Over-reporting vs. overreacting: Commuters’ perceptions of travel times

Transportation Research Part A 69 (2014) 476–494

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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra

Over-reporting vs. overreacting: Commuters’ perceptions of travel times Stefanie Peer a,c,⇑, Jasper Knockaert a, Paul Koster a,b, Erik T. Verhoef a,b a

Department of Spatial Economics, VU University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands Tinbergen Institute, Gustav Mahlerplein 117, 1082 MS Amsterdam, The Netherlands c Institute for the Environment and Regional Development, Vienna University of Economics and Business, Welthandelsplatz 1, 1020 Vienna, Austria b

a r t i c l e

i n f o

Article history: Received 16 August 2013 Received in revised form 27 May 2014 Accepted 14 July 2014 Available online 6 September 2014 Keywords: Travel time perception Reported travel times Valuation of travel time Scheduling choices Panel latent class models SP & RP data

a b s t r a c t In a large-scale, real-life peak avoidance experiment, we asked participants to provide estimates of their average in-vehicle travel time during their morning commute. After comparing the reported travel times with the actual corresponding travel times, we found that the average travel times were overstated by a factor of 1.5. We showed that driverand link-specific characteristics partially explained these exaggerations. Using the stated and revealed preference data, we investigated whether the driver-specific reporting errors were consistent with the drivers’ scheduling behaviors in reality and in hypothetical choice experiments. In both cases, we found no robust evidence that drivers behave as if they misperceive travel times to a similar extent as those they misreported, thereby implying that the reported travel times did not represent the actual or perceived travel times in a truthful manner. The results of this study suggest that caution should be recommended when reported travel time data are used in an uncritical manner during transport research and when determining policy. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Reported travel times are used mainly in situations where it is difficult, expensive, or even impossible to measure travel times directly. In these situations, the reported travel times usually act as a substitute for the actual travel times. Moreover, in the spirit of the literature on time perception,1 reported travel times are sometimes used as an indicator of perceived travel times. Clearly, these two ways of using and interpreting reported travel times rely on different assumptions. In the first case, the reported and actual travel times are assumed to be equal, whereas the reported and perceived travel times are assumed to be equal in the second case. In this study, we investigated the validity of these assumptions and we give recommendations regarding the usage of reported travel time data. Previous studies suggest that reported travel times are not an appropriate indicator of actual travel times. Most found that individuals substantially overstated their travel times (e.g. O’Farrell and Markham, 1974; Burnett, 1978; Henley et al., 1981; MVA Consultancy, 1987; Rietveld et al., 1999; Van Exel and Rietveld, 2009). Based on this evidence, they typically concluded that travel times are perceived as longer than the actual times. Thus, they interpreted the reported travel times as perceived

⇑ Corresponding author at: Institute for the Environment and Regional Development, Vienna University of Economics and Business, Welthandelsplatz 1, 1020 Vienna, Austria.. E-mail address: [email protected] (S. Peer). 1 For example, see Grondin (2010) for a recent overview. http://dx.doi.org/10.1016/j.tra.2014.07.005 0965-8564/Ó 2014 Elsevier Ltd. All rights reserved.

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travel times. Only a few studies have considered reporting errors (e.g. Van Exel and Rietveld, 2009) or the possibility that actual travel times might have been measured incorrectly (e.g. Rietveld et al., 1999) as plausible explanations for the overstated travel times. In agreement with the results obtained in previous studies, we also found that travel times were exaggerated greatly, i.e., by a factor of 1.5 on average. The implications of exaggeration for the usage of reported travel time data depend strongly on whether overstatement is a consequence of reporting errors, or whether travelers indeed perceive their travel times as longer than they actually are. In the first case, the main conclusion is that reported travel times are untrustworthy, so they should not be used as a representation of travel times. Therefore, this would demand further research into improved methods of data collection. If the second case is appropriate, misperceptions would be expected to affect the actual and hypothetical travel decisions in situations where the travel times differ between alternatives. Brownstone and Small (2005) speculated that this may lead to biased estimates of the value of travel time (VOT)2 if the VOT is derived from stated preference data. VOT is a core parameter used for the evaluation of transport policies. For example, Hensher (2001) estimated the benefits (or costs) attributable to changes in travel times as 60% of the total user benefits. The VOT is usually derived from stated preference (SP) or revealed preference (RP) data, which differ according to the characteristics of the underlying choice situations, i.e., SP data are collected from choice experiments where the respondents are asked to decide between hypothetical travel alternatives, whereas RP data are collected from real-life choice situations. Brownstone and Small (2005) argued that if travel times are perceived as longer than they actually are, it is likely that travelers will react to the stated travel times as if they were overstated in an SP setting. This means that their response to the time difference stated in an SP experiment would correspond to how they may respond to a relatively smaller time difference in reality. Therefore, deriving the VOT based on the observed SP choices would yield a relatively low estimate of the VOT. For example, an individual who perceives a real travel time of 10 min as 20 min will probably react to a stated travel time of 20 min in an SP setting in the same manner as he would react to a travel time of 10 min in reality; thus, the VOT derived in the SP setting would be half of the VOT that would be derived if RP data3 were analyzed. Thus, substantial biases can arise if the SP-based VOT is then used to appraise transport policies and it is applied to obtain objective measures of changes in travel times, simply because the benefits from travel time gains comprise a major category during the appraisal of most transport policies. In agreement with the hypothesis of Brownstone and Small (2005), previous studies frequently report that RP-based estimates of the VOT are higher than SP-based estimates (e.g. Ghosh, 2001; Hensher, 2001; Brownstone and Small, 2005; Small et al., 2005; Isacsson, 2007). However, other theories have been proposed in addition to the well-supported hypothesis that drivers misperceive travel times. Most of these can be categorized as ‘hypothetical biases,’ which arise if people behave differently in an SP setting compared with an RP setting (e.g. see Louviere et al. (2000) and Carlsson (2010) for overviews). In particular, it has been speculated that people are more sensitive to monetary attributes in hypothetical choice situations than real life. More specifically, Brownstone and Small (2005) argued that such an increase in sensitivity might be caused by time inconsistencies in actual behavior (e.g. by failing to plan departure times so the reward is obtained) that are not considered in hypothetical scheduling choices. Recent research shows that the occurrence of hypothetical biases can be reduced by providing choice options to the respondents that closely resemble the choices they face in real life (e.g. Hensher, 2010). In this study, we first analyzed the reported versus actual travel times. As mentioned earlier, we detected a clear tendency for travelers to exaggerate their travel times. Various specifications of ‘travel time ratios’ were computed, which represented the ratios of the reported travel times relative to the actual travel times. We tested whether the travel time ratios could be explained by driver- and link-specific characteristics. In addition, the variation in the travel time ratios across individual drivers was used to investigate whether drivers misperceived travel times in their SP and RP travel choices to the same extent as they misreported them. If this is not the case, we must conclude that reported travel times are not an appropriate representation of actual or perceived travel times, but instead they are subject to substantial reporting errors that have a systematic upward bias. The possible causes of these reporting errors include strategic behavior, social desirability biases, inaccurate recall, or a misunderstanding of the reporting task. All of the data used in this study were collected during a real-life peak avoidance experiment, which was conducted in the Netherlands for a period of 4 months. The study included approximately 2000 participants who received a monetary reward for not using a specific highway link during morning peak hours. Their actual travel behavior was monitored on the highway link using cameras that were capable of number plate detection. In addition to these RP data, the reported travel times were collected via a questionnaire and an SP experiment was conducted with the same set of drivers. The observed behaviors were measured directly along the highway link to allocate the rewards, whereas the specific day and time of day door-to-door travel times were approximated using the method described in Peer et al. (2013). This model combined speed measurements obtained from loop detectors along the highway and GPS-based speed measurements derived from links using geographically-weighted regression when no continuous speed measurements were available. This real-life experiment provided a

2 Recent meta-analyses of relevant empirical research on the value of (travel) time (VOT) can be found in Zamparini and Reggiani (2007), Small and Verhoef (2007), Shires and De Jong (2009), and Abrantes and Wardman (2011). 3 If the VOT is derived from RP data, travel time misperceptions generally do not induce biased estimates of the VOT, provided that the model estimates objective rather than subjective travel time measurements to define the travel time attributes of the choice alternatives. If objective travel time measurements are used, the estimated hourly VOT represents the travelers’ willingness to pay for a reduction of 1 h in the objective travel time, which is the relevant measure used in policy appraisals. Indeed, changes in travel times related to policy interventions are almost always predicted in objective terms, e.g. from traffic assignment models.

