Electronic copy available at: http://ssrn.com/abstract=1976170

TI 2011-181/3 Tinbergen Institute Discussion Paper

Long-Run vs. Short-Run Perspectives on Consumer Scheduling: Evidence from a Revealed-Preference Experiment among Peak-Hour Road Commuters

Stefanie Peer* Erik Verhoef* Jasper Knockaert Paul Koster* Yin-Yen Tseng*

Faculty of Economics and Business Administration, VU University Amsterdam. * Tinbergen Institute.

Electronic copy available at: http://ssrn.com/abstract=1976170

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Long-run vs. short-run perspectives on consumer scheduling:

Evidence from a revealed-preference experiment among

peak-hour road commuters

Stefanie Peer,Erik Verhoef,

Jasper Knockaert,Paul Koster,

Yin-Yen Tseng

VU Amsterdam, Tinbergen Institute Amsterdam/Rotterdam

December 22, 2011

Abstract

Theoretical and empirical studies of consumer scheduling behavior in commuting,and the associated valuation of time and schedule delays usually ignore that consumershave more flexibility to adjust their schedule in the longer run than in the shorterrun, implying that also these valuations may differ. We propose a framework thatdoes distinguish between a long-run choice of routines over the day, based on long-run expectations of travel times, and a short-run choice of departure time, takingthese routines as given and using more precise expectations of travel time that can beformed when getting closer to the moment of traveling. Our empirical results show thatsignificant differences exist in the valuation of time and of schedule delays between thelong-run and the short-run model. Travel time is valued higher in the long-run model,as changes in travel time are more permanent and can therefore be exploited betterthrough the rescheduling of routines. Schedule delays are valued higher in the short-runmodel, since scheduling restrictions are typically more binding in the short-run.

1 Introduction

Values of time and schedule delay are central concepts in transport economics. They are amain component of the generalized costs of travel, and key ingredients in the evaluation ofpolicy options such as congestion pricing and investments in road capacity. Research onthe valuation of non-working time dates back to Becker (1965) and DeSerpa (1971). Small

1

2 1. INTRODUCTION

(1982), building on the work of Vickrey (1969), extended their models by adding schedulingcosts. The latter are defined as the disutility that arises from arriving earlier or later thanthe preferred arrival time (PAT). The scheduling model has become the workhorse modelfor analyzing departure time choices, as it explicitly takes into account time-of-day specificcongestion patterns (e.g. Arnott et al., 1993). Empirically, the values of time and scheduledelays are usually determined by estimating discrete-choice models (McFadden, 1974), usingdisaggregate stated (SP) or revealed preference (RP) data.To identify the appropriate values of time and schedule delay, and to use them in the rightway, a good understanding of the underlying scheduling behavior of travelers is crucial. In thispaper, we decompose scheduling decisions into long-run choices of what we will call ’routines’and short-run choices of departure times. Furthermore, we distinguish different degrees ofinformation. Specifically, in the long run, drivers only know time-of day-specific averagetravel times, whereas in the short run, more information about day-specific characteristicsand realizations of travel times becomes available.We find that drivers value more permanent travel time gains higher as these can be exploitedbetter through adjustment of the routines. After all, an unanticipated minute of time gaincan typically be used less effectively than a foreseen minute. This result is consistent withthe findings by Tseng et al. (2010) that the value attached to a permanent one-hour traveltime gain is 14.5 Euro/hour, compared to 3 Euro/hour for an incidental travel time gainof one hour on a random day. On the other hand, we find a lower value of schedule delayfor less permanent changes in travel times. This finding can be attributed to the fact thatscheduling restrictions are typically more binding in the short-run. Borjesson (2009) obtaina similar result, however, without explicitly distinguishing between long and short-rundecisions, and Borjesson et al. (2010) argue along similar lines to explain discrepancies inscheduling coefficients by differences in the setup of SP choice experiments.The relevance of distinguishing explicitly between short- and long-run scheduling decisionsas we propose in this paper, may be limited for deterministic equilibrium models, whichimplicitly assume that successive days are exact replicas. The long-run choice of routines,and the short-run departure time choices are then identical, and cannot be meaningfullydisentangled. The same is in fact true for stochastic models when assuming that travel timeexpectations do not vary between days (e.g., when ignoring learning or information-updating).If the travel time expectations do not change, departure time choices will not be adjustedbetween the days, and again, long-run and short-run behavior coincide. However, as ourresults demonstrate, the distinction is very pronounced, when travel time expectations dochange between days, as it is generally true in reality.Here, we assume that home and work locations are fixed, also in the long-run model. Incontrast, most studies in transport and labor economics that also aim at determining thevalue of time define the long run as allowing changes in residential and work location choices(e.g Van Ommeren and Fosgerau, 2009; Van Ommeren et al., 2000). The values derivedin these studies are not directly comparable to the values derived from the schedulingmodel, not in the least place because they usually do not distinguish between time andscheduling-related costs.Given the differences between short-run and long-run valuations that we find we believe

