VALUATION OF TRAVEL TIME SAVING WITH REVEALED PREFERENCE DATA IN JAPAN: FURTHER ANALYSIS

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1 VALUATION OF TRAVEL TIME SAVING WITH REVEALED PREFERENCE DATA IN Hironori Kato, The University of Tokyo, Takanori Oda, Creative Research and Planning Co., Ayanori Sakashita, Creative Research and Planning Co., ABSTRACT This paper presents the latest estimation results of the value of travel time savings of Japanese road users based on revealed-preference travel data from the nationwide 2005 Road Traffic Census Survey of Japan. This paper extends our earlier study (Kato et al., 2011) using the same dataset. It uses standard binary logit and mixed binary logit models in the context of an expressway versus no-expressway route choice for subgroups categorized by gender, passengers, type of job, age, departure time, and travel distance, as well as three travel purposes: home-to-work, business, and private. The mixed logit models assume parametric distributions normal and triangular of travel time and cost coefficients. Then, the estimation results of the modes are compared among different distribution types. Keywords: Value of travel time saving, revealed preference, route choice, mixed logit, Japan INTRODUCTION The value of travel time saving (VTTS) is widely used for transportation project evaluation. In many countries, such as the UK (Mackie et al., 2003) and Denmark (Fosgerau et al., 2007), the national VTTS is estimated mainly with stated-preference (SP) data. Although VTTS estimation based on SP data may overcome the difficulties associated with revealedpreference (RP) data, the principal drawback of the SP approach is that stated preferences may not correspond closely to actual preferences (Bonsall, 1983). Thus, VTTS estimation with RP data could be used to verify SP-based findings. This paper estimates VTTSs using RP-based travel data from Japan and compares the results with earlier studies using SP data and the meta-analysis findings mainly based on SP data from other countries. This paper extends Kato et al. (2011) by carrying out further analyses. First, VTTSs are estimated with a standard binary logit model for different travel purposes and different road user subgroups 1

2 based on age, gender, departure time, and travel distance. Next, VTTS distributions are estimated with a mixed binary logit model based on travel time and travel cost coefficients in the utility function. This paper is organized as follows: The next section describes the data used in our empirical analysis. The VTTS estimation method is then presented based on a standard binary and a mixed binary logit model in the context of an expressway versus no-expressway route choice. The estimation results are then explained. The results of the standard logit model are categorized into individual attribute subgroups and three travel purposes, and those of the mixed logit model are sorted by distribution function type in travel time and travel cost coefficients. Finally, the findings are summarized and further issues presented. DATA The empirical analysis will use the RP travel data from the 2005 Road Traffic Census Survey of Japan. This survey was conducted by prefecture governments and major cities under the supervision of the Ministry of Land, Infrastructure, Transport and Tourism of Japan. The survey covered the entire nation. Sample-based travel datasets are constructed from the original dataset from this survey according to the following steps. First, this paper covers home-to-work trips, business trips, and private trips. It excludes home-to-school and pick-up trips because the sample size of expressway route choice data for these cases is small compared to other trip types. The sample sizes of expressway home-to-school and pick-up trips are 31 and 336, respectively, whereas the number of trips in the home-to-work, business, and private categories are 2,769, 1,125, and 2,080, respectively. This paper also excludes work/school/others-to-home trips because the original dataset does not distinguish between work-to-home and private- or business-to-home trips. Next, intra-zone trips; trips whose origin, destination, vehicle type, or travel purpose is not available; and trips that include ferry use are eliminated from the original dataset. Intra-zone trips are excluded because, first, travel data for short-travel-time trips are not sufficiently accurate and, second, expressway use for intra-zone trips is probably rare. Ferry-use trips are excluded because our empirical analysis focuses on the choice between expressway and other routes rather than on modal choice. Trips to and from Shikoku Island are also eliminated from the dataset because it is connected to Honshu Main Island only by expressway and travelers cannot choose a no-expressway route. Finally, trips limited to a no-expressway route choice were eliminated. For example, a person who resides very far from the expressway or one who travels to a destination very far from the nearest expressway interchange may not consider the expressway route. Figure 1 plots expressway route choice rates versus travel time differences between expressway and noexpressway routes. The chart shows that the expressway choice rate increases as travel time decreases by 20 min to 70 min compared to the no-expressway route, whereas the choice rate does not vary over time difference ranges of less than 20 min and 70 to 120 min. Choice 2