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unique opportunity to compare the reported and actual travel times on a door-to-door basis, as well as testing whether their differences also manifested themselves in real-world and hypothetical travel choice behavior. The remainder of this paper is organized as follows. Section 2 reviews previous studies of (travel) time perception and it highlights the contribution of the present study. Section 3 describes the peak avoidance experiment and the travel time data used in this study. Section 4 introduces the travel ratio. Section 5 discusses the theoretical framework that allowed us to test whether the observed real-life and hypothetical scheduling choices were consistent with the reported travel times. Section 6 gives an overview of the SP and RP data used in the analysis. Section 7 presents the econometric framework and the results estimated by the choice models. Section 8 concludes by considering whether the reported travel time data may be used as representations of actual and/or perceived travel times. Finally, the appendix provides an overview of the relevant variables and the abbreviations used in the main text.

2. Related studies of (travel) time perception To the best of our knowledge, this is the first study to investigate the difference between reported and actual travel times (reporting errors), as well as between reported and perceived travel times (perception errors), using actual and reported travel times, as well as SP and RP travel choices from the same set of travelers. However, related research was conducted by Ghosh (2001) who tested whether reported travel times can explain travel behavior to a greater extent than that explained by the actual travel times. Some evidence was presented to show that the difference between reported and actual travel times had explanatory power, but it was also shown that the VOT changed little when this difference term was included in the choice model. Only RP data were used in this previous analysis of travel time misperceptions Ghosh (2001), whereas we also use SP data. The latter allowed us to test the hypothesis proposed by Brownstone and Small (2005), thereby providing a possible explanation why SP estimates of the VOT often diverge greatly from their RP counterparts. Other studies in the area of transport economics have attempted to analyze travel time misperceptions. For example, Brownstone and Small (2005) speculated that the common finding that the VOT is higher under congested and slow traffic conditions (e.g. Recarte and Nunes, 1996; Wardman, 2001; Hensher, 2001; Zhang et al., 2005; Wardman and Nicolás Ibáñez, 2012) might indicate that the time spent in these traffic conditions may appear to pass more slowly due to the annoyance of heavy traffic. However, a definite conclusion on this subject is difficult to obtain because perceived and evaluated travel times are hard to disentangle if only the travel choices and actual travel times are known. We aimed to circumvent this problem by considering reported travel times and explicitly testing whether they reflected travel time perceptions. In our analysis of travel choice behavior, we emphasize the role of departure time decisions. Given that peak hour congestion poses a major problem in most urban areas, scheduling models have attracted increasing interest over the last few decades because they can provide insights into how transport policies affect departure time choices, and thus peak congestion as a whole (e.g. Vickrey, 1969; Small, 1982; Noland and Small, 1995). Empirically, departure time decisions are usually represented as choices between discrete departure time alternatives. The relevant models are then estimated using discrete choice analysis (McFadden, 1974; Train, 2003). In addition to using standard multinomial logit (MNL) models, we also employed panel latent class models, which can consider the unobserved heterogeneity between individuals as well as the panel nature of the underlying data. We estimated separate models based on the SP and RP data, but we also produced models that combined these two data sources. A few studies of travel choice behavior have been conducted using both data sources as inputs (e.g. Ghosh, 2001; Small et al., 2005; Brownstone and Small, 2005; Börjesson, 2008), whereas most use fairly simplistic travel time measurements in their RP models.4 By contrast, the estimated door-to-door travel times used in the present study allowed us to consider travel time stochasticity and specific driver, day, and time of day travel time expectations. The present study is also related to general research into time perception. Studies in this field generally assume that the reported and perceived durations are equal. This may be a reasonable assumption in controlled experimental conditions and for short time spans,5 but it is more questionable in situations where the analyst has less control over the experiment and where the durations are generally longer (as in the present study). Evidence about whether durations tend to be over- or under-estimated varies substantially among studies. The main consensus is that the perception of durations becomes increasingly inaccurate if the cognitive load is high during the time interval under consideration, possibly because fewer mental resources are available for ‘temporal processing’ (Block et al., 2010). This finding has been confirmed in the context of car travel (Baldauf et al., 2009). Another pattern relevant to travel is that familiar tasks (such as commuting) tend to be perceived as shorter (e.g. Boltz et al., 1998). However, this effect might be offset by another because it has been shown that activities that are not highly predictable, which holds true for most car trips, are perceived as longer than they are in reality (e.g. Boltz, 1998). In addition, the role of emotions is frequently highlighted. A main finding is that time passes more slowly in very stressful conditions (e.g. Droit-Volet and Meck, 2007). The evidence is more mixed in cases with very low mental arousal, i.e., some studies claim that time seems to pass faster in such situations (e.g. Block and Zakay, 1996), whereas others report the opposite (e.g. Flaherty, 1999; Glicksohn, 2001). Based on these findings, we must conclude that the literature on time perception does not provide unequivocal evidence about whether the travel time (specifically morning commutes) is expected to be perceived as passing more slowly or faster than it does in reality. 4 5

See Peer et al. (2013) for a discussion of possible biases related to imprecise travel time measurements. Some studies on time perception consider time intervals of only few seconds.

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S. Peer et al. / Transportation Research Part A 69 (2014) 476–494 Table 1 Descriptive statistics for the subset of participants used in the analysis. Variable

Value or fraction of sample

No. of individuals

443

Socio-economic characteristics Age <30 years >50 years Female Monthly (net) household income <3500 Euro >5000 Euro Unknown Households with children 0–5 years 6–10 years 11–15 years Commuting-related variables Preferred arrival time (PAT) <7:30 am >9:00 am

0.10 0.11 0.26 0.33 0.15 0.22 0.21 0.21 0.17

0.16 0.13

3. Data 3.1. Peak avoidance experiment All of the data used in this paper were collected during a peak avoidance experiment (Spitsmijden in Dutch). The experiment was performed in the Netherlands along a 9.21 km stretch of the A12 highway leading to The Hague. This link was bounded by two cameras (C1 and C2), which were used for number plate detection. Thus, we denote the start and end locations as C1 and C2, respectively. The entire experiment lasted for more than a year, but our analysis focused on the period between September 2009 and December 2009 due to better data availability. Approximately 2000 commuters participated in the experiment during that time period. Before participating in the experiment, we measured their average number of weekly trips through the C1–C2 link and defined this as their reference behavior. Between September and December, the participants received a reward of 4 Euros for each trip they avoided making along the C1–C2 link during the morning peak hours (6:30–9:30 am), compared with their reference behavior. A more detailed description of the experiment can be found in Knockaert et al. (2012). 3.2. Participants In this study, we only considered a subset that comprised 443 of the 2000 participants in the peak avoidance experiment, mainly because the reported travel times and preferred arrival times (PATs) at work were available for those who completed a specific questionnaire (ca 600). Moreover, we only considered the participants for whom sufficient data were available to approximate door-to-door travel times according to the method developed by Peer et al. (2013), which we describe in more detail below.6 Table 1 shows descriptive statistics for the 443 participants. The participants were mostly males aged 30–50 years and they tended to live in households with a relatively high net income (the average Dutch household disposable income was 2760 Euros/month in 20087). Moreover, Table 1 shows that the distribution of the PAT at work was strongly clustered between 7:30 and 9:00 am. 3.3. Reported travel times The main source of the reported travel times was an online questionnaire, which was completed by the participants of the peak avoidance experiment in November 2009. The response rate was approximately 30%. The reported travel times were based on the answers provided by the participants, who were asked to state their average travel times for three stages of their door-to-door trip: home–C1, C1–C2, and C2–work. Thus, the reported travel times were collected once only. In their answers, the respondents were asked to consider their 20 most recent morning commute trips. To prompt them to provide realistic answers, maps of the C1–C2 link were shown next to the questions. We also emphasized that only in-vehicle times should be reported. 6 The sample used for the choice models was smaller (406) because we also excluded drivers who stated that they made their choices randomly in the stated preference experiment, as well as those who indicated that their preferred arrival time at work was outside the peak hours. 7 URL: http://statline.cbs.nl/StatWeb/publication/?DM=SLNL&PA=71511ned&D1=a&D2=a&D3=0&D4=a&VW=T.

