year, and 17-year lag models.

In these models, there are coefficients of the

Depending on the number of the maximum lags ofdifference in the adoption rates, for example, thethe models, statistical significance of each coefficient

coefficients of “the concrete sleeper ratio in t－10

changes. However, the sign of the coefficients ofyear minus that in t year.” These are the coefficientsthe two adoption rates, passenger kilometers, andof 50kg/m and over rails’ adoption rate in t－s year,

operating kilometers is the same for all models. The

δ , and the coefficients of concrete sleepers’ adoption

results are thus almost robust for the lag length ofrate in t－s year, δ , in the equations (1), (2), (3), andthe models.

HR
S

CS
S

Looking at the goodness of fit of the model with(4). As shown in the equation (2) and (3) in section 3,
from s＝0 to s＝S, and θ is sum

Adjusted R-squared, “Adjusted R-squared” of thefrom s＝0 to s＝S. Some coefficients of themodel that took up to 18 years lag (S＝18) was thedifference show statistical significance at the 10%,highest, with a value of 0.878. Therefore, we discuss

5%, or 1% significance levels, and other coefficientsthe 18-year lag model hereafter.

θ is sum of the δ
HR

HR
S

of the δCSSCSof the difference do not show statistical significanceIn the 18-year lag model, the sign of the coefficientat any conventional significance levels. Note that theof adoption rate of concrete sleepers is negative andestimates of θ is the sum of not only the statisticallyshows statistical significance at the 10% significancesignificant estimates of δSlevel. Since the coefficient is −0.714, it can beHRHR

but also the statistically― 60 ―

国際公共経済研究第31号

2 0 2 0 年

International Public Economy Studies Vol. 31 2020

interpreted that if the railroad company increases

relative to track maintenance costs, it is importantthe concrete sleepers ratio by 1 percentage point

to reduce any costs for railroad companies that face

every year, the maintenance cost will be reduced

severe financial situations.

by 0.714% in 18 years. Although this is not directly

As opposed to concrete sleepers, since the estimatedcomparable because of the different definitions ofcoefficient of the adoption rate of 50kg/m and overtrack improvements, it is consistent with the results

rails, no long-run track maintenance cost reduction

by Johansson and Nilsson [2004] demonstrated in

effect was observed with respect to introducing heavy

Swedish railways that derived the results that therails. The reason for this result is that replacing

higher the track quality index, the lower the trackwooden sleepers with concrete sleepers is a change

maintenance cost. On the other hand, the sign of theto a product made from another raw material, while

coefficient of the adoption rate of 50kg/m and overreplacing light rails with heavier ones is just a change

rails, the long-run elasticity of track maintenancein the weight of the product made from the same

cost with respect to 50kg/m and over rails ratio, is

raw material. Therefore, the change in the resistancepositive and does not show statistical significance(strengthening) of the track equipment will be smallerat any conventional significance level, which means

when the weight of the rail is increased compared tothat the maintenance cost reduction effect due towhen the wooden sleepers are replaced by concrete

introducing heavy rails was not detected.

ones. Hence, by installing concrete sleepers, railroad

Due to the small number of observations, 64, wecompanies will not only improve safety and prevent

need to carefully interpret the results from the 18-

derailment accidents caused by track gauge spread,year lag model. However, a positive coefficient of the

but will also achieve long-run cost reductions and

50kg/m and over rails ratio and negative coefficientsurvivability improvements.

of concrete sleepers ratio are obtained in the other2) Robustness Checkmodels with more observations and a smaller lags

As the maximum lag of the distributed lag model(97 observation for 17-lag, 132 observation for 16-lag,increases, the number of railroad companies in theamong others). Furthermore, the coefficients of thesample decreases gradually, from 45 companies in theconcrete sleepers ratio show statistical significancemodels with non-lag to 32 companies in the models

at the 10%, 5%, or 1% significance level when the lagwith 18-year lags—via 39 companies in the model withof the model is 11 or more. Therefore, the results are

10-year lags. This is because the data are unbalanced

almost robust as mentioned before.

panel: some companies entered and exited during
the study period as mentioned in section 4. However,