3 Figure 1 Expressway route choice versus travel time differences between expressway and no-expressway routes rates seem to vary randomly in subgroups with time differences of greater than 120 min, mainly because the data size of these subgroups is extremely small. The above results suggest that the expressway is one of the route options when the time difference is between 20 min and 70 min. Therefore, trips with time differences of less than 20 min or more than 70 min were eliminated. As a result of data screening, 146,409 observations were obtained, including 82,068 home-towork, 12,305 business, and 51,555 private trips. Table 1 shows the descriptive statistics of our dataset. First, 77.2% of home-to-work, 85.6% of business, and 61.5% of private trips are made by males. These numbers indicate that most car drivers are male. Second, people in agricultural occupations account for 1.8%, 15.8%, and 5.1% of home-to-work, business, and private trips, respectively. This reflects the small agricultural population in Japan. Persons who hold retailing/service jobs undertake 22.5% of home-to-work and 32.3% of business trips. This means that retailers and/or service workers travel more for business purposes than other workers do. Third, people in their fifties make 39.0% of business trips. This means that senior workers travel on business more than young workers do. Those in their sixties make 30.5% of private trips. The fact that retired people have more free time for private trips than the younger generation does could account for this. Fourth, 47.1% of home-to-work trips commence during the time frame. This means that, on average, the time between 0700 and 0800 is the peak hour in Japan. Fifth, trip distances in 70.0% of home-to-work, 64.1% of business, and 75.0% of private trips are 20 km or less. Finally, the correlation between travel time and cost is in expressway trips. This is probably because the expressway toll is determined on the basis of route distance whereas travel time is highly dependent on trip distance. This may be one of the unavoidable characteristics of the RPbased dataset. 3

4 Table 1 Descriptive statistics of the sample dataset Home to work Business Private Obs. % Obs. % Obs. % Gender Male Female Job Agriculture Production/Transport Retailing/Service Office work/tech Others Age Departure Time Travel distance (km) METHODS Two methods are used for empirical analysis of VTTSs based on the above dataset: a standard binary logit model and a mixed binary logit model. Both of these are applied to expressway and no-expressway route choices. Binary Logit The utility functions of using the expressway and no-expressway routes are assumed to be V ex, n TTTTex, n TCTCex, n ex, n (1) TT (2) V no, n TT no, n no, n 4

5 where V i, n is the indirect utility function of an individual n who has chosen the route option i ; TT i, n is the travel time of route option i for individual n ; TC i, n is the travel cost of route option i for individual n ; i, n is the error component of route option i for individual n ; TT is the coefficient of travel time; and TC is the coefficient of travel cost. Route option i ex represents the expressway route, and i no the no-expressway route. As a linear utility function is assumed, the VTTS is derived as. The probability of choosing the route option i in the binary logit is shown as P i, n 1 1 exp V j, n V i, n TT TC (3). Then, the unknown coefficients are estimated by maximizing a log-likelihood with respect to as max LL max P (4) where i, n n i, ln i n i, n is equal to 1 if individual n chooses route option i and 0 otherwise. Mixed Binary Logit A mixed logit model can incorporate taste variation with a flexible substitution pattern in a standard logit model. The probabilities in a mixed logit model are formulated by the integral of the probability in a standard logit over a density of parameters (McFadden and Train, 2000; Train, 2003), Pi, n Li, n f d (5) where L i, n is the standard logit probability of equation (3) and f is a density function. We will use a mixed logit model assuming random coefficients. The function f is specified to be continuous; in particular, the density of is normal and triangular. The choice probability under this assumption is expressed as Pi, n Li, n d (6) where is a density function with parameters. The unknown parameters are estimated by maximizing the log-likelihood function with respect to : max LL maxi, n ln Pi, n (7). n i The value of P, is simulated by sampling over and is given by i n SP R 1 i, n, R r1 Lni r (8) where R is the number of random draws r, which is taken from the distribution function of. Finally, is computed as the solution of the simulated log-likelihood maximization problem as max SLL max SP (9). n i i n, ln i, n Although the Monte-Carlo method could be utilized to simulate choice probability, its slow convergence rate is a drawback. Quasi Monte-Carlo approaches have been attempted to speed up convergence by a more selective approach in the choice of sampling points to evaluate 5