3

that the distinction between the long-run and short-run scheduling decisions may also helpexplaining the large dispersion of the values of time and schedule delays that is found inthe literature (see for instance the Brownstone and Small (2005) for an overview). So, thedefinition of the PAT differs considerably across studies. Most authors define the PAT asPAT under uncongested conditions (e.g. Borjesson, 2009), or as the official work start time(e.g. Noland et al., 1998; Small, 1982). Only few studies define the PAT as based on actual(stated or observed) behavior, which is more consistent with the concept that drivers haveroutines that are adapted towards average traffic conditions (one such exception is the studyby Tseng et al. (2010)).The paper is structured as follows. Chapter 2 provides an overview of the modeling framework,Chapter 3 discusses the underlying data. In Chapter 4, the results are presented, whileChapter 5 accounts for a robustness check of the findings. Finally, Chapter 6 concludes.

2 Models

2.1 General Framework

In this paper, we study the differences between long-run and short-run scheduling behaviorin the morning commute. There is reason to expect that these are inherently different in atleast two senses.First, in the long run, drivers are able to adapt their routines. Specifically, in a world withouttraffic congestion, a driver’s PAT may, for instance, be 9:00 in the morning, whereas recurringcongestion may induce her to make a different planning for the day. As a consequence, shemay for instance make appointments at work earlier than that, but given those appointments,the PAT also shifts to an earlier instant. In the terminology that we will use, drivers canthus choose an ’adapted PAT’ (APAT, henceforth) that is different from the ’structuralPAT’ (SPAT, henceforth). The SPAT is here defined as PAT that would apply if there wereno congestion ever, while the APAT is defined as the PAT given that routines are adjustedin the face of the (long-run) expected pattern of travel times over time of the day. In theshort run, routines and therefore also the APAT is still fixed, in the sense that drivers areexpected to experience scheduling costs from arrival times different from their APAT.Second, also the availability of information on travel times is likely to differ between the longand the short run. In the long run, only average traffic conditions can be expected to beknown, whereas in the short run, drivers can take into account day-specific characteristicsthat may affect travel times (e.g. weather conditions), as well as more incidental changes inthe travel time distribution.We refer to the drivers’ choices of APAT, given the SPAT and given expectations on traveltime distributions, as the long-run model; and, to the departure time choice on a given day,given the APAT and more up-to-date information on travel times, as the short-run model.Based on differences between this long-run and short-run model, we can derive values oftime and of schedule delay that differ with respect to the degree of permanentness of theunderlying changes in travel times and delays. Differences in travel times and delays over

4 2. MODELS

time of the day are obviously of a more permanent nature in the long-run model than in theshort-run model. We expect the value attached to permanent changes in the travel timedistribution to be higher than the value attached to incidental changes in travel time, sincepermanent gains can be exploited better as drivers can adapt their routines. The value ofschedule delay, however, is expected to be higher for incidental changes in schedule delays,as there is less flexibility to reschedule in the short-run than there is in the long-run.This paper intends to provide an answer to three main questions. First, we investigatewhether a difference exists between the SPAT and the APAT, based on qualitative insightsgained from the distribution of APATs and SPATs over time of the day, but also based onthe success of both measures to describe scheduling behavior in the shorter run. Second,we examine to which extent the values of time and schedule delay vary with the degree ofpermanentness of the change in travel time. To answer this question, we will compare thecoefficients obtained for the long-run and the short-run model. Finally, we test whetherthe APAT affects short-run departure time decisions more strongly than the SPAT, using amodel that is able to identify whether drivers experience utility or disutility from movingaway from the APAT, towards the SPAT. If this is the case, we can conclude that short-rundeparture time decisions are indeed driven by the APAT rather than the SPAT.