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We define the reported average home–work travel times as the sum of the average travel times given for each of the three sub-links. The reported travel times are denoted by T Rzl , where l indicates the link l = {Home–C1, C1–C2, C2–Work, Home– Work} and z ¼ 1; . . . ; Z indicates the participant. In addition to the above ‘standard’ definition of the reported travel time, we introduce an alternative measure that we used to investigate whether the ‘standard’ measure was biased because it was based on the sum of the travel times along the sub-links rather than the total home–work travel times. The alternative measure of the reported (home–work) travel times, denoted as the ‘total’, was derived from a survey conducted when the participants joined the experiment. They were asked to state their average home–work travel time, without distinguishing between sub-links. 3.4. Actual travel times Multiple data sources were used to define the actual travel times. The travel times through the C1–C2 link were observed directly and individually for each driver using number plate detection at the beginning and the end of the link. However, the home–C1 and C2–work travel times had to be approximated because no camera observations were available. The approximation method is described in detail in Peer et al. (2013). This method involved geographically weighted regression, which is used to measure the level of correlation between the speeds on the C1–C2, home–C1, and C2–work links. The speeds on the C1–C2 link were measured continuously by loop detectors, whereas a limited number of GPS-based speed measurements were available for the home–C1 and C2–work links. As a result, specific day and time of day travel times could be estimated for most combinations of the home and work locations in the dataset. Peer et al. (2013) demonstrated that this method yields reliable travel time predictions. The actual travel times are denoted by T Azld , where l denotes the link and z is the driver. Moreover, d ¼ 1; . . . ; Dz is the index attached to the observed passages of the C1–C2 link, where d ¼ 1 indicates the most recent trip before completing the survey, d ¼ 2 is the second most recent trip, while Dz denotes the overall number of observed passages between September 1, 2009 and the date driver z completed the questionnaire. Certain conditions had to be met before an observed passage was considered in this list of previous trips. In the ‘standard’ definition, passages on the C1–C2 link between 6:00 and 11:00 were considered to be commuting trips. In addition, we introduce an alternative definition of this time interval, which we used to test whether the ‘standard’ definition included an excessively broad peak, thereby leading to a downward bias in the actual travel times (because travel times tend to be shorter at the boundaries and outside the peak period) and thus to an upward bias in the travel time ratio. The alternative definition, which is denoted as ‘peak,’ only considered trips that resulted in a passage on the C1–C2 link between 6:30 and 9:30 am. This coincided with the interval when rewards were allocated in the experiment. When reporting the average travel times in the questionnaire, the participants were asked to consider their last 20 commuting trips. For 69% of the participants, over 20 commuting trips had been recorded before the date when the questionnaire was completed.8 For these participants, only the 20 most recent trips were considered in the analysis. For the remaining participants with 20 trips or less, we only considered the available observations. Thus, the average actual link- and driver-specific travel time T Azl is defined as:

T Azl ¼

1 min½20; Dz 

min½20;D X z

T Azld

ð1Þ

d¼1

4. Travel time ratio 4.1. Specification This section focuses on the computation of the driver- and link-specific travel time ratios.9 We define the travel time ratio szl as the ratio of the reported average travel time relative to the average actual travel time. Therefore, the travel time ratio exceeded 1 in all cases of overstatement, whereas it ranged between 0 and 1 for cases of understatement. The identical formulation was used by Parthasarathi et al. (2013) to compare reported and observed travel times.

szl ¼ T Rzl =T Azl

ð2Þ

Some studies of time perception used a power law function to control for nonlinearities in the relationship between reported and actual durations (e.g. Eisler et al., 2007). However, most found that the exponential term was close to 1, thereby implying that the nonlinearities were small (e.g. Eisler, 1976; Allan, 1979). Leiser and Stern (1988) obtained similar results for travel times, which suggests that the linear formulation performs almost as well as the power law function. We found some nonlinearities in our data (see the regression results in Table 4), but we did not employ a more complex specification because our main research interest was to use the travel time ratio as a simple input for departure time choice models. 8 9

The average number of trips observed was 33.7. Note that this ratio is also referred to as the duration judgment ratio in time perception studies (e.g. Block et al., 2010).

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S. Peer et al. / Transportation Research Part A 69 (2014) 476–494 Table 2 Reported vs. observed travel times (in minutes). Link

Label

Nr. obs.

Reported

szl

Observed

Mean

St. D.

Mean

St. D.

Mean

Median

St. Dev.

H–C1 C1–C2 C2–W

– – –

443 443 443

25:56 15:51 16:13

13:38 6:03 7:34

17:24 9:54 10:21

11:01 2:38 4:10

1.75 1.66 1.77

1.57 1.56 1.53

0.71 0.66 0.99

H–W H–W H–W

Stand. Total Peak

443 434 398

58:00 60:03 58:26

18:50 16:21 19:00

37:40 37:40 38:35

12:17 12:17 12:06

1.58 1.68 1.55

1.55 1.63 1.51

0.37 0.42 0.37

4.2. Descriptive statistics Table 2 provides the descriptive statistics for the reported and observed average travel times, as well as the travel time ratios. The two bottom lines of the table show the alternative measures for the reported (‘total’) and observed (‘peak only’) home–work travel times. In total, valid measures of reported and actual travel times according to the ‘standard’ definitions were derived for 443 respondents. Overstatement was found to be a persistent phenomenon for all the sub-links and according to all definitions of the travel time ratio, where the average ranged from 1.55 to 1.77 (the median was slightly lower: 1.51–1.63). The first three rows of Table 2 show that the average travel time ratio exceeded 1 on all sub-links, thus we rejected the hypothesis that (on average) drivers over-reported travel times only for some of the sub-links (e.g. those most affected by congestion) and that they compensated for this by understating travel times on the remaining links of the commute.10 A comparison of the ‘total’ definition of the travel time ratio with the ‘standard’ definition showed that the level of overstatement was even higher when drivers were asked for the total average home–work travel time rather than the average travel times on the sub-links (1.68 vs. 1.58). Thus, we conclude that the observed extent of overstatement for the ‘standard’ definition was not biased upward as a consequence of allowing participants to report their travel times for the three sub-links rather than for their home–work journey. Finally, we found that the travel time ratio for the ‘peak’ definition was almost as high as that for the ‘standard’ definition (1.55 vs. 1.58). Thus, the overstatement detected by the ‘standard’ definition cannot be attributed to an excessively broad definition of the morning peak. Therefore, we conclude that the ‘standard’ formulation of the travel time ratio was an appropriate representation of the extent of travel time overstatement, i.e., it did not differ substantially from alternative measures that were available.

4.3. Variation among participants and links The travel time ratio varied considerably among subjects, as shown in Fig. 1, where the histogram depicts the person-specific home-work travel time ratio based on the ‘standard’ definition. Only a few respondents had a travel time ratio of less than 1, thereby showing that they understated their travel times. The figure also shows that the distribution of the travel time ratio was slightly skewed to the right, with a median of 1.55, a mean of 1.58, and a few outliers toward the right-hand side of the distribution. We aimed to explain the variation in the travel time ratio among drivers and links by regressing the ‘standard’ travel time ratios on the driver- and link-specific characteristics. The descriptive statistics for the variables considered in these regressions are provided in Table 3. In addition, we also tested the significance of various socio-economic variables (age, gender, education, income, children, and flexibility of working hours), alternative measures of travel frequency (as a proxy for experience), measures of travel time variability (specifically percentile differences and standard deviations), the characteristics of the most recent trip, and person-specific outliers in terms of travel times. However, all of these variables were insignificant.11 No data were available for other variables that might have affected the travel time ratio, such as the road type or free-flow speed. The first model presented in Table 4 used the travel time ratios for the home-work link as the dependent variable, whereas the second model used the travel time ratios of the three sub-links. The former includes person-specific explanatory variables and variables that characterize home–work trips. In addition, the second model also considers variables defined at the level of the sub-links. A standard ordinary least squares (OLS) estimation was performed for Model 1. For Model 2, a random effects (RE) regression was used in order to account for the panel structure of the dataset because three sub-links were defined for each driver. The estimates yielded an R-squared value of 0.17 for the OLS and 0.28 for the RE model, thereby demonstrating that a considerable proportion of the travel time ratio could be explained by driver- and link-specific characteristics. The first 10 The finding that the average home-work travel time ratio was smaller than the corresponding travel time ratios on the sub-links was attributable to some outliers on the sub-links. 11 Our finding that the travel time ratio was independent of income differed from the result obtained by Burnett (1978), who concluded that individuals with low incomes overstated travel times more than others, possibly due to their lower education levels or less experience of traveling.

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S. Peer et al. / Transportation Research Part A 69 (2014) 476–494 90 80

Nr. of Observations

70 60 50 40 30 20 10 0 0.5

1

1.5

2

2.5

3

3.5

Travel time ratio (τ) Fig. 1. Histogram of the travel time ratio (Home–Work).

Table 3 Descriptive statistics of the variables considered in the regressions. Variable

Specification

Driver-specific variables No. of trips Proportion of trips outside the peak period

Within the last 20 working days Since September 1, 2009

Link- (& driver-) specific variables Mean speed home–work Mean speed home–C1 Mean speed C1–C2 Mean speed C2–work Distance home–work Distance home–C1 Distance C1–C2 Distance C2–work

in in in in in in in in

km/h km/h km/h km/h km km km km

Mean

St. Dev

5.08 0.20

3.68 0.29

69.63 72.93 66.96 63.06 43.30 22.88 9.21 11.21

11.29 17.36 13.71 11.70 17.13 15.92 – 4.86

Table 4 Regression results: explanation of the travel time ratio. Variable

Dependent Variable

sHome—Work

sHome—C1;C1—C2;C2—Work

Coefficient

t-stat.

Coefficient

t-stat.