6 choice probability. Then, instead of Monte-Carlo random draws, we apply Halton draws following Bhat (2001), using 125 draws as in Cirillo and Axhausen (2006). Weighted Likelihood Maximization The weighted likelihood maximization procedure is used for parameter estimation because the sampling rate varies among zones in the survey. Let n m be a respondent whose vehicle is registered at zone m. The weight of the individual, n m, is defined as follows: H m n m N (10) m 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 maximization of the log-likelihood function in the binary logit and the mixed binary logit is respectively redefined as W max LL P (11) RESULTS nm i nm i nm, ln i, nm W max SLL n i, n ln SPi, n (12). nm i m m m VTTS Estimation by Traveler Attributes versus Travel Purpose Table 2 shows estimation results based on the standard binary logit, originally shown in Kato et al. (2011). The summaries of results are as follows: First, personal VTTSs of home-to-work, business, and private trips are estimated to be 24.5, 33.9, and 21.0 JPY per min per person, respectively. The estimated personal VTTS of business trips is nearly equal to or a little lower than the average wage rate in Japan. Second, the personal VTTS of males is a little higher than that of females. Third, the estimated personal VTTS when driving alone is equal to 26.6 JPY per min per person while the estimated average personal VTTS when driving with passengers is equal to 15.4 JPY per min per person. The difference between the driver s and the passengers VTTS is probably due to the fact that the driver experiences less fatigue from driving time saved while passengers will not since they do not drive the car. Fourth, the personal VTTS of production/transport workers is apparently lower than the estimated personal VTTSs of other jobs. Fifth, the estimated personal VTTS of individuals in their twenties is the lowest among all age groups and is followed by that of individuals in their sixties. Sixth, the estimated personal VTTS of trips starting between 0800 and 0859 is the highest in a day, followed by that of trips between 0700 and 0759 and between 0900 and VTTSs between 0700 and 0959 are higher because traffic congestion is serious during the morning peak hours. Finally, the longer the travel distance, the higher is the estimated personal VTTS. 6

7 Table 2 Estimation results by travel purpose, gender, passenger, job, age, departure time, and travel distance based on the standard logit model Num of Ave. pax. VTTS per Travel time Travel cost Initial LL Final LL obs. per car person Coeff. T stat. Coeff. T stat. JPY/min Travel purpose Home to work Business Private Gender Male Female Passengers Drive alone Drive with passenger(s) Job Agriculture Production/Transport Retailing/Service Office work/tech Others Age Departure time Travel distance (km) Source: Kato et al. (2011) 7