Long-run Model

In the long run, travelers are able to choose their routine, and specifically their APAT,given their SPAT and expected travel times. The APAT is not only driver-specific but alsoweekday-specific, as travel times differ substantially between weekdays (see Section 3.3).The corresponding utility for driver z of choosing time t on weekday l as APAT is denotedby ULRt,l,z, where the superscript LR stands for long-run (LR). A driver z trades off deviationsbetween t and his SPAT(z), but also differences in expected travel times T and a financialincentive (a reward R to be explained below) for arriving at t rather than at SPAT(z).The travel time expectations in the long-run model are based on what we will call a ’roughinformation’ (RI) regime, which implies that the travel time and reward expectationsfor weekday l at time t are determined as a weighted average of all travel time (reward)observations on the days k = 1, . . . ,K for time t, defining the the weights wk,RI(l) as follows1:

wk,RI(l) =

{1 if weekday(k) = l

0 if weekday(k) 6= l(1)

The corresponding standardized weights (summing up to 1) are denoted by wk,RI(l). We usethe greek characters α, β, γ and δ to indicate the coefficients estimated for time, earliness andlateness (with respect to the SPAT) and for the monetary reward, respectively. Monetaryvaluation measures then can be obtained by dividing the regarding time and schedulingcoefficients through −δ. The utility can thus be written as:

1The notation used in Equation 1 may seem unnecessary tedious, but it is used for consistency with themodeling of ’fine information’ in Equations 4–6.

2.1. GENERAL FRAMEWORK 5

ULRt,l,z = α∗K∑k=1

wk,RI(l) ∗ (Tt,k,z − TSPAT(z),k,z)+ (2)

β∗max[SPAT(z)− t, 0] + γ ∗max[t− SPAT(z), 0]+

δ∗K∑k=1

wk,RI(l) ∗ (Rt,k,z − RSPAT(z),k,z)

Our long-run model in Equation 2 does not take into account differences in travel timevariability since these were found to be too strongly correlated with the differences in traveltimes.2 The coefficient obtained for travel time therefore can be interpreted as capturingboth the disutility from expected travel time as well as the disutility from travel timevariability insofar as it moves in parallel with expected travel time.

Short-run Model

In the short run, drivers choose their departure time, while their routines are fixed and theAPAT is therefore given. The schedule delays early and late for driver z and a departuretime t on day k, SDEt,k,z and SDLt,k,z, are now computed relative to the APAT:

SDEt,k,z = max[APAT(z)− t− Tt,k,z, 0], (3)

SDLt,k,z = max[t+ Tt,k,z −APAT(z), 0]

Besides the scheduling variables, the drivers trade-off expected travel time and a financialincentive (again the rewards).Expectations with respect to travel times, scheduling variables and rewards are based ontwo measures: ’perfect information’ (PI) and ’fine information’ (FI)3. Travel times in thePI regime are simply the actual realizations of travel times on that day. Although it isunrealistic that these actual travel times are known to drivers at the moment of departure,the regime offers a benchmark for the maximum extent of information that could have beenpossibly available to drivers.The FI regime uses expected travel times that can be predicted using a number of day-specificfactors such as weekday, month and weather-related variables. To derive the day-specificweights for the FI regime, we use a local constant estimator (e.g. Li and Racine, 2007). Theintuition behind this approach is that travel times on days with more similar characteristics,are more similar to each other. We assume that travelers do not take into account informa-tion about future travel times. Therefore the weights for all days k ≥ k are equal to 0. Wedenote the weight specific to day k that enters the travel time expectation for day k ∈ Kby wk,FI(k), and the standardized weights by wk,FI(k). The weights are determined from a

2The correlation coefficient between expected travel times and rewards is equal to 0.79.3We do not take into account the rough information (RI) regime in the short-run model as we can show

that the RI is already captured in the long-run model.

6 2. MODELS

multiplicative function of the day- and variable-specific weights for variables v = 1, . . . , V .

wk,FI(k) =V∏v=1

wv,k,FI(k) (4)

The variable-specific weighting functions depend on the variable type. For categorical andordinal variables, the following functional form is assumed (Racine and Li, 2004):

wv,k,FI(k) =

1 if xv,k = xv,k and k < k

h|xv,k−xv,k|v if xv,k 6= xv,k and k < k

0 if k ≥ k,(5)

where hv is the bandwidth or smoothing parameter related to variable v, while xv,k is thevalue of the variable v on day k.4 For continuous variables, a Gaussian function is assumed:

wv,k,FI(k) =

1hv√

2πexp

[−1

2

(xv,k−xv,k

hv

)2]

if k < k

0 if k ≥ k(6)

Table 1 shows the variables taken into account in the FI regime, the variable type, and theoptimal bandwidths that are determined using leave-one-out cross-validation (e.g. Fan andGijbels, 1996). We find a bandwidth for the ’distance in days’ variable close to 1, indicatinga fairly flat time decay function. Both the bandwidths for weekday and month are closer to0 than to 1, indicating that only small weights are attached to observations with weekdaysand months that are different from those of the calibration observation k. The weathervariables, however, have rather high bandwidths, implying that they have a relatively smalleffect on travel times.

