Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
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Submission date: November 15, 2010
Word count 6 576

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Estimation of Road User's Value of Travel Time Savings Using Large-Scale Household
Survey Data from Japan
Hironori Kato (Corresponding Author)
Department of Civil Engineering, University of Tokyo
7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Phone: +81-3-5841-7451; Fax: +81-3-5841-7496
E-mail: kato@civil.t.u-tokyo.ac.jp
Ayanori Sakashita
Creative Research and Planning Co., Ltd.
1-5-4, Higashiyama, Meguro-ku, Tokyo 153-0043, Japan
Phone: +81-3-5773-0001; Fax: +81-3-3-5773-0012
E-mail: sakashita@crp.co.jp
Takayoshi Tsuchiya
Creative Research and Planning Co., Ltd.
1-5-4, Higashiyama, Meguro-ku, Tokyo 153-0043, Japan
Phone: +81-3-5773-0001; Fax: +81-3-3-5773-0012
E-mail: tsuchiya@crp.co.jp
Takanori Oda
National Graduate Institute for Policy Studies
7-22-1 Roppongi, Minato-ku, Tokyo 106-8677, Japan
E-mail: mjd10013@grips.ac.jp
Masayoshi Tanishita
Department of Civil and Environmental Engineering, Chuo University
1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
E-mail: tanishi@civil.chuo-u.ac.jp1Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
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Abstract. This paper uses a large Japanese database to empirically estimate road users’ value of travel time saving(VTTS). The results of parameter estimation show that the estimated VTTS of business travel is nearly equal to theaverage wage rate in Japan whereas the estimated VTTSs of home-to-workplace and personal travels are lower thanthe estimated VTTS of business travel; VTTS increases with the trip length; estimated VTTSs during 8:00 and 10:59
and 18:00 and 19:59 are higher than those during other periods; estimated VTTSs of individuals in their 20s and intheir 60s are lower than those of individuals in other age groups; estimated VTTS of males is similar to that offemales; estimated VTTS per vehicle when driving alone is higher than the estimated VTTS per vehicle in drive withpassenger(s); and estimated VTTS of production/transport workers is lower than the estimated VTTSs of other jobs.
Keywords. Value of travel time saving, route choice, expressway, Japan

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Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
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INTRODUCTION

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Generally, expressways provide road users with high-quality service by reducing traffic congestion to reduce travel
time and providing safer driving conditions. These benefits encourage drivers to choose the expressway rather thanordinary roads although they are required to pay toll. With increasing consumer demand for high-speed, high-quality,
but high-priced road services, nationwide expressway networks have been developed in many regions. Toll charge
has been one of the most important issues in expressway planning. The user’s willingness to pay (WTP) for saving
travel time by using an expressway service could be one of the most important factors when examining toll charges
for expressways. As Hensher and Goodwin (1) noted, the value of travel time savings (VTTS) has recently beenutilized to estimate the toll charge; here, the important issue is not the hypothetical WTP, but the actual money paid.
However, thus far, the VTTS has not worked well for determining the toll charge of an expressway service in Japan.
One of its reasons is because the VTTSs have not been well analyzed with the empirical data in Japan.
In Japan, the cost-benefit analysis guideline for road projects in Japan sets the overall framework of project
evaluation including the VTTS (Morisugi, 2). It shows that the VTTS is determined on the basis of the average wage
rate for the entire nation. The average-wage-rate approach is applied, not only to business travel, but also to nonbusiness travel. Although the VTTS estimates based on the average wage rate could be used for approximations of
the WTP values for saving time in business travel, this may not be the case for non-business travel (Small andVerhoef, 3). Thus, there is a great need to estimate the VTTSs on the basis of the preference data of travelers. The
guideline also assumes that the VTTSs do not vary based on the trip distance or departure time. However, paststudies in other countries, such as Mackie et al. (4) and Axhausen et al. (5), have shown that the VTTS changes as
the trip distance increases. The VTTSs could also vary based on the departure time. This is partly because the traffic
conditions including the traffic congestion could vary among the time of a day. For example, the guideline of VTTS
in UK (Department for Transport, 6) shows that the VTTSs vary among the time of a day. Although several studies
have estimated the national VTTSs empirically in Japan, these have not been estimated in the context of the route
choice in the road network, but rather in the context of the modal choice (Kato and Onoda, 7) or urban rail route
choice (Kato, 8).
This paper empirically estimates the VTTSs in a choice context where the expressway service is chosen or
not in Japan. Rather than push the state of the art in discrete choice modeling, this paper contributes to thediscussions on the VTTSs used for the project evaluation and the toll setting of expressways in Japan. To ourknowledge, this is the first report that uses national-level revealed preference data from Japan to estimate the VTTS
for road users in the context of choosing the expressway service. The paper is organized as follows: the first section
shows the research motivation and goals. Next, the analytical method and data used for the empirical analysis will bepresented. Then, the empirical analysis will be presented. The policy implications are discussed on the basis of theanalysis results. Finally, the findings of the empirical analysis are summarized, and further research issues arepresented.