8 Table 3 Estimated VTTSs of individual attribute subgroups categorized by travel purpose (JPY/min per person) Home to work Business Private Gender Male 24.4 (25.3) 34.1 (38.6) 21.4 (33.6) Female 23.8 (24.6) 29.4 (33.5) 19.5 (28.3) Passengers Drive alone 25.0 (25.0) 37.3 (37.3) 28.4 (28.4) Drive with passenger(s) 14.1 (32.5) 19.8 (45.5) 15.2 (35.9) Job Agriculture 24.9 (26.3) 20.5 (33.5) 24.9 (26.3) Production/Transport 20.3 (20.6) 32.2 (36.7) 20.6 (30.4) Retailing/Service 24.7 (25.6) 34.9 (38.7) 23.5 (35.4) Office work/tech (26.3) 36.4 (41.4) 22.4 (32.7) Others 25.8 (27.1) 29.4 (34.0) 21.5 (32.3) Age (19.7) 19.8 (34.4) 17.2 (26.5) (26.2) 32.9 (38.0) 18.5 (31.8) (27.4) 34.1 (38.3) 22.0 (31.8) (25.3) 34.8 (39.1) 24.4 (34.6) (24.1) 33.2 (37.5) 21.4 (33.1) Departure time (23.1) 35.3 (44.2) 28.7 (43.6) Travel distance (km) (25.7) 37.8 (44.5) 26.7 (40.0) (27.0) 35.8 (42.2) 24.0 (35.6) (26.4) 36.2 (39.9) 20.9 (32.4) (31.8) 31.6 (34.9) 20.4 (31.6) (27.2) 39.0 (42.9) 16.2 (25.5) (23.7) 30.3 (34.2) 19.7 (30.1) (29.0) 27.3 (31.6) 19.9 (29.0) (25.3) 38.8 (45.9) 18.7 (27.4) (14.4) 25.7 (28.7) 7.3 (10.6) (13.7) 15.6 (17.4) 9.4 (13.8) (16.5) 14.4 (16.1) 11.5 (17.7) (21.2) 27.2 (30.8) 13.7 (23.0) (23.9) 31.5 (36.9) 15.3 (27.4) (33.6) 36.0 (44.3) 18.3 (33.5) (35.2) 47.9 (60.0) 21.3 (41.1) (42.2) 46.9 (56.2) 21.5 (43.1) Note: Values in parentheses are estimated VTTSs per vehicle. This study examines the characteristics of VTTSs in more detail with the standard logit model using the same dataset. Table 3 shows the estimated VTTSs of individual attribute subgroups categorized by travel purpose. First, the estimated personal VTTSs for home-to-work, business, and private trips are 24.4, 34.1, and 21.4 JPY per min per person, respectively, for males and 23.8, 29.4, and 19.5 JPY per min per person, respectively, for females. Personal VTTSs for business and home-to-work trips are, respectively, about 16% and 2.5% higher for males. The difference for business VTTSs reflects the wage rate difference between males and females in Japan. The lower difference for home-to-work VTTS is probably because both male and female commuters experience the same disutility with respect to travel time, such as traffic congestion during 8

9 morning peak hours, and the same arrival time constraint in home-to-work trips; thus, these factors influence the VTTS more than the wage rate does. Second, the estimated personal VTTSs of home-to-work, business, and private trips are 25.0, 37.3, and 28.4 JPY per min per person, respectively, for driving alone and 14.1, 19.8, and 15.2 JPY per min per person, respectively, for driving with passengers. Personal VTTSs of driving with passengers are lower than those of driving alone by 43.6%, 46.9%, and 46.5% for home-to-work, business, and private trips, respectively. These figures may mean that the personal VTTS ratio of driving with passengers to driving alone is not much affected by travel purpose. These results may also show that the ratio of VTTSs of car passenger to that of drivers is much lower than that of other studies such as Fosgerau et al. (2007) showing that the value of travel time is 20% to 35% lower for a car passenger than the car driver. Third, the personal VTTSs for business trips in production/transport, retailing/service, office work/technology, and others are higher than those for other travel purposes in the corresponding type of job. In agriculture, the personal VTTS for business trips is lower than those for other travel purposes. These differences may reflect the number of passengers in a car. In business trips, the average number of passengers, including the driver, is 1.63 for agriculture and 1.14 for production/transport, 1.11 for retailing/service, 1.14 for office work/technology, and 1.16 for others. Our results suggest generally that the more passengers, the lower the average personal VTTS. Fourth, among different age subgroups, business and private personal VTTSs are highest for individuals in their fifties, followed by those in their forties. This reflects the fact that people in their forties and fifties have a higher wage rate than others. Home-to-work personal VTTS is highest for those in their forties, followed by those in their thirties. One of the possible reasons is that workers in their thirties and forties are middle-level managers, such as a subchief or vice manager working under a manager, who are strictly required to arrive at the workplace before the given start time of work; this leads to higher willingness-to-pay for saving commuting time. In the Japanese labor market, people in their twenties are less responsible in their commuting behavior, while those in their fifties or older are managers with more flexible commuting options. Fifth, the relationships between departure time and estimated personal VTTS may not be well characterized. The estimated home-to-work personal VTTS is highest for trips starting between 1000 and 1059, probably because individuals with higher income, such as managers and employers, tend to commute after the morning peak hours. Trips commencing between 1800 and 1959 yield the second highest VTTS in this category, perhaps because those who work in the evening and night hours tend to have a higher wage rate than daytime workers. The estimated personal VTTS is highest for business trips starting between 1100 and A possible reason is that the most valuable business activities are typically implemented just after lunchtime and many businesspersons commence their business trips before lunch for after-lunch business activities. The 1100 to 2359 time slot follows, with the second highest VTTS for business trips, probably because those who work in the evening tend to have a higher wage rate than daytime workers. Finally, the estimated personal VTTS for private trips 9