Table 1: Bandwidths in the FI regime

Variables Type Optimal Bandwidth

Distance in days ordinal 0.9963Weekday categorical 0.0140Month categorical 0.1358Precipitation (in mm) continuous 5.9972Temperature < 5℃ categorical 0.7114

Finally, Equation 7 shows the utility function applied in the short-run model. The short-run

4The bandwidth hv is between 0 and 1 for categorical and ordinal variables and can assume any positivevalue for continuous variables.

2.1. GENERAL FRAMEWORK 7

(SR) utility of driver z to depart at time t on day k is denoted by USRt,k,z

. The attributes

for the PI and FI regime are weighted by the coefficients θPI and θFI, respectively, wherebyθPI = 1− θFI.

USRt,k,z

= α∗(θPI ∗ Tt,k,z + θFI ∗K∑k=1

wk,FI(k) ∗ Tt,k,z)+ (7)

β∗(θPI ∗ SDEt,k,z + θFI ∗K∑k=1

wk,FI(k) ∗ SDEt,k,z)+

γ∗(θPI ∗ SDLt,k,z + θFI ∗K∑k=1

wk,FI(k) ∗ SDLt,k,z)+

δ∗(θPI ∗ Rt,k,z + θFI ∗K∑k=1

wk,FI(k) ∗ Rt,k,z)

Again monetary values for time and schedule delays can be determined by dividingα, β, and γ by −δ. The resulting ratios give the value for a shift of the travel timedistributions that affect both the FI and the PI regime. In order to determine the willingnessto pay for a shift in the PI travel time only, given the FI prediction, these ratios need tobe multiplied by θPI. Note that Equation 7 implies that for the computation of expectedschedule delay cost as a function of departure time, we do not compute schedule delay costsfor some single expected travel time, but instead we compute the schedule delay costs foreach individual past travel time that then determines the expected value. As a consequence,a given expected departure time can have both positive schedule delay cost early and late.

Three Domains Model

Finally, we will also test whether a move away from the APAT towards the SPAT increasesschedule delay costs in the short-run departure time choice model. For instance, is it truethat for an APAT at 7:00 and an SPAT at 9:00, an arrival time at 8:00 would bring costsof schedule delay late rather than early. To do this, we will distinguish between the casesAPAT≤SPAT and APAT>SPAT, and introduce an intermediate domain for both cases.In this intermediate domain, the arrival time associated with departure time t leads to aschedule delay early with respect to one PAT type and to schedule delay late for the otherPAT type. Depending on its delay with respect to the APAT, the according attributesare denoted by SDMEt,k,z (for drivers with APAT>SPAT) and SDMLt,k,z (for drivers withAPAT≤SPAT). The schedule delay variables for this 3-domains model are therefore re-definedin the following way:

8 2. MODELS

1. APAT > SPAT

SDEt,k,z = max[SPAT(z)− t− Tt,k,z, 0] (8)

SDLt,k,z = max[t+ Tt,k,z −APAT(z), 0]

SDMEt,k,z = min[APAT(z)− SPAT(z),max[APAT(z)− t− Tt,k,z, 0]]

SDMLt,k,z = 0

2. APAT ≤ SPAT

SDEt,k,z = max[APAT(z)− t− Tt,k,z, 0] (9)

SDLt,k,z = max[t+ Tt,k,z − SPAT(z), 0]

SDMEt,k,z = 0

SDMLt,k,z = min[SPAT(z)−APAT(z),max[t+ Tt,k,z −APAT(z), 0]]

The according utility function for the three domains model is then given by:

U3 domainst,k,z = USR

t,k,z+ µ∗(θPI ∗ SDMEt,k,z + θFI ∗

K∑k=1

wk,FI(k) ∗ SDMEt,k,z)+ (10)

ν∗(θPI ∗ SDMLt,k,z + θFI ∗K∑k=1

wk,FI(k) ∗ SDMLt,k,z)+

We expect ν to be between −β and γ, and µ to be between β and −γ (see Figure 1 fora diagrammatic exposition for the case APAT≤SPAT). If ν and µ are negative, we haveconfirmation that deviations from the APAT towards the SPAT indeed increase scheduling