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APPROACH

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Three major approaches are used for empirically estimating the VTTSs for road users. The first is the stated choice
approach (Louviere et al., 9). It typically involves asking an individual to compare the given times and costs of acurrent route with a proposed toll road. The VTTSs are estimated with a discrete-choice type model such as the logit,
probit, or mixed choice models (Hensher, 10; 11). Unfortunately, no national survey data for the stated choices areavailable in the context of road route choice in Japan. The second approach is the meta-analysis approach. Wardman(12, 13) analyzed the characteristics of VTTSs using about 1000 data sets collected from UK studies on urban andinterurban travel choices. Kato et al. (14) also reported the results of a VTTS meta-analysis that used 216 VTTSs
estimated during the past decades in Japan. However, the implications of this meta-analysis of the VTTS for road
users may be limited since few studies have evaluated the time saving of road use in Japan. The third approach
involves estimating the VTTS base on the revealed preference data from road users. This typically includes the route
choice from an origin to a destination. This paper applies this third approach to the estimation of the national VTTS
for road users in Japan. The dataset from a large-scale car-use trip survey, the Road Traffic Census, is used for theempirical estimation. It includes over 4,436,000 car-use trips covering the entire nation collected using a paper-based
in-person interview survey. The Road Traffic Census has been mainly used for traffic assignment to forecast future
traffic demands. No study has attempted to estimate the VTTS empirically using this dataset. Because the dataset
includes an origin, destination, start point for using an expressway, and end point for using the expressway, the routeused by the individual who chose the expressway service can be identified with a high accuracy. Thus, it is expected
to provide useful information for estimating the VTTS with a route choice analysis.
A simple binary logit model (15) is used for the route choice analysis to estimate the VTTSs. It is assumed
that there are two route options from a given origin to a given destination for any observed trip: an “expressway
route” that includes both ordinary road links and expressway links and a “no-expressway route” that includes only3

Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
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ordinary road links. Two types of models are used: a model that utilizes all of the samples in the dataset and one thatutilizes subgroups of samples from the dataset.
First, it is assumed that an individual maximizes his/her utility function subject to the constraints ofmonetary budget and time budget. Suppose the individual faces a discrete choice of routes from a given choice set
with a fixed pair of an origin and a destination. Then, the individual maximizes his/her utility function under thecondition that a specific route is chosen. It is assumed that the conditional indirect utility function for the model thatuses all of the samples in the dataset is identified as follows:⎛⎞
vi ,n = θ c Ci ,n + ⎜θ t + ∑θ tj X i , j ,n ⎟Ti ,n + ε i ,n
(1)
⎜
⎟
j
⎝
⎠
where vi ,n is the indirect utility function of an individual, n , under the condition that route option i is chosen, Ci ,n10

is the travel cost of route option i of individual n , Ti ,n is the travel time of route option i of individual n , ε i,n is11the error component of route option i of individual n , X i , j ,n is the j th variable of route option i of individual n ,12θ c is the travel cost parameter, θ t is the travel time parameter, and θ tj is the parameter of the j th variable relating

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to the travel time.
The weighted likelihood maximization procedure is used for the parameter estimation because the sampling
rate varies among zones in the survey. Let nm be a respondent whose vehicle is registered at zone m . The weight of
the individual, nm , is defined as follows:8ω nm =

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Hm
Nm

(2)

where N m is the number of respondents at zone m and H m is the number of registered vehicles at zone m . Then,the log-likelihood function is defined asln L = ∑∑ ω nm ⋅ δ i ,nm ⋅ ln Pi ,nm
(3)
nm

i

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where δ i,nm is equal to 1 if individual nm chooses route option i and is 0 otherwise; and Pi ,nm is the probability that

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individual nm chooses route option i . As the binary logit model is assumed, the probability is shown as
Pi ,nm = 1 1 + exp v j ,nm − vi ,nm .

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Next, in the same way as the above model, the conditional indirect utility function in the model estimatedusing subgroups of samples from the dataset is assumed to be as follows:(4)vi ,nk = θ c ,k Ci ,nk + θ t ,k Ti ,nk + ε i ,nk

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where vi ,nk is the indirect utility function of an individual belonging to subgroup k under the condition that route

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option i is chosen, Ci ,nk is the travel cost of route option i for an individual belonging to subgroup k , Ti ,nk is the29

travel time of route option i for an individual belonging to subgroup k , ε i ,nk is the error component of route option

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i for an individual belonging to subgroup k , θ c ,k is the travel cost parameter of subgroup k , and θt ,k is the travel

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time parameter of subgroup k . Again, the weighted likelihood maximization procedure is used for estimating theparameters of each subgroup of the sample dataset.
⎞⎛
Then, the VTTS is estimated using VTTS = ⎜θ t + ∑θ tj X i , j ,n ⎟ θ c from the model estimated using all of
⎟
⎜
j
⎠
⎝
the samples in the dataset, while the VTTS of a subgroup is estimated using VTTS k = θ t ,k θ c,k from the model

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(

(

))

estimated using a subgroup of the dataset. In the empirical analysis shown later, the travel cost is assumed to beequal to the toll charge if the route includes the expressway service, while it is equal to 0 if the route does notinclude any expressway service. This means that the estimated VTTSs are regarded as the estimated values for the
WTP for saving travel time by choosing the expressway service. It should be noted that no other costs such as forfuel and maintenance are included in the travel cost. This is because of the difficulties in estimating these costs for
an individual trip. Because the differences in the fuel cost and maintenance cost resulting from using one routeinstead of the other are expected to be very small in the context of fuel/maintenance market in Japan, the impact ofthese costs on the route choice should be insignificant.

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Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
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DATA

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Original travel data

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The empirical analysis will use the 2005 Road Traffic Census Data. This survey was conducted in 2005 by thegovernments of prefectures and major cities under the supervision of the Ministry of Land, Infrastructure, Transport
and Tourism of Japan. This data includes two types of origin-destination (O-D) surveys: an O-D survey based onintercept interviews with drivers crossing given survey points and an O-D survey based on household interviews
with vehicle owners. Our empirical analysis uses the vehicle-owner-based O-D survey data. This survey covered theentire nation. It includes information about three types of vehicles, i.e., including private vehicles, privately owned
business vehicles, and private trucks; it covers both weekdays and weekends. Surveyors visited households that wererandomly selected from an official list of vehicle owners and interviewed individuals about their vehicle use. The
survey data includes the vehicle-use travel episodes of any vehicle in an interviewed household on a given survey
day and contains information about the origin, destination, departure time, arrival time, number of persons in thevehicle, travel purpose, and origin/destination interchanges in the case of expressway use. It also lists the types ofvehicles owned, locations of registered vehicles, household attributes such as the number of people in the household
and the vehicle ownership, and the attributes of individual drivers such as their age, gender, and job type. The travel
purposes are categorized into the following six types: home-to-workplace travel, home-to-school travel,
workplace/school/others-to-home travel, pick-up travel, personal travel, and business travel. Personal travel includes
travel for shopping, travel for carrying out maintenance activities, travel for dining, travel for daily leisure, travel for
leisure with overnight stay, travel for visiting relatives/friends, travel for driving, and travel for private lessons.
Business travel excludes the travel for transporting the business goods or cargos.