10 starting between 0000 and 0659 is the highest in a day, followed by those between 0700 and This may reflect the fact that leisure trips commencing early in the morning have a higher value than those starting at other times because individuals can enjoy longer leisure time in a day. Sixth, the estimated personal VTTSs of home-to-work and private trips increase with travel distance. For business trips, however, they decline from 0 to 30 km but increase from 30 to 100 km as the travel distance increases. The different characteristics of urban and inter-urban trips may account for business trips U-shaped VTTS over travel distance. The marginal utility with respect to travel time may decrease as travel time increases in urban business trips in which the time constraint is not very serious. However, the marginal utility starts increasing when the travel time is longer because less time is allocated to leisure activities, which results in higher marginal utility of leisure time in a condition of declining marginal utility with respect to the leisure time. However, as similar results have not been reported so far in other countries, we are afraid the estimated VTTS for business trips of less than 10 km might be an anomaly. Finally, we calculate the distance elasticities of VTTS with the estimated results using the equation VTTS DIST (13) where VTTS is the personal VTTS (JPY/min) and DIST the travel distance (km). The representative distances of the travel distance subgroups are the means of subgroup bandwidths: 5, 15, 25, 35, 45, 55, 65, and 80 km. Figure 2 shows regression curves of the estimated VTTS distributions versus distance by travel purpose. The figure shows that Figure 2 Travel distance vs. estimated personal VTTSs by travel purpose 10

11 distance elasticities of VTTS are estimated to be 0.36 for all travel purposes, 0.39 for hometo-work trips, 0.77 for business trips, and 0.41 for private trips. Note that VTTS estimates for trips of 10 km or less are eliminated from business VTTS estimation for the reason mentioned earlier. Thus, the results imply that the distance elasticity of inter-urban business trips is much higher than that of other trips. From meta-regression analysis in the UK, VTTS distance elasticity is estimated to be 0.08 for leisure trips and 0.45 for business trips (Abrantes and Wardman, 2011). By comparison, our distance elasticity based on RP data is slightly higher. One of the possible reasons is that our estimation does not include fuel cost in travel cost data. Longer-distance travelers tend to prefer the expressway route partly because the average fuel cost is lower fuel is consumed more efficiently in the expressway than in the no-expressway route. This means the difference between the actual expressway and no-expressway route costs, where both expressway charge and fuel cost are considered, is smaller than the calculated cost difference, in which only the expressway charge is reflected. Thus, the estimated willingness-to-pay may be a little biased, and larger than the actual willingness-topay. As incorporating fuel cost in the route-choice model could require additional data such as fuel consumption by travel speed, by acceleration/deceleration pattern, and by vehicle type, it may be quite difficult to do so. Thus we have identified this issue as a topic for further research. Estimated VTTSs for Peak and Off-peak Hours People who travel in congested road networks expectedly experience unreliable travel times. A number of recent studies have analyzed the reliability of transportation services. Two different approaches have been proposed to model travel-time variability effects so as to allow for economic analysis (Hollander, 2006). The first approach is the mean-variance approach, in which it is assumed that travelers see travel-time variance as a direct source of inconvenience (e.g., Jackson and Jucker, 1982; Senna, 1994). The second approach is the scheduling approach, which considers that the entire utility attributed to travel-time variation can be captured by modeling travelers earliness and lateness considerations when choosing the time at which they depart for their journey (e.g., Bates et al., 1995; Small et al., 1999). Although these studies highlight travel-time variability in their modeling approach, the value of reliability may be captured in a more simple way, by a comparison of VTTSs under reliable versus unreliable conditions. Accordingly, this study simply compares estimated VTTSs of trips made during congested versus less congested hours. The original dataset of the 2005 Road Traffic Census Survey contains peak-hour and off-peak-hour travel data. Peak hours implies that the departure time is in peak hours of the day, while off-peak hours mean the departure is during off-peak hours. Peak hour is defined as hours in which the traffic volume in an origin zone of a road network is the highest in a day. Table 4 summarizes the estimated VTTSs in peak and off-peak hours by travel purpose based on the peak/off-peak VTTS ratio. This shows that the estimated personal VTTS of trips starting during the peak hours is higher than that of trips during off-peak hours by 21.9% for all travel purposes, 9.5% for home-to-work trips, 13.3% for business trips, and 13.8% for private trips. These differences are caused mainly by the unreliability of travel time in congested traffic. Calfee et al. (2001) found that VTTSs in congested traffic are valued 200% 11