Constant Little experience Proportion of trips outside peak period Mean speed home–work (MSHW) Distance home–work (DHW) Mean speed link/MSHW Distance link Distance link/DHW Dummy home–C1 Dummy C2–work

1.33 5:30  102 0.28 1:10  102 1:11  102 – – – – –

12.24 1.51 4.32 5.41 8.77 – – – – –

2.10 9:07  102 0.37 9:90  103 2:85  102 0.91 4:30  102 -4.47 0.36 0.18

9.38 1.97 4.29 3.67 11.08 5.76 7.31 14.70 6.49 4.09

Estimation method No. of observations R-squared

OLS 443 0.17

RE 1329 0.28

model shows that the home–work travel time ratio was relatively high for commuters with short commuting distances and high average speeds. In addition, we obtained some evidence that drivers with little commuting experience12 tended to overstate their travel times more, and that those with a relatively large proportion of trips outside the peak period13 tended to overstate travel their times less. These results were also confirmed at the link level. 12 This variable is defined as a dummy that assumes a value of 1 if a driver had made less than four trips since the start of the reward period in September 2009. 13 Peak trips are defined as trips that resulted in passages on the C1–C2 link between 6:30 and 9:30 am.

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The relatively high levels of travel time overstatement on the home–C1 and C2–work links might have occurred because the drivers also considered the time required to walk to and from their car to reach the office in their answers, although we asked them explicitly to only consider their in-vehicle commuting time. This effect was probably more common on the home–C1 and C2–work links, rather than on the intermediate C1–C2 link. The home–C1 and C2–work links were longer than the C1–C2 link (see Table 3), which may also explain why longer link lengths tended to be associated with a higher travel time ratio. Moreover, it is reasonable to assume that the time spent in ‘out of vehicle commuting’ was independent of the commuting distance, which might also explain the higher travel time ratios for shorter commutes. The travel times on sub-links with high speeds (relative to the average speed for this person) were possibly overstated to a greater extent because drivers knew the lengths of the sub-links (e.g. traffic signs were installed on the roads). Thus, when they were asked to indicate their travel times on the sub-links, they might have attributed their perceived total travel times to the sub-links more or less in proportion to their lengths, but without considering the differences in speed among the links. Based on a comparison of the actual and reported travel times, we could not reach any conclusions about the travel time perceptions because we had not investigated whether the reported travel times reflected the travel time perceptions. Thus, we could only conclude that some of the results obtained from the regressions were consistent with previous studies of (travel) time perception. For example, the drivers with little commuting experience overstated their travel times to a greater degree, which agreed with previous time perception research, where the duration of familiar tasks is typically perceived as shorter than that of an unfamiliar task (e.g. Boltz et al., 1998). Our findings were also consistent with previous studies of the relationship between mental arousal and time perception, i.e., the regression results supported the hypothesis that time is perceived as passing more slowly during periods with presumed low mental arousal, such as when speeds are high, so congestion and interruptions (e.g. due to traffic lights) are limited. By contrast, our finding that the travel time variation was insignificant contradicted previous studies, because related time perception research predicts a positive correlation between unpredictability and the perceived duration (e.g. Boltz, 1998). 5. Choice models: theoretical framework 5.1. Introduction This section introduces the theoretical framework used to test whether the differences between the reported and actual travel times influenced travel choices. We modeled travel choices using the scheduling model of Vickrey (1969), which was the first to define departure time decisions as a consequence of trade-offs between travel times and schedule delays, thereby characterizing the extent of earliness and lateness with respect to an exogenous PAT. This so-called ‘bottleneck model’ was later extended to theoretical (e.g. Arnott et al., 1993; Arnott et al., 1994) and empirical lines of research (e. g. Small, 1982: Noland and Small, 1995). Small (1982) was the first to estimate monetary valuations of travel time and schedule delays, while Noland and Small (1995) were the first to incorporate travel time variability in the scheduling model. In agreement with previous studies, our model assumes that commuters select their optimal departure time from home by trading off expected travel times (T), early (SDE) and late (SDL) schedule delays, and monetary trip costs (monetary rewards, R). The early and late schedule delays are defined by:

SDEðtÞ ¼ max½PAT  t  TðtÞ; 0

ð3Þ

SDLðtÞ ¼ max½t þ TðtÞ  PAT; 0;

where TðtÞ denotes the travel time associated with the departure time from home t. For simplicity, we omit the indices related to the individual z, choice alternative j (which is associated with the departure time t), and choice situation k. We allow for stochasticity in the travel times, which is made explicit using the expectation operator E with respect to the attribute values. The marginal utilities associated with the reward, travel time, and early and late schedule delays are denoted by bR ; bT ; bE , and bL , respectively. We assume an additive form of the expected utility function, as follows.

EVðtÞ ¼ bR  ERðtÞ þ bT  ETðtÞ þ bE  ESDEðtÞ þ bL  ESDLðtÞ

ð4Þ

The VOT and early (VSDE) and late (VSDL) schedule delays can be defined as (1) times the ratio of the time and schedule delay coefficients and the reward coefficient. The resulting values represent the willingness to pay for reducing the expected travel time and schedule delays:

VOT ¼ bT =bR

VSDE ¼ bE =bR

VSDL ¼ bL =bR :

ð5Þ

5.2. RP model The systematic part of the utility function associated with RP-based departure time choices includes the additive terms in EVðtÞ (see Eq. (4)). In the RP context, we denote the corresponding utility function by EV RP ðtÞ. In the model used to test whether the drivers behaved in real life as if the travel times they considered during their decision making were consistent with the person-specific travel time ratio, additional terms must be added to the utility function, which is then denoted by EV s;RP ðtÞ. For all four attributes, i.e., rewards, travel times, and early and late schedule delays, we must include the difference

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between the attribute of the choice alternative obtained if the drivers made a perception error consistent with their travel time ratio and the corresponding objectively measured attribute values. We compute these terms for all attributes because it is implausible that travelers would overestimate their travel times when considering the trip duration, but not when considering the other travel time-dependent attributes, notably schedule delays and rewards. Thus, a driver who overestimates the travel time is expected to underestimate early schedule delays and overestimate late schedule delays, and for a given departure time, this driver expects to arrive later than a person who departs at the same moment and does not overestimate the travel time. The coefficients that correspond to the difference terms and the attribute values generated if the travel times were misperceived according to the (individual-specific) travel time ratio are labeled with the superscript s.

EV s;RP ðtÞ ¼ bR  ERðtÞ þ bsR  ðERs ðtÞ  ERðtÞÞ þ bT  ETðtÞ þ bsT  ðET s ðtÞ  ETðtÞÞ þ bE  ESDEðtÞ þ bsE  ðESDEs ðtÞ  ESDEðtÞÞ þ bL  ESDLðtÞ þ bsL  ðESDLs ðtÞ  ESDLðtÞÞ

ð6Þ

The s-related coefficients are expected to be insignificant if drivers considered the objective attribute levels in their decision making rather than those attribute levels associated with overestimation (or underestimation in a few cases). By contrast, if bsR ; bsT ; bsE ; and bsL have the same sign and they are roughly equal in size to bR ; bT ; bE ; and bL , respectively, we can conclude that the behavior of the individuals in real life was consistent with the travel times they reported, particularly the differences in the reported and actual travel times. Thus, we could interpret the reported travel times as a valid indicator of the perceived travel time. 5.3. SP model In the SP model, we distinguish between EV SP ðtÞ and EV s;SP ðtÞ. The former includes the additive terms in EVðtÞ (Eq. (4)), whereas the latter also considers the difference between the travel time attribute generated if the travel times were affected by a perception error consistent with the (individual-specific) travel time ratio and the objectively measured travel time attribute. In contrast to the RP model, this difference term is only considered for the travel time attribute, but not for the reward and scheduling attributes. This is because the SP experiment incorporate rewards for the respondents as well as the actual arrival times at work .14 Therefore, it is unlikely that the respondents perceived the reward and the schedule delays differently from those presented to them, even if they misperceived the travel times.

EV s;SP ðtÞ ¼ bR  ERðtÞ þ bT  ETðtÞ þ bsT  ðET s ðtÞ  ETðtÞÞ þ bE  ESDEðtÞ þ bL  ESDLðtÞ s

ð7Þ s

The interpretation of bT is similar to its interpretation in the RP utility function, except we expect a positive bT in the case of overestimation (whereas bT is expected to be negative, as in all of the models). If the travel time is overestimated to a greater extent, the ‘real’ duration that corresponds to a stated amount of time X becomes smaller, and thus the impact of that amount of time X on the utility should become less negative (e.g. respondents with a travel time ratio of 1.5 are expected to react to a 15-min delay in an SP setting in the same way as they would react to a 10-min delay in reality). If this is true, the monetary value attached to the difference between the travel times multiplied by the travel time ratio and the objectively measured ones (i.e., VOTs ¼ bsT =bR ) would be negative, thereby reducing the overall value attached to the travel time (VOT þ VOTs ), as suggested by Brownstone and Small (2005). 6. Choice models: data 6.1. RP data RP data have the advantage that they are based on real choices rather than hypothetical ones. Therefore, they are exempt from the possible effects of hypothetical biases, which arise if people make different choices in a laboratory setting compared with real life. This is because RP data are usually more difficult and expensive to collect than SP data, and they be affected by strong correlations between the model variables. Moreover, the attribute values of RP choices and the choice set itself are often ambiguous, which makes them difficult to identify. Clearly, in RP studies, the ranges of the attribute values are limited to the values that exist in reality, thereby implying that responses to nonexistent alternatives (e.g. new transport modes) cannot be measured (e.g. Swait et al., 1994). RP data are defined in a similar manner to the actual travel times used to compute the travel time ratio. The main difference is that for the choice analysis, the attributes of the selected departure time alternatives as well as the unselected alternatives need to be known. Hence, for each departure time alternative j for driver z and choice situation k, the expected rewards, travel times, and schedule delays had to be derived. To estimate the door-to-door travel times, we used the model developed by Peer et al. (2013). We also used this model to approximate the selected departure time at the home location. These choice situations refer to days when the drivers were observed passing the C1–C2 link, where the reward experiment took place. Therefore, we defined the departure time choice as conditional on making a commute trip and passing the C1–C2 link, so the overall number of RP choice situations was driver-specific. The departure time was formulated as a discrete variable. The choice set comprised 17 distinct 15-min intervals during the morning peak (from 5:30 to 9:45 am). Departures 14

The exact setup of the SP experiment is discussed in Section 4.2 and it is shown in Fig. 2.