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Level-of-service data

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The level-of-service data including the travel distance, travel time, and travel cost are prepared for the empiricalanalysis. First, a zoning system and a nationwide road network were prepared. The entire nation is assumed to becovered by 6 795 zones. The road network including prefectural roads, national roads, and expressways is used on
the basis of the Digital Road Map Database in Japan (Japan Digital Road Map Association). The DRM database wascreated on the basis of the 1:25,000 topographical maps issued by the Geographic Survey Institute, Japan.
Next, link-based level-of-service data for all links in the network was prepared. First, in the case of the linkbased link length, the length of links shown in the Digital Road Map Database was applied to the road network. Next,
the link-based travel time was estimated using the following BPR function:β⎛ xl ⎞ ⎫⎪Ll ⋅ 60 ⎧⎪⎜⎟(5)t ( xl ) =⎨1 + α ⎜ ⎟ ⎬Vlo ⎪⎝ Cl ⎠ ⎪⎭⎩where t ( xl ) is the travel time of link l under the link flow xl (min), Ll is the length of link l (km), Vlo is the freeflow travel speed (km/h), Cl is the capacity of link l , and α and β are the parameters. Japan Society of Civil
Engineering (16) was followed; it proposes α = 0.48 and β = 2.82 on the basis of the observed travel data in Japan.
To estimate the free-flow travel speed of each link, the observed link flows and the observed travel speed that werecollected in the 2005 Road Traffic Census were used. The following equation is satisfied during peak hours:β⎧⎛ xlC ⎞ ⎫⎪Ll ⋅ 60 Ll ⋅ 60 ⎪
⎜
⎟
(6)
1
=
+
α
⎨
⎜ Cl ⎟ ⎬
VlC
Vlo ⎪
⎪
⎝
⎠
⎩
⎭

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where VlC is the travel speed during peak hours, and xlC is the link flow during peak hours. Thus, the free-flow
travel speed is derived as follows:β⎧⎛ xlC ⎞ ⎫⎪
o
C⎪
⎟
(7)
Vl = Vl ⎨1 + α ⎜⎜ Cl ⎟ ⎬⎪⎩⎝⎠ ⎪⎭The estimated free-flow travel speed of a link Vˆ o and the maximum speed of the link required by the trafficlregulation, Vl , are adjusted as follows if Vˆlo is higher than Vl o :V o = Vˆ o
if Vˆ o ≤ V o + 50
o

l

l

o

= Vˆlo + 50

l

l
o
ˆ
Vl > Vl o + 50

(8a)

Vl
if
(8b).
The traffic regulation in Japan imposes penalties on the drivers who drive at the maximum speed or higher in that,particularly, the drivers lose their driving licenses if they drive at speeds higher than the maximum speed plus 50

5Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
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km/hr. Finally, the link travel time is estimated in the following two cases: the first case is the travel during peak
hours, and the second case is the travel during off-peak hours. The link travel time of peak hours is applied to the trip
whose departure time belongs to the peak hours, whereas the link travel time of off-peak hours is applied to the trip
whose departure time belongs to the off-peak hours. It is noted that the original dataset contains data on whether atrip was made during the peak hours or not. It should be noted that a long-distance journey may cover both the peak
hours and off-peak hours even if its departure time belongs to the peak or off-peak hours. The results show that thecorrelation of the total travel time estimated with the estimated link travel time versus that estimated with theobserved departure time and arrival time is over 0.999. This may mean that the accuracy of estimating the link travel
time is high enough to be used for the model estimation. Finally, with regard to the link-based travel cost, it isassumed that the only travel cost incurred by the drivers is the toll charge for using the expressway service. Although
they also incur the fuel cost for driving, this cost is not taken into account. This is mainly because it is difficult toprecisely evaluate the energy efficiency of a vehicle. The fare tables provided by expressway operators are used forcost calculation. In Japan, the cost of most of the inter-urban expressway services includes an initial charge plus 24.6
yen per kilometer.
Next, route-based level-of-service is prepared on the basis of link-based level-of-service. First, if an
observed trip made by an individual used a route including only an ordinary road link, the expressway route of theindividual is identified by searching the minimum-travel-time route in the road network whereas the no-expressway
route of the individual is identified by searching the minimum-travel-time route in the road network without anexpressway link. Next, if an observed trip made by an individual used a route including both the ordinary road links
and the expressway links, the expressway route of the individual is identified by searching the minimum-travel-timeroute under the condition that the observed expressway links are included in the route whereas the no-expressway
route of the individual is identified by searching the minimum-travel-time route in the road network without theexpressway link. It should be noted that the travel data includes the origin/destination interchange of expressway, if
the trip uses the expressway service.