12 higher than in free-flow conditions whereas Abay et al. (2003) found the time values in congested traffic to be only 25% higher. Wardman and Ibanez (2012) show evidences of the congestion multiplier in the UK and the US. The preferred time relatives are 1.14 for busy, 1.23 for light congestion, 1.31 for heavy congestion, 1.45 for stop-start, and 1.78 for gridlock in the UK, whereas they are 1.02 for busy, 1.05 for light congestion, 1.21 for heavy congestion, 1.43 for stop-start, and 1.60 for gridlock in the US. As exact peak hour traffic conditions are not available in our database, our results cannot be directly compared with UK and US results. Table 4 Estimated peak/off-peak VTTSs per person by travel purpose (JPY/min) All Home to work Business Private purposes Off peak 21.9 (28.9) 23.1 (24.2) 32.3 (36.5) 20.3 (31.0) Peak 26.7 (29.7) 25.3 (26.1) 36.6 (41.8) 23.1 (35.2) Peak/Off peak ratio 1.22 (1.03) 1.10 (1.13) 1.13 (1.15) 1.14 (1.14) Note: Values in parentheses are estimated VTTSs per vehicle. Distributions of VTTSs Estimated with the Mixed Logit Model Table 5 shows the estimation results of route choice by travel purpose based on the mixed logit, incorporating random coefficients of utility functions. Two types of distributions (normal and triangular) plus fixed are applied to the coefficients of travel time and travel cost; thus a total of nine patterns of random coefficients models, including a standard logit model, are estimated for home-to-work, business, and private trips. First, the final log-likelihood (LL) is lowest in the standard logit (fixed-fixed) for all travel purposes; the final LLs in the mixed logit models are higher. This is reasonable because the mixed logit model with randomized coefficients could reflect taste variation among individuals more appropriately. Second, the coefficients of mean travel time and travel cost are estimated to be significantly negative in all models. The coefficients of variation are also significant in all models. Third, the estimated coefficients do not seem to differ very much among the models, except for the standard logit (fixed-fixed) model, in which the absolute values of coefficients are significantly lower than in other models. Fourth, among the hometo-work and business trip models, the triangular-triangular model has the highest final LL, followed by the normal-triangular model, and then the triangular-normal model. Among the models for private trips, the triangular-triangular model has the highest final LL, followed by the normal-triangular model and then the normal-normal model. These results indicate that models with a triangular distribution of coefficients tend to have a higher log-likelihood than other types. 12