6. Discussion

there is the possibility that companies’ cost structure1) Interpretation of Estimation Results of Long-run

changes largely in the years when they enter or drop

Elasticity

from the market. This subsection examines whether

As described in the previous section, as a result

the main results are robust when we use only the 32

of estimating the distribution lag model, we revealed

companies that existed throughout the 20-year period,that the track maintenance cost of railroads would

the balanced panel data.

be reduced by 0.714% in 18 years if the adoption rate

Using the 32 companies, we estimated theof concrete sleepers increased by 1 percentage point

distributed models, beginning from maximum lag

every year. Although these cost savings are smallorder and then progressively increased value of by― 61 ―

― 62 ―

Table 30.099 ***
0.141 **
0.634 ***

0.595
0.316
4.328
1.58
1.83
0.830
128

Notes: ***, **, and * indicate statistical significance at the 1%, 5%, and 10% significance levels, respectively. Standard errors are robust for company-level clustering structure. The number of companies is 32.

0.590
0.305
4.400
1.44
1.71
0.809
160

0.098 ***
0.139 *
0.692 ***

0.610
0.283
4.284
1.40
1.61
0.788
192

0.265 ** －0.746
2.000－2.1362.027 **
5.404
1.715
0.584
3.087
5.524
2.302
－1.596
3.065
3.651
1.403
－8.286
0.969
2.165
0.900
－0.7570.783 *** －2.510
2.481－1.382
2.460－3.718
2.454
3.446
6.320
9.049
4.299 －10.419
3.319－0.685
0.308
5.312
2.657
1.065
1.249
－4.439－0.5470.566－0.317－2.891－1.718－1.2581.810
1.961－0.0400.269 **
1.923
2.047 **
1.444
2.422
3.011 *
0.813 **
1.136
0.988
1.001
1.084 **
2.014
2.604
2.473
2.945

－0.638
2.766
4.868
0.006
1.728
－5.1761.687－0.9580.149
0.152－2.757－1.015－1.285－0.147
3.362

17 lags
18 lags
Coef. Std. Err.
Coef. Std. Err.
0.549
0.239 **
0.456
0.273
－0.803
0.899
0.293
2.046
－0.0442.686－13.318
3.536 ***
0.737
4.323
10.8956.336 *
2.208
4.620
11.1109.456－2.3794.998－12.836
7.797
2.185
4.211
7.487
3.506 **
－1.300
3.456
0.704
7.775
－6.4293.061 ** －6.708
5.005－0.8491.514－2.3462.677
4.003
1.544 ** －0.079
2.236－1.582
1.702
2.459
2.042
5.056
3.163
5.716
5.553
－1.026
3.953
3.771
9.760
－4.5743.203－7.253
9.702
3.173
3.757
－5.944
3.682
2.742
3.388
9.715
3.595 **
－1.6782.167－7.319
6.950
4.409
4.366
0.278 ** －0.850
0.334 ** －0.714
0.386 *
2.125
3.052
4.200
2.414
5.397
3.037 *
2.105
3.344
－1.169
4.500
1.958
1.218
2.190
－4.874
4.583
3.516
6.844
4.378
18.924 10.288 *
2.949
2.222
2.591
－7.205 12.350
2.357－3.193
4.463
4.100
7.330
3.028 **
1.245
4.089
－9.0945.944
1.478－5.141
3.936
7.911
5.479
1.314
0.592
1.464
－8.0663.643 **
1.293 *
－3.5851.534 ** －0.708
2.398
2.642
－2.5172.963－7.8422.660 ***
3.050
－3.299
3.549
1.642
1.917
3.374
4.934
4.456
－0.892
9.252
6.219
15.4679.351
20.994 13.199
5.623 *
－6.322
8.234
1.929 12.980
3.900－11.9936.729 *
－9.811
6.631
4.785
4.579
－20.850
7.604 **
13.9874.572 ***
0.103 ***
0.592
0.098 ***
0.639
0.102 ***
0.156 *
0.288
0.157 *
0.188
0.153
0.623 ***
4.414
0.611 ***
4.282
0.940 ***
1.89
2.57
2.25
2.91
0.837
0.878
96
64