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Sample travel data

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Sample-based travel datasets are constructed by the following steps. First, this paper covers home-to-workplace
travel, business travel, and personal travel. It excludes the home-to-school travel and pick-up travel because the sizeof sample data regarding the choice of the expressway route in these cases is much smaller than that of sample data
regarding the choice of the expressway route for other travel types. The sizes of sample data regarding the choice ofthe expressway route in the home-to-school travel and pick-up travel are 31 and 336, respectively, whereas those ofsample data regarding the choice of the expressway route in the home-to-workplace, business, and personal travels
are 2 774, 1 130, and 2 083, respectively. This paper also excludes the workplace/school/others-to-home travel
because the original dataset does not distinguish workplace-to-home travel from personal- or business-to-hometravel.
Next, the intra-zone trips; the trips whose origin, destination, vehicle type, or travel purpose is not available;
and the trips including ferry-use are eliminated from the original dataset. The reason for eliminating the intra-zone
trips is first that the accuracy of travel data is not sufficiently high for a short-travel-time trip and second that theexpressway-way use of the intra-zone trips is expected to be too rare. The reason for eliminating the ferry-use trips isthat our empirical analysis highlights the individual’s choice of using expressway or not rather than the modal choice.
The trips to and from the Shikoku Island are also eliminated from the dataset. The reason for this is that the travelers
cannot choose a no-expressway route to and from the Shikoku Island because the Shikoku Island is connected with
the Honshu Main Island only by expressways.
Finally, the trips that were made by the individuals whose route choice set have only the no-expressway
route were eliminated. For example, an individual who resides very far from the expressway or an individual who
travels to a destination that is very far from the nearest expressway interchange may not take the expressway route
into consideration.
The results show that the choice rate of the expressway route increases as the travel time of the expressway
route becomes less than that of the no-expressway route when the time difference is between –20 min and 70 min,whereas the choice rate does not vary over the time difference when the time difference is less than –20 min or from70 min to 120 min. The choice rates vary in the subgroups whose time difference is greater than 120 min, mainly
because the data sizes in those subgroups are extremely small. The above results suggest that the expressway route isone of the route options for individuals when the time difference is between –20 min and 70 min. Therefore, the trips
whose time difference was less than –20 min or over 70 min were eliminated.
As a result of data screening, 146 409 samples were obtained, including 82 262 samples for home-to-worktravel, 12 363 samples for business travel, and 51 784 samples for personal travel. TABLE 1 summarizes thedescriptive statistics of the sample dataset. First, 77.2% of the home-to-workplace trips are made by males, while
85.6% of the business trips and 61.6% of the personal trips are made by males. These indicate that the majority ofcar drivers are males in car-use travels. Second, the share of home-to-workplace, business, and personal trips made6

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Trip distance

Departure time

Age

Job

Gender607

Retailing/Service

710
654 10.7
465 17.8
495 28.4
233 38.4

21km - 30km

31km - 40km

41km - 50km

51km - 70km

71km - 100km

0.3
4.7

1.5

87

4.0

3.2

525

52

20:00 - 23:59

2.8

4.1

5.6

3.7

2.8

3.5

5.2

3.7

3.6

3.9

3.6

1.7

3.9

3.9

3.4

2.0

2.4

2.3

3.7

0km - 10 km

54

18:00 - 19:59%

11km - 20km

3671

10:00 - 10:59
138

142

9:00 - 9:59

12:00 - 17:59

463

11:00 - 11:59

1,407

8:00 - 8:59

272

60 -

7:00 - 7:59

866

50 - 59
839

781

40 - 49

0:00 - 6:59

193
615

20 - 29593

30 - 39

Others1,169

298

Production/Transport

Office work/Technology

34

422

FemaleAgriculture

2,352

Exp.

Male

%

Total

%

Exp.

1,413

1.8

7,406

9.2

1,298

1,697

4,845

882

1,263

3,848

1.5

2.0

374 61.6

1,248 71.6

2,142 82.2

607

1,743

2,607

6,138

0.7

2.0

3.0

7.0

14,360 95.3 15,070 17.3

33,462 98.5 33,987 38.9
5,484 89.3

8.6

9.1

9.8

6.1

9.7

8.3

8.6

8.3

8.7

397 12.6

398 10.1

454 12.2

381 16.8

264 20.9

172 25.9

191

399

303 10.7

159 10.2

43250

384 10.7

384

64

30

108

%

1.2
5.2

603 56.9

711 44.1

483 34.1

578 25.2

554 13.8457

121

55 16.1

91 12.1

5.6 1,536 11.3

1.0

1.5

4.4

27,033 99.7 27,120 31.1

1,246 96.0

1,643 96.8

4,707 97.2

846 95.9

1,192 94.4

3,706 96.3

15,982 97.2 16,445 18.9

38,924 96.5 40,331 46.4

15,423 94.8 16,262 18.7

7,134 96.3

23,154 96.4 24,020 29.9

19,488 96.1 20,269 25.2

16,509 96.4 17,124 21.3

11,441 98.3 11,634 14.5

14,658 96.1 15,251 19.1

28,846 96.1 30,015 37.6

17,302 96.6 17,909 22.5

14,843 98.0 15,141 19.0

1,379 97.6

18,324 97.7 18,746 22.8

61,164 96.3 63,516 77.2 1,022

No-Exp.

Home-to-workplace
Total

%

Exp.