13 Table 5 Estimation results based on the mixed logit model by travel purpose Travel time (mean) Travel cost (mean) Travel time (var.) Travel cost (var.) Dist. of TT Dist. of TC Coeff. t stat. Coeff. t stat. Coeff. t stat. Coeff. t stat. Final LL Home to work (N=82,068, Initial LL= 14212) Normal Normal Normal Triangular Normal Fixed n.b.d n.b.d 3952 Triangular Normal Triangular Triangular Triangular Fixed n.b.d n.b.d 3963 Fixed Normal n.b.d n.b.d Fixed Triangular n.b.d n.b.d Fixed Fixed n.b.d n.b.d n.b.d n.b.d 4503 Business (N=12,328, Initial LL= 2233) Normal Normal Normal Triangular Normal Fixed n.b.d n.b.d 1024 Triangular Normal Triangular Triangular Triangular Fixed n.b.d n.b.d 1025 Fixed Normal n.b.d n.b.d Fixed Triangular n.b.d n.b.d Fixed Fixed n.b.d n.b.d n.b.d n.b.d 1152 Private (N=51,621, Initial LL= 9868) Normal Normal Normal Triangular Normal Fixed n.b.d n.b.d 2785 Triangular Normal Triangular Triangular Triangular Fixed n.b.d n.b.d 2796 Fixed Normal n.b.d n.b.d Fixed Triangular n.b.d n.b.d Fixed Fixed n.b.d n.b.d n.b.d n.b.d 3357 Note: n.b.d means not available by definition. Then, using the estimation results shown in Table 5, distributions of VTTSs per vehicle are calculated by simulations (Hensher and Greene, 2003). From these distributions, we generate 50,000 draws of travel time and travel cost coefficients and calculate the ratios over the two values. Then, VTTS distributions over those draws are computed. The mean is also calculated based on the 50,000 draws after two percentiles, the highest and lowest, are removed from the VTTS distribution so most of the sample distribution is reflected, according to Cirillo and Axhausen (2006). Table 6 summarizes the distributions of coefficients and VTTSs per vehicle computed from the 50,000 random draws. Figures 3, 4, and 5 illustrate the distributions of VTTSs per vehicle for eight models of home-to-work, business, and private trips, respectively. First, over 75% of the computed coefficients of travel time and travel cost are non-positive for all models. The triangular-normal models have a significantly lower share of negative travel cost coefficients in the population; they produce a significantly higher share of negative VTTSs in the population, which leads to lower VTTS means for all travel purposes. 13

14 Second, 0% to about 25% of the VTTSs computed have negative values. VTTSs below or equal to zero account for, on average, a share of 9.1 for home-to-work, 12.0 for business, and 9.6 for private trip models. Although we had expected the share of negative VTTS for private trips to be higher than those for business and home-to-work trips, the share of private trips is the lowest among them. Third, the normal-normal models yield, on average, VTTSs of 17.2 JPY per min per vehicle for home-to-work, 28.5 JPY per min per vehicle for business, and 22.9 JPY per min per vehicle for private trips; travel time coefficients are negative for over 95% and travel cost coefficients for over 94% of the population for all travel purposes. VTTSs are zero or negative for 6.1% of the population for home-to-work, 9.5% for business, and 6.1% for private trips. These results are similar to those shown by earlier studies, including Cirillo and Axhausen (2006) showing 10% and Algers et al. (1998) indicating 11% of negative VTTSs in the population. Fourth, triangular-triangular models, which have the highest final LL among different distributions, produce an average VTTS of 16.2 JPY per min per vehicle for home-to-work, 27.6 JPY per min per vehicle for business, and 24.1 JPY per min per vehicle for private trips; travel time and travel cost coefficients are negative for over 94% of the population for all travel purposes. VTTSs are zero or negative for 6.9% of the population for home-to-work, 10.0% for business, and 8.2% for private trips. Finally, both the normal-normal and triangular-triangular models yield lower VTTS means than the fixed-fixed models for all travel purposes. The ratios of the average normal-normal model VTTS to the standard logit model VTTS are 0.68 for home-to-work, 0.75 for business, and 0.71 for private trips. The ratios of the average triangular-triangular model VTTS to the standard logit model VTTS are 0.64 for home-to-work, 0.73 for business, and 0.75 for private trips. 14