Figure 1: Diagrammatic exposition: APAT < SPAT

APAT SPAT

Time

Schedulin

g c

osts

β γν= γ

ν= 0

ν= − β

APAT SPAT

Time

Schedulin

g c

osts

β γν= γ

ν= 0

ν= − β

9

costs. In particular, if ν = γ and µ = β, we find that the SPAT has no effect at all ondeparture time decisions, and we end up with a conventional scheduling cost structure:piecewise linear, with a single kink at APAT. In the other extreme, if we would find thatν = −β and µ = −γ, we can only conclude that the SPAT is the relevant focus point also forshort-run departure time decisions, as we would have conventional piecewise linear schedulingcost structure but now with the kink at SPAT. The three domains model, therefore, helpsidentifying the degree to which the APAT rather than the SPAT determines short-runscheduling behavior.

3 Data

3.1 Experiment

We use revealed preference data that were gathered during a peak avoidance experiment(’Spitsmijden’ in Dutch) taking place in the Netherlands.5 It included approximately 2000participants, and was conducted over a period of four months (2009/09–2009/12). Driverswere eligible for a monetary reward of 4 Euro if they avoided traveling on a specific highwaylink (of 9.21 km length) during the morning peak (6:30–9:30). We will refer to this specificlink as C1–C2, as it is confined by two cameras (’C’) that register whether and when aspecific driver was using the C1–C2 link. Rewards could not be earned on weekends orschool vacation days, but also not if the drivers had already exceeded the maximum numberof days per week for which a reward could be obtained. This maximum is driver-specific,and was set equal to the average number of weekly trips he had undertaken during thepre-experimental period.

3.2 Door-to-door travel times

In the above equations, time-, day-, driver- and information-regime specific travel timesTt,k,z referred to door-to-door travel times. As we do not observe door-to-door travel timesdirectly, they need to be approximated. We only observe C1–C2 travel times, TC1−C2

t,k , whichare measured continuously (i.e. at any time of the day) using loop-detectors, and are thenaggregated into 15-minute intervals. Door-to-door travel times are calculated from theseusing geographically weighted regression (Peer et al., 2011):

Tt,k,z = f(TC1−C2k , H(z),W (z)), (11)

where H(z),W (z) are the home and work location of person z, and f is the function thattranslates the C1–C2 travel time vector on day k into door-to-door travel times for person z.Peer et al. (2011) discuss this model in detail, and provide evidence of the plausibility of thedoor-to-door travel times thus computed.

5See Ben-Elia and Ettema (2009) for an analysis of the decision to participate in the Spitsmijdenexperiment, and Knockaert et al. (2009) and Ben-Elia and Ettema (2011) for further analyses of theparticipants’ behavior.

10 3. DATA

3.3 Operationalization of the SPAT and APAT

By nature of its definition, SPAT refers to a guaranteed congestion-free situation, and cantherefore be determined only using questionnaire techniques. The data on the SPAT aretherefore obtained from a questionnaire conducted among the participants of the experiment.They were asked to state their preferred arrival time at work if they knew that they wouldnot face any congestion during their commuting trip6.The APAT is defined as the weekday-specific median arrival time at work. For a givenweekday, a driver is considered to have a valid measure of the APAT only if he was observedto pass the C1–C2 link on at least three such weekdays during the experimental period.On all of these days, he must have been eligible for a reward (drivers might have differentroutines during non-rewarded days). The APAT is defined as weekday-specific becausethe time pattern of travel times depends strongly on the day of the week (see Figure 2a).However, it was verified that our results remain valid if the APAT is defined independentlyfrom the weekday.Figure 2b shows a scatterplot for all drivers and weekdays for which valid measures of APATand SPAT were calculated. As expected, we find that the APATs are more dispersed overtime. If a line were fitted through the data points, it would be substantially steeper thanthe 45°–line shown in the figure. This pattern is confirmed by the histograms of the SPATand APAT distributions, shown in Figures 2c and 2d, respectively. We find that the densityof the SPAT distribution is highest between 8:00 and 9:00, hence, around the typical workstarting time. In contrast, arrival times at the begin and the end of the peak are preferredby a much lower number of participants. The distribution of the APAT is much flatter. Dueto the fact that the reward can be gained for passing C1–C2 before 6:30 a very pronouncedpeak can be observed for arrival times at work between 6:30 and 7:00. A relatively smallnumber of participants has an APAT that makes them receive a reward after the end of thepeak (9:30).