5.9

2.6

4.4

7.6

4.2

2.2

3,148 10.6

3,943 13.3

3,707 12.5

2,271

1,262

663

2,307 19.5

4,605 39.0

2,827 23.9

1,552 13.1

521

2,916 24.4

3,573 29.9

4,465 37.3

704

306

1,780 14.4

341

755

1.1

2.5

456 43.1

900 55.9

934 65.9

1,716 74.8

3,455 86.2

8,358 94.8

1,059

1,611

1,417

2,294

3.6

5.5

4.8

7.8

4,009 13.6

8,815 29.9

10,188 98.8 10,309 34.9

286 83.9

664 87.9

12,071 88.7 13,607 45.8

2,751 87.4

3,545 89.9

3,253 87.8

1,890 83.2

998 79.1

491 74.1

2,116 91.7

4,206 91.3

2,524 89.3

1,393 89.8

478 91.7

2,666 91.4

3,189 89.3

4,081 91.4

640 90.9

276 90.2

1,672 93.9

%

4.6

4.4

3.9

3.6

3.4

4.4

4.6

5.1

3.7

4.4

2.5

5.0

5.1

1.4

0.2

3.8

2.7

3.1

3.0

4.1

5.2

8.0

394 34.3

470 25.6

316 18.4

328 11.1

301

236

57

53

112

706

163

316

319

275

192 10.9

204 17.4

628

533

338

251

123

332

357

393

114

95

495

9,561 90.3 10,583 85.6 1,588

No-Exp. %Business

TABLE 1: Descriptive statistics of sample dataset

Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita

Total

%

7.7

8.2
8,620 19.2

6,934 15.4

3,668

7,553 26.7

7,809 27.6

7,677 27.1

3,075 10.9

2,181

6.3

3.3

2.2

5,484 10.1

7,681 14.1

6,092 11.2

3,442

1,769

1,172

1,398

4,219

2.6

7.8

754 65.7

1,366 74.4

1,400 81.6

2,636 88.9

5,649 94.9

1,148

1,836

1,716

2,964

7

2.1

3.4

3.2

5.5

5,950 11.0

16,391 98.6 16,627 30.7

23,906 99.8 23,963 44.2

1,345 96.2

4,107 97.3

22,385 96.9 23,091 42.5

5,321 97.0

7,365 95.9

5,773 94.8

3,167 92.0

1,577 89.1

968 82.6

13,113 95.4 13,741 30.6

11,466 95.6 11,999 26.7

8,282 96.1

6,683 96.4

3,545 96.6

7,221 95.6

7,452 95.4

7,284 94.9

2,961 96.3

2,086 95.6

19,368 97.5 19,863 38.4

30,333 95.0 31,921 61.6

No-Exp. %Private7

Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
8
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by individuals whose job is agriculture amount to 1.8%, 2.6%, and 7.7%, respectively. This reflects the small
share of agricultural population in Japan. The share of home-to-workplace trips made by individuals whose job
is retailing/service is 22.5% while that of business by them is 37.3%. This means that the retailers and/or service
workers travel more for business purposes than those who work in other jobs. Third, 39.0% of the business trips
are made by individuals in their 50s. This means that senior workers travel for business more than young
workers. 30.6% of the personal trips are made by individuals in their 60s. This may reflect that the retired
people have more free time for personal travels than the younger generation. Fourth, 46.4% of the home-toworkplace trips commence during 0700–0759. This means that, on an average, the period of 0700–0800 is thepeak hour in Japan. Fifth, the trip distances of 70.0% in the home-to-workplace trips, 64.8% in the business trips,
and 74.9% in the personal trips are 20 km or less. Sixth, the shares of expressway users account for less than
10 % in the short-distance trips. Although the dataset was screened carefully, it is afraid that the database may
include many captive individuals who may use only expressway route or only no-expressway route. The
improvement of data screening method is one of the further research issues. Finally, the correlation between
travel time and cost in the sample trips using expressway is 0.765. This is probably because the toll charge of
expressway is determined on the basis of route distance whereas the travel time is also highly dependent on thetrip distance. This may be one of the unavoidable characteristics in the revealed-preference-based dataset.

18

EMPIRICAL ANALYSIS

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25
26
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35
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59

TABLE 2 lists the estimation results of models and VTTSs with a subgroup of the sample dataset. Note that thisanalysis excludes mini-vehicles from the empirical dataset. Note also that the original standard in Japan defines
a mini-vehicle as one having a length, width, and height of up to 400 mm, 1,480 mm, and 2,000 mm,
respectively, and an engine displacement of up to 660 cc. Such vehicles are used for both personal and freighttransportation. Mini-vehicles are excluded in the subgroup analysis of VTTS because the sample size ofchoosing the expressway route by a mini-vehicle is too small to be analyzed by the subgroup.
TABLE 2 shows that all models are well estimated from a statistical viewpoint. The test results formost of the coefficients indicate that they are highly significant. The likelihood ratios are also sufficiently high.
In addition, the signs of all coefficients are reasonable. Although the models including the alternative-specificconstant were also estimated, they are not statistically acceptable. Because the route is chosen by a vehicle, theVTTSs estimated from the route-choice model should be the VTTSs per vehicle. Then, the VTTSs per person
are calculated by dividing the VTTSs per vehicle by the average number of persons per vehicle. Note that the
VTTS per person is calculated under the assumption that all persons including a driver and passenger(s) in a car
have the same VTTS.
First, the estimated VTTSs of home-to-workplace, business, and personal travels are found to be 25.1, 35.2, and21.6 yen per min. per person. The estimated VTTS of business travel is nearly equal to the average wage rate inJapan. Note that the average wage rate in Japan is 37.2 yen per min. The estimated VTTSs of home-toworkplace and personal travels are 71.3% and 61.4% of the estimated VTTS of business travel. These results areslightly higher than those that have been found in the results of meta-analyses carried out in other countries (forexample, in Great Brain, 12). One of the possible reasons is that the traffic congestion is more serious in Japan
than that in other countries. Other is that the time constraint is tighter in the home-to-workplace travels because
the most of Japanese companies apply the fixed-work-hour system in which the official-work start time is fixedsuch 9:00 am. Second, the estimated VTTS of males is 25.3 yen/min and that of females, 24.6 yen/min. Thisimplies that the gender does not affect the VTTS. Third, the estimated VTTS per vehicle and per person whendriving alone are 25.9 yen/min./veh. and 25.9 yen/min./per., respectively, whereas those when driving withpassenger(s) are 36.2 yen/min./veh. and 15.5 yen/min./veh., respectively. This means that the estimated VTTS
per vehicle when driving alone is 39.8% greater than the estimated VTTS when driving with passenger(s). This
may imply that the driver’s VTTS is more than twice that of a passenger’s. Fourth, the estimated VTTSs ofagriculture, production/transport, retailing/service, office work/technology, and others are 24.3, 20.2, 24.7, 25.4,
and 25.5 yen/min./per., respectively. The VTTS of production/transport workers is apparently lower than theestimated VTTSs of other jobs. This is probably because the wage rate in production/transport is lower than thatin other jobs. Fifth, the estimated VTTS of individuals in their 20s, 30s, 40s, 50s, and 60s or more are 19.2, 25.2,
26.5, 24.2, and 22.7 yen/min./per., respectively. The estimated VTTS of individuals in their 20s is the lowest
among all age groups and is followed by that of individuals in their 60s. Their VTTSs are lower than those ofother age groups simply because they have lower WTP for saving time by using the expressway service becauseof their lower wage rate. Sixth, the estimated VTTS of trips starting between 1000 and 1059 is the highest in aday, followed by that between 1800 and 1959, between 0800 and 0859, and between 0900 and 0959. The VTTS
is the highest between 100 and 1059 probably because more business trips are made during this period thanduring other period. The VTTSs between 0800 and 0959 and between 1800 and 1959 are high because thetraffic congestion is serious during morning and evening peak hours. Finally, the longer the trip distance, the8