15 lags
16 lags
Coef. Std. Err.
Coef. Std. Err.
0.497
0.231 **
0.485
0.221 **
－1.927 －1.927 **
0.387
0.808
2.455
1.141 ** －1.480
2.104－0.434
1.139
3.004
2.827
2.689
1.130 **
1.249
2.924
－2.6451.421 * －1.555
2.886－2.730
2.546
0.444
2.408
－0.3772.029－3.0653.029－1.227
1.171－3.6901.838 *
－1.076
0.685
0.097
1.331
3.452
0.927 *** 2.831
1.205 **
0.077
0.975
－0.701
1.531
1.502
2.370
3.811
2.990
1.651
2.204
－0.106
3.701－3.965
1.898 ** －1.660
2.938
2.070
1.521
－0.206
3.251
1.108
2.041

14 lags
Coef. Std. Err.
0.439
0.240 *
－1.8190.988 *
2.568
1.741
－0.289
2.046
2.927
1.862
－5.4802.307 **
－0.551
0.973
0.228
1.143
－1.1080.944－0.6860.791
2.904
1.088 **
－0.020
1.285
0.458
1.928
0.314
2.064
0.298
1.944

Estimation Results of Distributed Lag Models (32 Companies)

10 lags
11 lags
12 lags
13 lags
Coef. Std. Err.
Coef. Std. Err.
Coef. Std. Err.
Coef. Std. Err.
50kg/m and over rails ratio
0.298
0.241
0.317
0.246
0.332
0.243
0.380
0.235
50kg/m and over rails ratio(t-1)-50kg/m and over rails ratio(t) －1.084
1.158－1.231
1.114－1.0221.010－1.7890.823 **
50kg/m and over rails ratio(t-2)-50kg/m and over rails ratio(t)
0.668
0.643
0.554
1.159
1.527
1.434
2.466
1.221 *
50kg/m and over rails ratio(t-3)-50kg/m and over rails ratio(t) －0.379
0.545－0.1270.580－1.145
1.404
0.306
1.114
50kg/m and over rails ratio(t-4)-50kg/m and over rails ratio(t)
0.271
0.914
－0.1770.975－0.7590.697－1.1171.482
50kg/m and over rails ratio(t-5)-50kg/m and over rails ratio(t) －0.861
0.912－0.8430.764－0.4050.986－2.1130.867 **
50kg/m and over rails ratio(t-6)-50kg/m and over rails ratio(t)
0.591
0.738
0.396
0.697
－0.1270.771－0.2420.972
50kg/m and over rails ratio(t-7)-50kg/m and over rails ratio(t)
0.562
1.119
0.546
1.444
0.620
1.219
0.396
1.110
50kg/m and over rails ratio(t-8)-50kg/m and over rails ratio(t) －0.585
0.607－0.2530.828－0.3940.937－0.5490.829
50kg/m and over rails ratio(t-9)-50kg/m and over rails ratio(t) －0.907
0.715－0.8040.820－0.4110.740－0.6150.746
50kg/m and over rails ratio(t-10)-50kg/m and over rails ratio(t)1.745
1.009 *
0.943
0.938
1.010
0.720
2.404
0.801 ***
50kg/m and over rails ratio(t-11)-50kg/m and over rails ratio(t)
0.687
1.055
－0.3251.168－0.3600.952
50kg/m and over rails ratio(t-12)-50kg/m and over rails ratio(t)
1.108
1.146
0.018
2.286
50kg/m and over rails ratio(t-13)-50kg/m and over rails ratio(t)
0.847
1.748
50kg/m and over rails ratio(t-14)-50kg/m and over rails ratio(t)50kg/m and over rails ratio(t-15)-50kg/m and over rails ratio(t)50kg/m and over rails ratio(t-16)-50kg/m and over rails ratio(t)50kg/m and over rails ratio(t-17)-50kg/m and over rails ratio(t)50kg/m and over rails ratio(t-18)-50kg/m and over rails ratio(t)Concrete sleepers ratio－0.4070.228 * －0.435
0.234 * －0.487
0.240 * －0.560
0.250 **
Concrete sleepers ratio(t-1)-Concrete sleepers ratio(t)－1.607
1.867
0.959
1.446
1.029
1.482
1.977
1.614
Concrete sleepers ratio(t-2)-Concrete sleepers ratio(t)
0.523
0.667
－1.092
1.351
2.760
1.714
3.640
2.121 *
Concrete sleepers ratio(t-3)-Concrete sleepers ratio(t)
0.543
0.419
0.494
0.558
－3.536
1.929 *
0.028
0.782
Concrete sleepers ratio(t-4)-Concrete sleepers ratio(t)－0.8100.961－0.499
1.211
0.683
0.527
－4.6052.533 *
Concrete sleepers ratio(t-5)-Concrete sleepers ratio(t)
1.113
0.718
0.982
0.891
－0.0140.998
1.643
0.770 **
Concrete sleepers ratio(t-6)-Concrete sleepers ratio(t)
0.605
0.735
0.783
0.704
1.265
0.910
1.009
0.738
Concrete sleepers ratio(t-7)-Concrete sleepers ratio(t)－1.3501.196－1.1741.359－1.2191.156－1.127
1.317
Concrete sleepers ratio(t-8)-Concrete sleepers ratio(t)－0.1900.463－0.4260.740－0.211
0.864－0.0490.674
Concrete sleepers ratio(t-9)-Concrete sleepers ratio(t)
0.082
0.689
0.285
0.664
0.019
0.753
0.199
0.815
Concrete sleepers ratio(t-10)-Concrete sleepers ratio(t)－0.2861.163－1.9050.910 ** －1.753
0.678 ** －2.742
0.775 ***
Concrete sleepers ratio(t-11)-Concrete sleepers ratio(t)
1.359
1.017
－1.3751.364－0.5301.729
Concrete sleepers ratio(t-12)-Concrete sleepers ratio(t)
2.510
1.551
－2.461
2.935
Concrete sleepers ratio(t-13)-Concrete sleepers ratio(t)4.365
1.873 **
Concrete sleepers ratio(t-14)-Concrete sleepers ratio(t)Concrete sleepers ratio(t-15)-Concrete sleepers ratio(t)Concrete sleepers ratio(t-16)-Concrete sleepers ratio(t)Concrete sleepers ratio(t-17)-Concrete sleepers ratio(t)Concrete sleepers ratio(t-18)-Concrete sleepers ratio(t)Log of passenger kilometers
0.634
0.101 *** 0.633
0.101 *** 0.630
0.095 *** 0.623
0.094 ***
Log of operating kilometers0.232
0.130 *
0.226
0.130 *
0.229
0.126 *
0.257
0.130 *
Constant term
4.173
0.782 *** 4.208
0.792 *** 4.244
0.744 *** 4.232
0.694 ***
Variance inflation factor of 50kg/m and over rails ratio
1.26
1.27
1.29
1.34
Variance inflation factor of concrete sleepers ratio
1.33
1.36
1.43
1.49
Adjusted R-squared
0.767
0.765
0.771
0.782
Number of observations
320
288
256
224