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observed outside this period were dropped. This is because trips that occurred outside this interval were likely to be undertaken for purposes other than regular commuting, so other scheduling preferences may have applied to them. The (person-specific) PAT for regular commuting trips was derived from the same questionnaire as the reported travel times. It is defined as the preferred moment of arrival at work if there is no congestion. Only drivers with a PAT between 6:30 and 9:30 am were considered because drivers with very early or late PATs rarely experienced any trade-offs between schedule delays and travel times. The rewards vary according to the time of day. The reward was 4 Euro if a driver passed C2 before 6:30 or C1 after 9:30, and 0 otherwise. Moreover, the maximum number of rewarded trips per two week period could not exceed the biweekly number of peak trips that a driver made before the start of the experiment.15 After the maximum number of rewards was obtained, no further rewards were distributed during the rest of the week. Holidays and weekends were excluded from the analysis, mainly because trips on these days were usually not commuting trips. Using the PAT, the rewards, and the specific driver, day, and time of day door-to-door travel times, and the attribute levels specific to the choice situation k, individual z, and choice alternative j could be derived. The expected levels of the attributes A 2 fR; T; SDE; SDLg; EA, were determined based on a compound measure of the actual, time of day-specific attribute levels on the day of travel, Azkj , and the time of day-specific average attribute levels, Azj over the duration of the experiment.16 The differences between Azkj and Azj were due exclusively to fluctuations in the travel times among days (for a given departure time). The actual travel times were actually unknown at the moment when the departure time decision was taken, but they represent an upper benchmark for the maximum extent of the information that was potentially available to drivers. The average travel times represented the long-term travel time patterns for the time of the day, which the experimental participants were unlikely to know. We estimated the weight h that drivers attached to the actual realizations based on the averages. h would have been equal to 0 if the travel time expectations were based only on the averages, but 1 if the drivers had perfect knowledge of the actual realizations and they did not consider the averages in their decisions. Thus, the expected attribute of the utility function for driver z, choice situation k, and choice alternative j; EAzkj was given as follows.

EAzkj ¼ h  Azkj þ ð1  hÞ  Azj

ð8Þ

Next, we used the ‘standard’ definition of the travel time ratio for the home–work link to compute the attribute values produced if the drivers had misperceived the travel times to an equal extent as they misreported them: EAszkj . To achieve this, we multiplied the actual time of day-specific and day-specific travel times for each of the sub-links (home–C1, C1–C2, C2–work) by the person-specific ‘standard’ travel time ratio.17 Based on the travel times obtained, we computed the corresponding rewards and schedule delays. We denote the resulting time of day-specific and day-specific attribute levels by Aszkj . By averaging Aszkj ¼ fRszkj ; T szkj ; SDEszkj ; and SDLszkj g over the relevant working days, we also obtained the remaining component, Aszj , of the compound attribute expectation measure EAszkj . We then computed EAszkj , as in Eq. (8).

EAszkj ¼ h  Aszkj þ ð1  hÞ  Aszj

ð9Þ

6.2. SP data Most SP experiments based on scheduling behavior ask the respondents to make hypothetical choices between alternatives with varying departure times, which may differ in terms of their costs, travel time, and travel time variability. Because the researcher determines the attribute levels, problems of collinearity between attribute levels can be avoided more easily in SP settings than RP settings. Furthermore, there is no ambiguity with respect to the attribute values and the definition of the choice set because both are provided to the respondents directly in the SP experiment. However, SP-based estimates may be affected by the attribute values presented to the respondents, as well as by the format and complexity of the choice task. Most importantly, they may be biased due to the hypothetical character of the choices (e.g. Swait et al., 1994). However, recent research has shown that these biases can be reduced by designing the SP experiments such that the realism of the choices and attribute levels is enhanced, e.g. by pivoting the design values around the status quo behavior of respondents (Hensher, 2010). This strategy was also used in our SP experiment. All of the travel times shown to the respondents in the SP experiment were designed so they were always situated between the minimum and maximum travel time reported by the driver, and the preferred arrival time shown to them was identical to their reported PAT. The SP choice experiment comprised 10 choices between two departure time alternatives. The travel time variability was considered by stating two possible travel time realizations for each departure time alternative, each of which occurred at random with a known probability. For a given departure time, the variation in the travel time also induces variations in the schedule delays, and in the reward in some cases. A reward of up to 8 Euros was available for passages on the C1–C2 15

The reference behavior was measured without the knowledge of the participants. Tseng et al. (2013) used a similar definition of the expected travel times. However, instead of applying the compound measure to all attributes of the utility function, they applied it only to travel times. 17 Note that we did not differentiate between the different magnitudes of the travel time ratio on the various sub-links, mainly because of outliers on the sublinks, which were less evident when considering the entire home–work trip. 16

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Fig. 2. Screenshot.

link between 6:30 and 9:30 am. To estimate the SP choice models, the attribute values of each alternative were defined as weighted averages across the two possible travel time realizations. Fig. 2 shows an example of the choice screen. After completing the choice experiment, the respondents were asked to indicate whether they answered some or all of the choice questions at random. Those who confirmed that they did (2% of the respondents) were excluded from the data. The efficiency of the choice experiment design was tested thoroughly using extensive simulations in order to ensure that a broad range of parameters could be reproduced (e.g. Koster and Tseng, 2010).18 A detailed description of the design of the SP experiment can be found in Knockaert et al. (2012). Finally, to compute the travel time attributes obtained if drivers had misperceived their travel times to the same extent as they misreported them, the travel times shown in the choice experiment were multiplied by the ‘standard’ definition of the person-specific travel time ratio for the home-work link. 7. Choice models: estimations 7.1. Econometric framework We estimated standard MNL models and more advanced panel latent class models that considered the heterogeneity between individuals as well as the panel nature of the data. We estimated separate MNL models for the SP and RP data, and a latent class model that pooled the two data sources. For notational convenience, this section introduces the pooled version of the models. In general, the underlying notion of a joint analysis of SP and RP data is that the SP data can correct for deficiencies in the RP data, such as correlations between attributes or the lack of identification of some attributes or attribute ranges, while retaining the inherent realism of the RP data (e.g. Louviere et al., 2000). The estimates of the pooled RP and SP data are most advantageous when the RP and SP choice situations are similar, and when they are also perceived in a similar manner by the participants (e.g. Börjesson, 2008). In that case, common coefficients may be possible for both the SP- and RP-based observations if individuals are found to react in consistent ways to trade-offs in the RP and SP choice situations. We defined the expected utility EU zkj as the utility associated with the choice situation k ¼ 1; . . . ; K z , individual z ¼ 1; . . . ; Z, and choice alternative j ¼ 1; . . . ; J zk . This comprised the systematic component defined in Eq. (4) (and in Eqs. (6) and (7) for the cases where the travel time ratio was considered) and a stochastic component zkj . The panel was unbalanced because the number of RP choices differed among drivers. In addition, the number of available alternatives, J zk , differed among the choices, i.e., 2 for SP choices and 17 for RP choices. The indicator function 1RP was used to distinguish between RP and SP choices, and thus the corresponding systematic parts of the utility function, i.e., 0 for SP choices (k 2 f1; . . . ; 10g) and 1 for RP choices (k 2 f11; . . . ; K z g). Moreover, any difference in the variance of the error term between SP and RP observations was considered by defining a multiplicative scale factor k, which was relevant for SP observations (the scale of the RP observations was fixed to 1).19 The random utility function to be maximized was then given as follows (note that EV RP zkj may be s;SP replaced by EV szkj;RP , and EV SP zkj by EV zkj , depending on the model that is estimated). RP SP EU zkj ¼ 1RP  EV RP zkj þ ð1  1 Þ  k  EV zkj þ zkj

ð10Þ

For the MNL models, the random component zkj was assumed to follow a Gumbel distribution, where the errors were assumed to be distributed identically and independently (iid) among observations. The parameter estimates obtained from the MNL models ignored the panel nature of the data, so we did not consider it during the computation of the standard errors using the panel specification of the sandwich estimator (e.g. Daly and Hess, 2011). The probability of driver z choosing alternative j 2 J zk in choice k; P zkj , was then defined as follows for the RP domain (an identical formulation holds for SP domain, where the superscripts differ accordingly). 18 19

Moreover, the layout and the phrasing were tested using focus groups and an online test. Differences in scale are only relevant if common coefficients for the SP and RP observations are estimated.