1

Trip distance

Departure time

Age

Job

Passengers

GenderTravel purpose

Home-to-workplace
Business
PrivateMale
FemaleDrive alone
Drive with passenger(s)Agriculture
Production/Transport
Retailing/Service
Office work/Technology
Others
20-29
30-39
40-49
50-59
60-69
0:00 - 6:59
7:00 - 7:59
8:00 - 8:59
9:00 - 9:59
10:00 - 10:59
11:00 - 11:59
12:00 - 17:59
18:00 - 19:59
20:00 - 23:59
0km - 10 km
11km - 20km
21km - 30km
31km - 40km
41km - 50km
51km - 70km
71km - 100km

Travel cost
Coeff.
T-stat.
-0.0057-78.0-0.0028-48.5-0.0049-63.1-0.0058-66.7-0.0074-31.5-0.0058-76.1-0.0035-14.6-0.0074-8.4-0.0076-30.3-0.0060-34.8-0.0058-45.1-0.0054-32.4-0.0084-24.5-0.0059-33.8-0.0057-36.9-0.0058-40.7-0.0057-23.7-0.0047-36.2-0.0062-50.2-0.0062-32.2-0.0060-16.2-0.0046-9.6-0.0055-8.2-0.0056-18.9-0.0053-11.0-0.0057-9.8-0.0150-21.5-0.0087-44.7-0.0054-33.1-0.0031-19.3-0.0020-10.8-0.0012-6.7-0.0008-3.0

Travel time
Coeff.
T-stat.
-0.1497-60.7-0.1224-47.0-0.1634-55.8-0.1458-51.0-0.1823-23.7-0.1512-58.8-0.1282-13.2-0.1901-6.8-0.1556-21.5-0.1528-26.7-0.1524-35.1-0.1466-25.6-0.1650-16.6-0.1549-26.1-0.1566-29.0-0.1469-31.4-0.1384-18.5-0.1133-26.5-0.1638-38.4-0.1751-26.0-0.1666-13.7-0.1626-8.5-0.1422-6.6-0.1412-14.8-0.1555-8.9-0.1459-8.3-0.2199-13.2-0.1224-20.8-0.0939-17.3-0.0688-12.2-0.0503-7.7-0.0420-6.1-0.0358-3.2-5200.5-3559.3-3709.7-3797.9-694.0-4864.7-266.8-51.9-640.4-1001.8-1716.8-934.9-379.4-951.3-1153.0-1412.5-493.9-1359.1-2023.4-836.1-225.1-93.3-60.0-301.8-109.3-88.6-312.2-1256.7-1039.1-655.1-344.5-259.4-88.1-15429.7-6224.9-10607.2-11144.6-3106.4-14813.8-542.3-214.5-2639.0-3132.4-5134.3-2661.7-1870.0-2964.7-3474.8-4192.1-1435.5-3036.5-6673.1-2987.9-736.7-243.2-165.8-913.1-312.6-243.8-5171.7-5882.6-2519.7-1010.5-438.0-287.3-94.0

Initial log- Final loglikelihood likelihood

Num ofAve. passengers EstimatedEestimatedobservation per car
VTTS per veh. VTTS per per.
yen/min./veh. yen/min./per.
0.66
87444
1.05
26.2
25.1
0.43
30076
1.23
43.3
35.2
0.65
54876
1.54
33.3
21.6
0.66
63516
1.04
25.3
24.3
0.78
18746
1.04
24.6
23.7
0.67
84395
1.00
25.9
25.9
0.51
2704
2.34
36.2
15.5
0.76
1413
1.06
25.7
24.3
0.76
15141
1.02
20.6
20.2
0.68
17909
1.04
25.6
24.7
0.67
30015
1.03
26.3
25.4
0.65
15251
1.06
27.0
25.5
0.80
11634
1.02
19.7
19.2
0.68
17124
1.04
26.2
25.2
0.67
20269
1.03
27.4
26.5
0.66
24020
1.04
25.3
24.2
0.66
7406
1.06
24.1
22.7
0.55
16262
1.06
24.0
22.7
0.70
40331
1.04
26.5
25.6
0.72
16445
1.05
28.4
27.1
0.69
3848
1.06
27.9
26.3
0.62
1263
1.08
35.1
32.5
0.64
882
1.07
26.0
24.3
0.67
4845
1.07
25.4
23.7
0.65
1697
1.05
29.2
27.8
0.64
1298
1.06
25.7
24.3
0.94
27120
1.05
14.7
13.9
0.79
33987
1.04
14.1
13.6
0.59
15070
1.04
17.4
16.7
0.35
6138
1.05
22.3
21.2
0.21
2607
1.09
25.1
23.1
0.10
1743
1.08
35.5
33.0
0.06
607
1.18
43.7
37.0

Rhosquared

TABLE 2: Models and VTTSs estimated with subgroup of sample datasets

Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita

99Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
10
1

TABLE 3: Estimation results of VTTS model estimated with all sample datasets
Variable
Travel time ( θ t )–0.0993t-statistic–15.0**

Travel time x ln(Distance) ( θ t _ dist )–0.0288–14.1**

Travel time x Dummy of senior generation ( θ t _ senior )0.0071

1.6

Travel time x Dummy of drive-alone ( θ t _ alone )0.03497.6**

Travel time x Dummy of mini vehicle ( θ t _ mini )0.0251

7.3**

Travel time x Dummy of early-morning departure time ( θ t _ morning )0.0126

3.8**

Travel time x Dummy of peak hours ( θ t _ peak )–0.0087–2.0*

Travel time x Dummy of business purpose ( θ t _ business )–0.0393–8.9**

Travel cost ( θ c )–0.0062–102.0**Initial log-likelihood
Final log-likelihood
Likelihood ratio