15 Table 6 Distributions of coefficients and VTTSs per vehicle computed from 50,000 random draws with the estimation results VTTS per vehicle: Distribution of VTTS per vehicle (JPY/min) Distribution of Distribution of Beta TT: below and Beta TC: below and below and including Beta TT Beta TC including zero (%) including zero (%) zero (%) 5% 25% Median 75% 95% Mean Home to work Normal Normal Normal Triangular Normal Fixed Triangular Normal Triangular Triangular Triangular Fixed Fixed Normal Fixed Triangular Fixed Fixed n.b.d. n.b.d. n.b.d. n.b.d. n.b.d Business Normal Normal Normal Triangular Normal Fixed Triangular Normal Triangular Triangular Triangular Fixed Fixed Normal Fixed Triangular Fixed Fixed n.b.d. n.b.d. n.b.d. n.b.d. n.b.d Private Normal Normal Normal Triangular Normal Fixed Triangular Normal Triangular Triangular Triangular Fixed Fixed Normal Fixed Triangular Fixed Fixed n.b.d. n.b.d. n.b.d. n.b.d. n.b.d Note: n.b.d means not available by definition. 15

16 VALUATION OF TRAVEL TIME SAVING WITH REVEALED PREFERENCE DATA IN Figure 3 Distributions of VTTSs per vehicle by combination of distributions of time and cost coefficients computed from 50,000 random draws (home-to-work trips) 13th WCTR, July 15-18, 2013 Rio de Janeiro, Brazil 16

17 Figure 4 Distributions of VTTSs per vehicle by combination of distributions of time and cost coefficients computed from 50,000 random draws (business trips) 17

18 VALUATION OF TRAVEL TIME SAVING WITH REVEALED PREFERENCE DATA IN Figure 5 Distributions of VTTSs per vehicle by combination of distributions of time and cost coefficients computed from 50,000 random draws (private trips) 13th WCTR, July 15-18, 2013 Rio de Janeiro, Brazil 18

19 CONCLUSIONS This paper presented the latest estimation results of the value of travel time savings for Japanese road users. It used RP travel data from the nationwide 2005 Road Traffic Census Survey of Japan. A standard binary logit and a mixed binary logit model were used in the context of an expressway versus no-expressway route choice for subgroups based on gender, number of passengers, type of job, age, departure time, and travel distance categorized into three travel purposes: home-to-work, business, and private. Distance elasticities of VTTS are also estimated. The mixed logit models assumed parametric distributions normal and triangular of travel time and cost coefficients. The results showed that the mean VTTSs produced from the estimated mixed logit models are lower than VTTSs estimated with the standard logit models for all travel purposes. Further research issues are as follows: First, this study applied the simplest form of linear utility function consisting of only travel time and cost, but factors other than travel time and travel cost may significantly influence VTTSs. Other types of utility functions incorporating individual attributes, as well as non-linear utility functions, should be explored. Second, this study used only normal and triangular distributions for travel time and cost coefficients in the mixed logit models. Model estimation with other types of distributions, such as censored logit and log-normal distributions, should also be tried. Third, a comparison between RP and SP data-based VTTS estimation may be valuable. Additionally, VTTS estimation could be updated using, for example, data from the 2010 Road Traffic Census Survey of Japan, which were not available at the time of this study. Thus, the temporal change in VTTS could be analyzed by a comparison of the 2005 and 2010 estimates. ACKNOWLEDGEMENTS This study 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 Professor Takayuki Ueda (University of Tokyo), Professor Kazusei Kato (Nihon University), Professor Masayoshi Tanishita (Chuo University), Dr. Yuichi Mohri (Institute of Behavioral Science), and Mr. Katsumi Uesaka (MLIT, Japan) for their support. We are also grateful to Mr. Tetsuya Tsujima (University of Tokyo), who performed the analysis of the mixed logit models. REFERENCES: Algers, S., Bergstrom, P., Dahleberg, M., and Lindqvist, D.J. (1998) Mixed logit estimation of the value of travel time, Working Paper, 1998:15, Department of Economics, University of Uppsala, Uppsala. Abrantes, P.A.L. and Wardman, M.R. (2011) Meta-analysis of UK values of travel time: An update, Transportation Research Part A, Vol.45, pp

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