国際公共経済研究第31号

2 0 2 0 年

International Public Economy Studies Vol. 31 2020

one (S＝1, S＝2, and so forth) again. Table 3 shows

resulting from ageing wooden sleepers. It is said thatthe results from “the model with 10-year lags” to “thetrack improvements, such as replacing light railsmodel with 18-year lags.”

with heavier ones and replacing wooden sleepers

The 18-year lag model estimated by using thewith concrete ones, not only increase the strength of

unbalanced panel data shown in Table 2 was

the track facility and improve safety, but also reduce

estimated by using the 32 companies that existed

the required track maintenance frequency, which

throughout the 20-year period. So, the results of theleads to cost reduction. In addition, replacing wooden

18-year lag model estimated by using the unbalanced

sleepers with concrete ones might prevent trackpanel data shown in Table 2 are the same as those ofgauge spread and derailment accidents caused by it.

the 18-year lag model shown in Table 3.

However, a certain period of time is required before

We obtained substantially similar results to those

the track maintenance cost reduction effect appearsof the unbalanced panel reported in Table 2. For all

after the implementation of track improvements

models shown in Table 3, the sign of the coefficients ofbecause track maintenance workers need to be

adoption rate of concrete sleepers are negative. The

skilled. Therefore, this study attempts to clarify how

coefficients of concrete sleepers’ adoption rate show

many years it will take for the track maintenancestatistical significance at the 10% significance level incosts to show a reduction after conducting trackthe 10-year, 11-year, 12-year, and 18-year lag models,

improvements and to what extent track maintenancethe 5% significance level in the 13-year, 14-year, 15-

costs will be reduced during that period by adopting

year, 16-year and 17-year lag models, respectively.

panel data of small and medium-sized regional

The sign of the coefficients of the adoption rate ofpassenger railroad companies in Japan.