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

Coefficient–34269–10892
0.68

196,672
Number of observation
Note: * means the significance at 95% confidence level and ** means the significance at 99% confidence level.

higher is the estimated VTTS. This is the same result as earlier studies in other countries including UK (4) and
Switzerland (5).
TABLE 3 lists the results of the model estimated with all sample datasets on the basis of eq (1). The
travel time is defined as the travel duration (min.) from an origin to a destination. The distance is defined as thelength (km) of a non-expressway route from the origin to the destination. The dummy for the senior generationis 1 if an individual making the trip is in his/her sixties or older and 0 otherwise. The dummy for drive-alone is 1
if an individual making the trip drives alone and 0 otherwise. The dummy for mini-vehicle is 1 if the car used in
the trip is a mini-vehicle and 0 otherwise. The dummy for early-morning departure time is 1 if the departuretime of the trip is between 000 and 659 and 0 otherwise. The dummy for peak hours is 1 if the departure time of
the trip is between 700 and 859 and 0 otherwise. The dummy for business purpose is 1 if the purpose of the trip
is business and 0 otherwise. The travel cost is defined as the expressway toll charge (yen) paid for using theexpressway service and this is 0 if the route does not include any expressway. The model is well estimated froma statistical viewpoint. The results of the tests for coefficients except Travel time × Dummy for senior
generation indicate that they are highly significant. The likelihood ratios are also sufficiently high. In addition,
the signs of all coefficients are reasonable. TABLE 3 shows that the VTTS increases with the travel distance. It
also shows that the VTTS of the senior generation is lower than that of other generations, VTTS when driving
alone is lower than that when driving with multiple passengers, VTTS of trips made using a mini-vehicle islower than that of trips made using standard vehicle, VTTSs of trips made in the early morning are lower thanthose of trips made in other hours of the day, VTTS of trips made during peak hours is higher than that of trips
made during other hours of the day, and VTTS of business travel is higher than that of non-business travel.

26

DISCUSSION

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First, our analysis results show that the VTTS increases with the trip distance. As shown in Mackie et al. (4),this is because a longer travel time increases the value of time as a resource. It should be noted that the VTTS istheoretically equal to the sum of the value of time as a resource and the value of time as a resource (De Serpa,
17). A long travel time reduces the individual’s leisure time. The marginal utility with respect to leisure time isexpected to increase as the leisure time decreases when it is assumed that the marginal utility with respect toleisure time is decreasing. The increase in marginal utility leads to an increase in the VTTS. The value of time
as a resource is defined as the ratio of the marginal utility with respect to leisure time to the marginal utility withrespect to income. This is because a longer travel time increases the value of time as a commodity. The value oftime as a commodity is defined as the ratio of the marginal utility with respect to travel time to the marginalutility with respect to income under the condition that the utility is maximized. A longer travel time causes
fatigue and/or boredom during travel and it is expected that they lead to an increase in the marginal utility withrespect to travel time. Higher VTTS of longer journey may imply that the toll charge per kilometer increases
with the trip distance. This suggests that the toll charge system should be nonlinear with respect to distance.

10

Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
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Note that the current toll-charge system of Japanese expressways is a linear system in which a distance-based
charge is levied in addition to an initial charge.
Second, our results suggest that VTTS of senior drivers is significantly lower than that of younger
drivers. This means that the income impacts the WTP for saving time significantly. As Mackie et al. (5) pointed
out the variation of VTTS by income should be incorporated into the VTTS estimation and even into the project
evaluation. One of the practical problems of introducing the variation by income into the project evaluation isthe difficulty of forecasting the future distribution of income among the road users. In terms of setting the toll
charge, this result may indicate that the toll charge of senior drivers should be discounted because they havelower WTP for saving time by choosing the expressway. Although a discount program for senior users is quite
popular in public transport services, for example, the subway service operated by the Tokyo Metropolitan
Government, it is rarely applied to the expressway service. To the best of our knowledge, the current Japanese
toll-charge system does not include any discount program for senior drivers.
Third, our results suggest that the VTTSs vary among the time of a day. One of the possible reasons isthat the share of road users by journey type varies among the time of a day. Many business travelers drive
during 1000 and 1059 while many commuters drive from home to workplace during 0800 and 0959. As theVTTSs of business travels and home-to-work travels are higher than that of personal travels, this could lead tohigher VTTSs in the travels departing at these periods. Other possible reason is that the traffic congestion
increases the value of time as a commodity. If the traffics of both the expressway route and the no-expressway
route are highly congested, the drivers must face the traffic congestion whether they choose expressway route ornot. The quality of service in the congested traffic should be lower than that in the less congested traffic. Thus,
the marginal travel time savings during the congested hours critically reduces the disutility of driving in the
traffic jam such as fatigues and boredom. This may result in higher VTTS of driving during the congested hours
than that during the less congested hours. This may also suggest that the toll charge for a trip starting in earlymorning or in late evening should be discounted. For example, the East Nippon Expressway Company Ltd. hasrecently introduced a discount program in which drivers pay 50% of the standard charge for using the givenroutes of their expressway network between 2200 and 0600. This aims to promote expressway demand during
off-peak hours. This may also suggest that the toll charge for a trip starting during peak hours should be
increased. Theoretically, this will lead to peak-load pricing or congestion charging. This may match the concept
of congestion pricing theory that aims to internalize the externalities of traffic congestion during the peak hours.
Note no congestion pricing scheme has been introduced for any Japanese expressway.
Finally, the VTTS per vehicle when driving alone is lower than that when driving with passengers,
whereas the VTTS per person when driving alone is higher than that when driving with passengers. This may be
one of the controversial issues in transportation planning. This is because it is unclear whether the vehicle-based
WTP or the individual-based WTP influences the decision-making process of route choice. If higher toll charge
is levied when driving alone, it may reduce the expressway demand when driving alone and reduce traffic
congestion. This follows the concept of a high-occupancy toll (HOT) lane. In contrast, if lower toll charge islevied when driving alone, it may promote expressway demand when driving alone and increase traffic
congestion. This goes against the HOT lane policy.