S. Peer et al. / Transportation Research Part A 69 (2014) 476–494

expðV RP Þ zkj Pzkj ¼ PJðzkÞ RP j¼1 exp V zkj

487

ð11Þ

The corresponding log-likelihood function is given below, which is conditional on the choices made by driver z in choice  zk to indicate the probability associated with the chosen alternatives. situation k. For simplicity, we use the notation of P

ln L ¼

Kz Z X X Pzk

ð12Þ

z¼1 k¼1

Moreover, we used a panel latent class model that allowed for heterogeneity among drivers and that considered the panel setup of the underlying data. The latent class models assumed that drivers could be sorted into a set of q ¼ 1; . . . ; Q classes. The preferences could then vary between the classes, which were assumed to be homogeneous within each class. Thus, some or all of the estimated coefficients could be class-specific. The term ‘latent’ is derived from the fact that heterogeneity is not observed by the analyst. The class membership probabilities and the size of each class were unknown in advance, and the analyst only had control over the number of classes Q. Thus, in addition to the (class-specific) coefficients, the driver-specific probabilities of being member of a specific class had to be estimated. According to the notation used by Greene and Hensher (2003), these are denoted by Hzq . Various formulations are possible for estimating class membership, but we employed a simple multinomial logit form (without additional explanatory variables20 other than a constant), which ensured that the relative class sizes summed up to 1. The log-likelihood function was then given by the following equation:

ln L ¼

Z X z¼1

"

Q Kz X Y  zkjq ln Hzq P q¼1

!# ;

ð13Þ

k¼1

 zkjq is equal to the probability associated with the alternative chosen by person z in choice situation k conditional on z where P Q z  P zkjq represents the probability of the sequence of choices being a member of class q. Therefore, the multiplicative term Kk¼1 k ¼ 1; . . . ; K z made by driver z, which is also conditional on class membership. In contrast to mixed logit models, which assume a continuous distribution for (some) parameters, latent class models do not require any assumptions regarding the shape of the distribution for a given parameter. Moreover, for a fairly small number of classes, it is usually not necessary to assume that specific coefficients are constant across classes, whereas this assumption is frequently made in mixed logit models in order to ensure the empirical identification of the models. 7.2. Estimation results: MNL models Table 5 shows the results obtained for the MNL models.21 The RP and SP data were not been pooled to produce this table. The first two models in Table 5 correspond to estimates of the standard scheduling model, while the third and the fourth models consider the travel time ratio using the specifications introduced in Eqs. (6) and (7) for the RP and SP departure time choices, respectively. All of the monetary valuations22 are given as Euros per hour. In contrast to most previous studies that compared RP- and SP-based valuations of travel time, we found that the VOT estimates derived from these two data sources for the standard scheduling model were fairly close.23 This result might be related to the design of the SP choice experiment because the choice situations presented to the respondents were personalized and they closely resembled those they faced in reality. However, it could also have been a coincidental finding that might disappear after the heterogeneity across drivers is considered. Thus, the results estimated for the panel latent class model (in the next section) provide insights into this issue. The finding that the VOT was relatively high in all models can probably be explained by the fact that participation in the peak avoidance experiment and the related questionnaire was voluntary, thus the sample was not selected randomly. The self-selection of participants generated a sample of individuals with fairly high household incomes (see Table 1), who were also likely to have a high VOT. Another possible explanation for the high VOTs may be that the travel time coefficient also incorporated the disutility from the travel time variability, which was strongly correlated with the travel time so it was not estimated separately. Moreover, the VOTs derived in this study were determined in the context of a reward experiment instead of the more common experimental setup where the monetary incentive is represented as a cost. In agreement with the concept of loss aversion, individuals may be more sensitive toward costs than rewards, thereby providing an explanation for low reward coefficients, which in turn leads to higher valuations. Finally, we considered fairly long trips (with an average duration of ca 37 min, see Table 2), which tended to be associated with a higher VOT (Daly and Carrasco, 2009). Nevertheless, given the similarity between the SP and RP estimates for the VOT and various (non-contradictory) possible explanations of the rather high valuations, the VOTs still appear to be trustworthy. Again, the results obtained with the panel latent class model (below) provide further insights into this issue. 20 We tested a panel latent class model where class membership was conditional on various socio-economic characteristics, but most of the corresponding coefficients were insignificant. This indicates that the between-class differences in the coefficient estimates are mainly due to unobserved heterogeneity. 21 All of the models were estimated using the Python BIOGEME software (Bierlaire, 2003). 22 The corresponding t-statistics were computed using the Delta method (e.g. Small, 2012). 23 Previous studies often show that they differ by a factor of 2 (where the RP-based VOT is typically higher than the SP-based VOT).

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Table 5 MNL models. Without

s

With

RP only

SP only

s

RP only

SP only

Coeff.

t-Stat.

Coeff.

t-Stat.

Coeff.

t-Stat.

Coeff.

t-Stat.

bR bT bE bL h

0.19 7.01 1.93 1.55 0.14

5.52 6.45 15.13 17.30 5.28

0.05 2.37 1.59 1.14 –

4.20 13.27 16.52 13.25 –

0.22 7.43 1.90 1.56 0.14

5.58 6.25 12.65 16.61 5.07

0.05 2.90 1.59 1.14 –

4.18 8.27 16.53 13.27 –

bsR bsT bsE bsL

– – – –

– – – –

– – – –

– – – –

0.05 – 1.60 1.74

1.21 – 1.41 1.50

– 0.79 – –

– 1.92 – –

VOT (Euro/h) VSDE (Euro/h) VSDL (Euro/h)

36.32 10.00 8.03

4.08 5.17 5.21

44.38 29.78 21.35

3.94 4.40 4.33

34.24 8.76 7.19

4.08 5.10 5.24

54.61 29.92 21.47

3.68 4.38 4.31

Nr. Obs. No. Individuals LogLik. Pseudo R2 adj.

8477 406 20,386 0.151

4060 406 -2223 0.208

8477 406 20,370 0.152

4060 406 -2220 0.209

In contrast to the valuation of travel time, the values of early and late schedule delays differed considerably, depending on whether RP or SP data were used. The VSDE and VSDL were significantly higher with the SP-based models than the RP-based models.24 It is possible that the hypothetical character of the SP choices made the scheduling restrictions appear more binding (and thus more costly) compared with their real-life counterparts. Similarly, in the SP environment, the participants may have assumed that they could re-schedule their activities in order to adapt to the delays, whereas they were not always able to do so in reality (thereby inducing relatively lower RP scheduling valuations). Furthermore, the higher SP scheduling valuations may also have been attributable to the explicit representation of travel time variability in the SP experiment. The fact that the random nature of schedule delays was stated explicitly may have induced respondents to attach more weight to schedule delays in their SP choices than they would have if the travel time variability had been expressed in a more implicit manner. Similarly, recent research by Peer et al. (forthcoming) has shown that unexpected delays are valued more highly than expected delays, possibly because re-scheduling becomes more difficult when delays are unexpected. In both the SP- and the RP-based standard scheduling models (without s), we found that earliness in terms of the PAT was more costly than lateness. This may have been because the participants with an early PAT experienced a larger disutility from switching to an even earlier departure time. Furthermore, with the RP-based models, we found that the weight of the actual travel time on the day of travel relative to the (time of day-specific) average travel time, h, was 0.14, regardless of whether the travel time ratio was considered or not. Thus, the travel time expectations were based mainly on long-term averages, although they were updated with day-specific information. We also tested the effect of including nonlinear terms for the travel time and scheduling attributes in the standard scheduling models. Some of these terms were significant, but we do not proceed with the nonlinear models because they made it difficult to test whether the travel time ratio affected choice behavior, especially when the travel time ratio was specified as a person-specific constant. For consistency, it would have been necessary to formulate the travel time ratio as a (possibly also nonlinear) function of the observed travel time. However, this would have been difficult because only a limited number of trips were observed for each participant. The third and fourth model presented in Table 5 considered the travel time ratios for the RP and SP data, respectively. In both models, we used the ‘standard’ (person-specific) definition for the travel time ratio from Table 2. As a robustness check, these models were re-estimated using the alternative definitions of the travel time ratio, but the results did not change significantly. Due to strong correlations in the attributes of the RP model when including the travel time ratio, we were not able to estimate the full model of Eq. (6). Instead, we omitted the ‘travel time ratio term’ for the travel time attribute. Even if these terms were significant for the remaining three attributes, we can still conclude that the reported travel times were a good representation of the drivers’ actual perceptions. However, from Table 5, we can see that this was not the case because all three coefficients were insignificant.25 Thus, we obtained no convincing evidence that drivers misperceived travel times to a similar extent because they over-reported (and in few cases under-reported) them when making their scheduling decisions in reality.