50kg/m and over rails are also positive for all models

The empirical results indicate that if the adoption

shown in Table 3. The coefficients of 50kg/m and overrate of concrete sleepers increased by 1 percentage

rails’ adoption rate show statistical significance at the

point every year, track maintenance cost would

10% significance level in the 14-year lag model, thebe reduced by 0.714% in 18 years. However, there

5% significance level in the 15-year, 16-year, and 17-

was no long-run track maintenance cost reduction

year lag models, respectively. Although the statisticaleffect with regard to introducing heavy rails. Thissignificance of the coefficients changed slightly, the sign

is because replacing wooden sleepers with concreteof coefficients is the same as the results of unbalanced

ones is a change to products made of different raw

panel data. Furthermore, in the model estimated bymaterials, while replacing light rails with heavier

using the 32 companies’ balanced panel data, the model

ones is a replacement for products made of the samewith the highest Adjusted R-squared was the 18-year

raw materials, and the change in the tolerance of thelag (S＝18) model. Therefore, the results are robust for

track equipment will be smaller when introducing

the railroad companies included in the sample.

heavy rails than when introducing concrete ones.
Track improvements are a large capital investment,

7. Concluding Remarks

and it is difficult for railroad companies to carry

In Japan, regional small and medium-sized

them out with their own funds, but national andpassenger railroad companies have faced difficult

local governments have provided subsidies for track

business conditions, and train derailment accidents

improvements. Therefore, with the help of public

have occurred because of track gauge spread

subsidies and by focusing on introducing concrete― 63 ―

sleepers, it is possible for railroad companies toreduce track maintenance costs in the long run.

achieve a reduction in total cost and improve
management performance in the long-run. Apart

Acknowledgmentfrom these long-term benefits, the immediate benefits

This study was supported by the Japan Researchwould be improved safety and prevention of train

Center for Transport Policy. We would like to thankderailment accidents caused by track gauge spread.

Editage (www.editage.com) for English language

This study has several limitations. First, although

editing.

the explained variable of the distributed lag model inthis study is defined as the track maintenance cost,

Notes

the input price is not included in the explanatory( １)

As for the models that are not shown in Table

variable, which is different from the normal cost

2, the number of observations is 785 for thefunction. However, input prices, such as the wages

non-lag (S＝0) model, 740 for the one-year lagof track maintenance workers and the price of(S＝1) model, 695 for the two-year lag (S＝2)

equipment used for maintenance, might have anmodel, 650 for the three-year lag (S＝3) model,

impact on track maintenance costs. Future studies

605 for the four-year lag (S＝4) model, 560 for

could control the input prices and derive a more

the five-year lag (S＝5) model, 517 for the six-

precise measure of the effect of track improvements.

year lag (S＝6) model, 474 for the seven-year

Second, we could not determine whether thelag (S＝7) model, 432 for the eight-year lag (Sreduction in track maintenance cost was larger than＝8) model, and 393 for the nine-year lag (S＝9)

the investment cost for track improvements becausemodel, respectively. The number of companies

the data on the price of heavy rails and concreteis 45 for the non-lag, one-year lag, two-year lag,sleepers is not available. This evidence needs to be

three-year lag, and four-year lag model, 43 forshown and provided for decision making by railroad

the five-year lag and the six-year lag model, 42

companies and governments. Finally, this study

for the seven-year lag model, 39 for the eight-

did not clarify the considerable differences in theyear lag and nine-year lag model, respectively.

adoption rates of improved tracks, time taken to( ２)

We also tried estimating the models whose

start upgrading rails and sleepers, or the speed of

dependent variable is logarithm of “theprogress of track improvements among companies

track maintenance cost per operating

because these are beyond the scope of this study.

kilometers” without using logarithm of the

Furthermore, there is a possibility that theoperating kilometers as an independent

technology of track improvements and the material

variable. However, the results did not changeof the track differ depending on the time. Therefore,

substantially. This suggests that the lack of

if railroad companies conduct track improvements

variation of the operating kilometers within

early, their track maintenance cost at that time

the companies does not affect the results

might be high. Future research should explore

significantly. Therefore, we mention thethe companies’ decisions on whether and when to

estimation results of the equation (4) only.

improve their tracks. Despite these limitations, we
make a meaningful contribution by quantitatively

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