40

CONCLUSIONS

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50
51
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This paper empirically estimates the WTP for saving travel time by choosing the expressway route that is equal
to the VTTS of road users with a large-scale database in Japan. Parameter estimation indicates that (1) the
estimated VTTS of business travel is nearly equal to the average wage rate in Japan whereas the estimatedVTTSs of home-to-workplace and personal travels are lower than the estimated VTTS of business travel; (2)VTTS increases with the trip length; (3) estimated VTTSs during 0800 and 1059 and 1800 and 1959 are higher
than those during other periods; (4) estimated VTTSs of individuals in their 20s and in their 60s are lower thanthose of individuals in other age groups; (5) estimated VTTS of males is similar to that of females; (6) estimated
VTTS per vehicle when driving alone is higher than the estimated VTTS per vehicle in drive with passenger(s);and (7) estimated VTTS of production/transport workers is lower than the estimated VTTSs of other jobs. Then,
policy implications for the toll charge of the expressway service are discussed assuming that toll charge shouldreflect the VTTS of road users.
Finally, it should be noted that the VTTS estimation presented in this paper uses one specific form of
the function, including the socio-demographics and travel environment. Another specification of utility function
should be explored. It is also noted that the variation of VTTSs by income was not analyzed because thedatabase does not include the individual’s income data. Additionally, the influences of other transportation
modes on road users should be also examined with another database. Further studies are still required toconclude the national VTTS study in Japan.

11Hironori Kato, Ayanori Sakashita, Takayoshi Tsuchiya, Takanori Oda, and Masayoshi Tanishita
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ACKNOWLEDGMENTS
This research was financially supported by a research project of the Japan Road Technology Convention under
the Ministry of Land, Infrastructure, Transport and Tourism (MLIT) of Japan. The authors thank Mr. Toshiyuki
Monma and Ms. Yuko Harada (MLIT, Japan) for supporting our project. The authors also thank Professor
Kazusei Kato (Nihon University), Dr. Yuichi Mohri (The Institute of Behavioral Sciences), and Mr. ShioHayasaki (Social System, Co.) for their valuable advice regarding our analysis.
REFERENCES
1.

Hensher, D. A., and P. Goodwin. Using Values of Travel Time Savings for Toll Roads: Avoiding Some
Common Errors. Transport Policy, Vol. 11, 2004, pp. 171–181.
2. Morisugi, H. Evaluation Methodologies of Transportation Projects in Japan, Transport Policy, Vol. 7, 2000,
pp. 35–40.
3. Small, K. A., and E. T. Verhoef. The Economics of Urban Transportation, Routledge, Abingdon, 2007.
4. Mackie, P., W. Wardman, A. S. Fowkes, G. Whelan, J. Nellthorp, and J. J. Bate. Values of Travel Time
Savings in the UK. Report to Department of Transport, Institute for Transport Studies, University of Leeds
and John Bates Services, Leeds and Abingdon, 2003.
5. Axhausen, K. W., S. Hess, A. Koenig, G. Abay, J. J. Bates, and M. Bierlaire. Income and Distance
Elasticities of Values of Travel Time Savings: New Swiss Results, Transport Policy, Vol. 15, 2008, pp.
173–185.
6. Department for Transport (2009) Values of time and operating costs, TAG Unit 3.5.6.
7. Kato, H., and K. Onoda. (2009) An Investigation of Whether the Value of Travel Time Increases as Travel
Time is Longer: A Case Study of Modal Choice of Inter-urban Travelers in Japan, In: Transportation
Research Record: Journal of the Transportation Research Board, No. 2135, pp. 10–16.
8. Kato, H. Variation of Value of Travel Time Savings over Travel Time in Urban Commuting: Theoreticaland Empirical Analysis, Transportation and Traffic Theory 2007: Papers selected for presentation at
ISTTT17 (eds. By Allsop, R. E., M. G. H. Bell, and B. G. Heydecker), Elsevier, 2007, pp. 179–196.
9. Louviere, J. J., D. A. Hensher, and J. Swait. Stated Choice Models: Analysis and Application. Cambridge
University Press, Cambridge, 2000.
10. Hensher, D. A. Stated Preference Analysis of Travel Choices: The State of Practice. Transportation, Vol.
21, 1994, pp. 107–133.
11. Hensher, D. A. The Valuation of Commuter Travel Time Savings for Car Drivers: Evaluating Alternative
Model Specifications. Transportation, Vol. 28, 2001, pp. 101–118.
12. Wardman, M. The Value of Travel Time: A Review of British Evidence. Journal of Transport Economics
and Policy, Vol. 32, No. 3, 1998, pp. 285–316.
13. Wardman, M. A Review of British Evidence on Time and Service Quality Valuation. Transportation
Research Part E, Vol. 37, 2001, pp. 107–128.
14. Kato, H., M. Tanishita, and T. Matsuzaki. Meta-analysis of Value of Travel Time Savings: Evidence fromJapan, Paper presented at the 12th World Conference on Transport Research, Lisbon, July 2010.
15. Ben-Akiva, M., and S. Lerman. Discrete Choice Analysis: Theory and Application to Travel Demand, MIT
Press, Massachusetts, 1985.
16. Japan Society of Civil Engineering. Theory and Application of Road Traffic Demand Forecast: Part 1
Application of User Equilibrium Method, Maruzen, Tokyo, 2003.
17. De Serpa, A.C. A Theory of the Economics of Time. The Economic Journal, Vol. 81, 1971, pp. 828–846.

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