24

In general, previous studies found no clear pattern in the relationships between RP- and SP-based scheduling values (e.g. Tseng et al., 2005; Li et al., 2010). In agreement with this finding, the reverse model that considered only the travel time ratio term for travel times also did not yield a significant coefficient estimate for this term. 25

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S. Peer et al. / Transportation Research Part A 69 (2014) 476–494 Table 6 Estimation results with truncated travel time ratios s. Trunc.

Data

No. Obs.

2 1.5 2 1.5

RP RP SP SP

7697 3820 3580 1810

bsR

bsT

bsE

bsL

Coeff.

t-Stat.

Coeff.

t-Stat.

t-Stat.

t-Stat.

Coeff.

t-Stat.

0.06 0.17 – –

1.23 2.31 – –

– – 1.16 0.45

– – 1.49 -0.22

0.71 3.18 – –

0.49 0.96 – –

0.89 3.61 – –

0.58 1.04 – –

In the SP-based model that considered the travel time ratio, bsT was found to be positive, as suggested by Brownstone and Small (2005). However, it was only just significant at the 5% level with a t-statistic of 1.92. Due to this inconclusive result, we present the estimation results for a joint SP–RP panel latent class model that considers possible misperceptions in the SP domain while allowing for heterogeneity across drivers. A robustness check was performed for both MNL models that considered the travel time ratio. This test involved the truncation of the distribution of the travel time ratio on the right-hand side (at 1.5 and 2). This was because many respondents has travel time ratios that exceeded 1.5, whereas none had travel time ratios less than 0.5 (see Fig. 1). It is possible that the results presented in Table 5 were affected (or even caused) by these high travel time ratios, which appeared to be too high to reflect true misperceptions (they were probably reflected reporting errors). Table 6 shows the relevant parameter estimates. The RP model where the travel time ratio distribution was truncated at 2 yielded similar results to the original estimates presented in Table 5. When all of the drivers with travel time ratios that exceeded 1.5 were excluded from the analysis, the scheduling coefficients that were consistent with a misperception similar to the travel time ratio (indicated by the superscript s) remained insignificant, whereas the reward coefficient was significant at the 5% level (t-statistic = 2.31). However, the positive and significant reward coefficient was insufficient to conclude that drivers misperceived the travel times in the RP setting. By contrast, the scheduling coefficients were not significant and bsE was positive (it should be negative if the travel times had been misperceived in a similar manner to that in which they were misreported), which did not support this conclusion. For the SP model, Table 6 shows that the relevant coefficients remained similar to those derived in the original estimation when the distribution of the travel time ratio was truncated at 2. Thus, bsT was still positive, but it had a lower t-statistic than the original estimation (1.49 compared with 1.92, respectively). When only the travel time ratios below 1.5 were considered in the estimation, bsT became negative (whereas a positive sign would be expected based on the proposition of Brownstone and Small (2005)) and the t-statistic decreased even further (to 0.22). The decrease in the t-statistic may be explained partly by the low number of observations, but the size of this decline and the fact that the coefficient moved closer to 0 suggest that the participants did not react to the travel times presented to them in the SP setting in a manner that was consistent with their misreporting. However, this result does not necessarily mean that the drivers reacted to the travel times presented to them in the same manner that they would have reacted to them in reality. Instead, it may imply that our specification of the travel time ratio was not an appropriate representation of the drivers’ travel time perceptions.

7.3. Estimation results: panel latent class model The MNL model presented in Table 5 and the robustness checks presented in Table 6 appear to suggest that the theory proposed by Brownstone and Small (2005) to explain the structural differences between SP- and RP-based valuations of the travel time does not hold for our data (it is possible that the reported travel times did not represent travel time perceptions, thus we were not able to test their theory in a valid manner). To gain further insights, we estimated results for a panel latent class model that considered the travel time ratio in the SP domain, while also considering both the SP and RP scheduling choices. It was expected that by pooling the data sources, the unobserved preference heterogeneity among participants would be represented better. Therefore, this estimation procedure could identify whether the groups of drivers who were presented with the travel times in an SP setting reacted as if they were overestimated in the case of over-reporting, or as if they were underestimated in the case of under-reporting. We estimated results for a panel latent class model with three classes (Q ¼ 3). Various statistical criteria such as the BIC or the AIC are considered to be adequate criteria for selecting the number classes (e.g. Greene and Hensher, 2003). However, as noted by Scarpa and Thiene (2005), the selection must also account for the significance of estimated parameters and it should be guided by the analyst’s own judgment of the meaning of the parameter signs. In this case, the statistical criteria suggested that a higher number of classes would be appropriate. Probably due to correlations between the attribute values, which were especially evident in the RP setting, several coefficients then assumed the reverse sign of that expected, thereby yielding negative valuations for the time and schedule delays, which were obviously not plausible from an economic view point. Nevertheless, the high number of classes suggested by the statistical criteria indicated a substantial level of heterogeneity in the participants’ scheduling preferences. This claim is supported by the fact that the fit of the panel latent class model (which was measured by the adjusted pseudo R2) was substantially better than that of the MNL models.

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Table 7 Panel latent class model. Class Prob.

Class 1 Coeff.

Class 2 t-Stat.

Coeff.

0.36 bRP R bRP T bRP E bRP L h bSP R bSP T bSP E bSP L s bSP; T VOTRP VSDERP VSDLRP VOTSP VSDESP VSDLSP No. Obs. Log-Lik. Pseudo R2 adj. a

0.21 5.06 2.60 0.70 0.12 0.19 4.26 1.10 0.94 1.36 23.87 12.26 3.30 22.19 5.73 4.89

Class 3 t-Stat.

Coeff.

0.19 3.14 2.43 9.04 6.25 5.34 6.99 3.57 5.04 5.41 0.99 1.92 2.97 2.81 3.19 4.09 4.28

=a

0.16 19.4 1.39 2.01 0.12 0.048 2.18 4.31 9.16 1.91 124.4 8.91 12.88 – – – 12,537 20,088 0.25

t-Stat.

0.45 1.93 5.73 4.76 5.66 5.34 0.69 1.39 5.15 5.42 0.85 1.83 1.79 1.82

=a

0 8.99 3.45 3.05 0.12 0 3.33 3.09 1.06 0.96 – – – – – –

– 6.01 13.43 13.84 5.34 – 3.25 9.93 5.88 1.16

Constrained to be equal.

In the model presented in Table 7, all of the coefficients are specific to one of the data sources, thereby demonstrating that no separate scale parameters were identified. Some coefficients did not differ significantly among data sources, but we preferred to keep them separate in order to unambiguously identify the effect of the travel time ratio on the SP choices (thereby s reducing the risk that bSP; might detect some difference between the SP and RP coefficients). Therefore, the SP and RP choices T were connected mainly via their class membership because the same class membership probability applied to all of their SP and RP choices for a given person. Based on extensive testing of alternative model formulations, some coefficients were restricted in the model presented in Table 7. Thus, we did not specify h as class-specific because it did not differ significantly among the classes. More importantly, for one class (‘Class 3’), the reward coefficient was fixed to 0 for both the SP and RP domains, because some of the reward coefficients were close to 0 or even negative if they were not restricted. As a consequence, the point estimates of the travel time and schedule delay valuations would have approached infinity or become negative, respectively. The size of the class probability for ‘Class 3’ (0.45) indicates that a considerable proportion of the participants did not consider the reward when deciding their actual and hypothetical departure times. In fact, we also found that the reward coefficient in the SP domain was close to 0 in ‘Class 2.’ A possible explanation for these findings is that a reward of 4 Euro was too low to make some participants willing to shift their departure times (actually or hypothetically) to off-peak periods. Because the reward coefficients in the SP domain of ‘Class 2’ were close to 0 and insignificant, and also because the reward coefficients were restricted to 0 in ‘Class 3,’ we could only derive willingness-to-pay estimates for ‘Class 1’ and the RP domain of ‘Class 2.’ We found that the resulting willingness-to-pay estimates were all significant at the 10% level. For ‘Class 1,’ we obtained consistent results for the SP and RP domains, where the point estimates of the VOT resembled each other particularly closely. However, the schedule delay valuations were also of the same order of magnitude (which was not the case in the MNL model where the SP-based scheduling valuations were about three times as high as the RP-based ones). We also found that the willingness-to-pay estimates for ‘Class 1’ were generally lower than those for the MNL models. This was because, unlike ‘Classes 2’ and ‘3’, ‘Class 1’ captured the behavior of the individuals with high reward preferences. This was reflected by the high reward coefficients in ‘Class 1’ (higher than those in the MNL models), which also implied lower willingness-to-pay values. For ‘Class 1,’ we could only compare the SP- and RP-based valuations. For the remaining two classes, we had to rely on comparisons between the SP and RP coefficient values. In general, although the coefficients varied between the two data types, there were some reassuring similarities between them. For example, in ‘Classes 1’ and ‘3’, the disutility of being early was found to be greater than that of being late in both the SP and RP domains, whereas the opposite applied in both domains for ‘Class 2.’ An exception was the travel time coefficient in ‘Class 2’ where the disutility due to the travel time was very large in the RP domain, but much lower in the SP domain. In the latter case, the disutility associated with X min of travel time was even lower than the disutility associated with X min of schedule delay. Finally, in agreement with the MNL results, the coefficients related to the objective SP travel time multiplied by the travel s time ratio, bSP; T , were again insignificant for all three classes. This is yet another indication that the theory proposed by Brownstone and Small (2005) was not supported by our study because the drivers did not misperceive the travel times in the SP setting, or the travel time ratio did not reflect their actual misperceptions. For the same reasons, we cannot explain any remaining differences between SP and RP willingness-to-pay values based on misperceptions that the travel time ratio

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could capture. The SP and RP results were fairly similar, and this may actually suggest that travel time misperception had a minor role in the context of our (RP and SP) choice experiments. Indeed, it suggests that there was a much lower extent of misperception compared with the misreporting we found.

8. Conclusions In this study, we compared the reported and actual travel times of car commuters who participated in a large-scale peak avoidance experiment. There were major differences between the reported and actual travel times at the level of the individual driver, which we expressed as ratio that we refer to as the ‘travel time ratio.’ On average, the participants overstated their travel times by more than 50% (the travel time ratio was greater than 1.5). We identified some major determinants of the travel time ratio, such as the link length and average speed, and we tested some previously proposed hypotheses regarding link- and driver-specific characteristics that may explain over-reporting. Next, we determined whether the overstated travel times were the result of reporting errors or if they reflected actual perception errors. Thus, we tested whether the person-specific travel time ratio affected the departure time choices in RP and SP settings. In both settings, we found that the travel time ratio only had very limited explanatory power. Therefore, we conclude that the travel time ratio was mainly attributable to reporting errors and that the reported travel times appeared to be a poor indicator of both the actual and perceived travel times, at least in the context of our research. Reporting errors can have numerous causes, as follows. First, although the questionnaire used to obtain the reported travel times focused explicitly on the in-vehicle time, drivers may also have included the time they required to walk from their home to their car, as well as the time they required to walk from their car to their workplace.26 Second, drivers might have unconsciously added a safety margin when thinking about their travel times.27 We expect that these reasons might be relevant mainly to those with inflexible work starting hours because they are more likely to include a safety margin in their scheduling choices compared with travelers who have flexible work starting hours. Third, our finding that the average travel time ratio was substantially higher than 1 might be related to a social desirability bias. For example, drivers might have assumed that it is considered socially desirable to drive slowly (i.e., being more considerate toward other road users, as well as toward the environment), thereby stating longer travel times than they actually experienced. Fourth, strategic behavior might also have played a role in the answers provided to the questionnaire. By overstating their travel times, the respondents might have hoped to push forward the implementation of policies targeted at decreasing travel times. Finally, reporting errors may have been caused by rounding errors or by asking drivers to state average time of day-independent travel times, which are not necessarily relevant to their actual scheduling behavior. However, in both of the latter cases, there is no clear reason why overstatement (rather than understatement) of the travel time might have occurred, thus we do not expect them to be major explanations for the results obtained in this study. It might be possible to avoid, or at least to reduce, reporting errors in travel time data if the data collection methods were improved. For example, instead of asking respondents to state their travel times, it might be beneficial to let them complete a schedule, indicating when they leave their home, start their car, park their car again, and finally arrive at their work location. This design is likely to limit any biases that might arise from respondents considering the in-vehicle time in their answers and it would make it more difficult for them to engage in strategic or socially desirable answering patterns compared with the situation where they only had to insert absolute travel times. This approach may be extended by asking for a set of previously experienced travel times rather than averages, thereby avoiding reporting errors caused by aggregating a set of commuting experiences. Clearly, these alternatives involve a trade-off between information gains for the researcher and additional time required by the respondents to complete the questionnaire. However, the results of this study suggest that the benefits may outweigh the costs. In this study, the main focus of the SP- and RP-based choice models was to test whether drivers misperceived travel times to the same extent as they misreported them. This could not be confirmed for either of the two data sources, but it is still possible that the drivers misperceived their travel times in a manner that was not reflected by the travel time ratio. However, an alternative pattern of misperception would be difficult to identify using the observed (SP or RP) choices alone because it was usually unclear whether the estimated coefficient values were attributable to misperception rather than reflecting actual preference structures. Thus, further research should focus on the challenging task of identifying (instrumental) variables that affect travel time misperception, rather than the preferences that cause the scheduling choices. The results of this study were obtained in a fairly specific context, i.e., a peak period avoidance experiment performed on a highway link in the Netherlands. Participation in the experiment was voluntary. As a result, the participants were not representative of the drivers who used this highway link, or of the Dutch population as a whole. Most importantly, the participants tended to have a higher salary and more flexible working hours than non-participants. We do not believe that this selection bias was responsible for our results in terms of over-reporting vs. overreacting, but we are aware that the evalu26 Drivers may also have included the time spent cruising around while parking in their reported travel times, although over-reporting is not expected to be a consequence of this behavior because cruising was not removed from the underlying GPS dataset used to estimate the door-to-door travel times. In general, we did not expect cruising to play a major role in our study because only morning commuting trips were considered in the analysis and most Dutch employers provide parking spaces for their employees. 27 We thank the referee who brought this to our attention.

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ations derived in this study are not representative of a larger population and we encourage follow-up research using alternative data sources. To conclude, we obtained strong evidence of ‘overstating’ but much less evidence of ‘overreacting’ in SP- and RP-based scheduling choices. Thus, these results suggest that caution should be taken when using reported travel time data as indicators of actual and perceived travel times. We demonstrated that this was the case for travel times but this conclusion can probably be generalized to various contexts. Acknowledgments This study was financially supported by the Dutch Ministry of Infrastructure and the Environment, and by the TRANSUMO Foundation. The financial support provided by the ERC (Advanced Grant OPTION #246969) to Paul Koster and Erik Verhoef, and by IPRISM to Jasper Knockaert is gratefully acknowledged. We wish to thank two anonymous reviewers for their constructive suggestions. Appendix A. List of variables

Variable

Description

Data sources RP SP

Revealed preference (also used as a superscript) Stated preference (also used as a superscript)

Indices d ¼ 1; . . . ; Dz j ¼ 1; . . . ; J zk k ¼ 1; . . . ; K z l q ¼ 1; . . . ; Q z ¼ 1; . . . ; Z

(Person-specific) trip index (Person- and choice situation-specific) index of choice alternatives (Person-specific) index of choice situations Link index 2 {home–C1, C1–C2, C2–work, home–work} Class index for latent class models Person index

Travel time ratio T Rzl T Azld T Azl

(Person- and link-specific) reported average travel time (Person-, link-, and trip-specific) actual travel time Average (person- and link-specific) actual travel time (Person- and link-specific) travel time ratio Reference to travel time ratio (e.g. bsR ; bsT ; bsE ; bsL ; U szkj ; V szkj )

szl s (superscript)

Utility function: attributes E Expectation operator (see Eqs. (8) and (9) for the definition) t Departure time from home PAT (Driver-specific) preferred arrival time at work RðtÞ; Rzkj ; Rzj Reward attribute (general, choice-specific, average) TðtÞ; T zkj ; T zj Travel time attribute (general, choice-specific, average)  zj Early schedule delay attribute (general, choice-specific. average) SDEðtÞ; SDEzkj ; SDE  SDLðtÞ; SDL ; SDL Late schedule delay attribute (general, choice-specific, average) zkj

zj

A ¼ fR; T; SDE; SDLg Azkj ; Azj

Attributes of the utility function (general) Attributes of the utility function (choice-specific, average)

Utility function: coefficients bR ; bT ; bE ; bL Reward, travel time, earliness and lateness coefficients h Relative weight drivers attach to actual travel time realizations vs. averages k Multiplicative scale factor for SP choices (scale for RP choices is fixed to 1) Utility function: general U zkj (Person-, choice situation-, and alternative-specific) utility V zkj Deterministic component of the utility function zkj Stochastic component of the utility function ln L Log-likelihood Pzkj Probability of person z choosing alternative j in choice situation k  zk P Probability associated with the alternative chosen by person z in choice situation k

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Appendix A. Variable  zkjq P

Description

Hzq

Probability associated with the alternative chosen by person z in choice situation k conditional on being member of class q Probability of person z being member of class q

Valuations VOT VSDE VSDL

Value of (travel) time Value of early schedule delay Value of late schedule delay

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