3.4 Selection of Observations, Choice Set and InformationRegime Definitions

The number of observations in the long-run model is equal to the number observations ofAPATs for which a corresponding SPAT is available (1271), while for the short-run modelit is equal to the number of departure time choices that used in the computation of theAPATs (7605). Overall, 405 drivers are considered in the analysis.For both the long-run and the short-run models, the choice sets consists of 16 15-minuteintervals. In the long-run models each driver is able to choose from APATs ranging from6:15 to 10:00. In the short-run model, in contrast, the choice is defined as person-specific.This is to ensure that despite of differences in home–work distances only the most relevantdeparture time alternatives are included for each driver, in particular those that yield a

6Drivers with an SPAT earlier than 6:30 or later than 9:30 were removed from the dataset as these driversdo not have an incentive to travel during the peak period.

3.4. SELECTION OF OBSERVATIONS, CHOICE SET AND INFORMATION REGIMEDEFINITIONS 11

Figure 2: Descriptives SPAT and APAT

(a) Average weekday-specific travel times

6 6.5 7 7.5 8 8.5 9 9.5 10 10.530

35

40

45

50

55

(arrival) time (in hours)

mean tra

vel tim

e (

in m

inute

s)

Monday

Tuesday

Wednesday

Thursday

Friday

(b) Scatter SPAT vs. APAT

6 6.5 7 7.5 8 8.5 9 9.5 10 10.56

6.5

7

7.5

8

8.5

9

9.5

10

10.5

Structural PAT

Adapte

d P

AT

45−degree line

(c) Histogram SPAT

6 6.5 7 7.5 8 8.5 9 9.5 10 10.50

200

400

600

800

1000

1200

1400

Time (in hours)

Nr.

of

Ob

se

rva

tio

ns

(d) Histogram APAT

6 6.5 7 7.5 8 8.5 9 9.5 10 10.50

200

400

600

800

1000

1200

1400

Time (in hours)

Nr.

of

Ob

se

rva

tio

ns

trade-off between with respect to the reward. Thus, given average traffic conditions duringthe time of the experiment, for each person the departure time choice set consists of 1215-minute intervals that are within the non-rewarded (peak) period, and 2 rewarded pre- aswell as 2 post-peak intervals.For the computation of the rough information (RI) measures, travel times between September1 and December 18, 2009 that are neither weekends nor school vacation days are taken intoaccount. This period corresponds to the period during which rewards could be received bythe respondents. For the fine information (FI) measure, travel times between September 1,2008 and December 18, 2009 (i.e. more than a year) are taken into account. The reasonwhy a longer period is taken into account for the FI than for the RI measure is that thisallows us to determine the effects of day-specific characteristics on expected travel timesmore precisely.

12 4. ESTIMATION RESULTS: BASIC MODELS

4 Estimation Results: Basic Models

Table 2 shows the results obtained for the long-run, the short-run and the 3-domains modelthat is used to test whether departure time decisions are indeed driven by the APAT.Standard multinomial logit (MNL) models will be estimated (e.g. McFadden, 1974). For thecalculation of the t-statistics, the panel sandwich estimator is used in order to correct forunder-estimated standard errors due to the panel nature of the dataset (e.g Daly and Hess,2010).

Table 2: Estimation results

Long-Run Short-Run Short-run: 3 domainsCoefficient Value t-Statistic Value t-Statistic Value t-Statisticα -6.61 -8.12 -1.21 -2.47 -1.64 -3.17β -2.05 -13.80 -3.50 -18.08 -4.45 -13.09γ -1.62 -15.05 -2.96 -21.62 -2.71 21.78δ 0.24 6.02 0.12 5.26 0.14 6.04θFI – – 0.53 10.49 0.55 15.34θPI – – 0.47 9.31 0.45 12.55µ – – – – -2.11 -11.02ν – – – – -3.86 -11.24−α/δ 27.59 10.31 11.54−β/δ 8.57 29.70 31.31−γ/δ 6.78 25.08 19.09−µ/δ – – 14.85−ν/δ – – 27.19−α/δ ∗ θPI – 4.85 4.68−β/δ ∗ θPI – 13.96 11.03−γ/δ ∗ θPI – 11.79 9.46−µ/δ ∗ θPI – – 6.68−ν/δ ∗ θPI – – 12.24Nr. Obs. 1271 7605 7605LogLik. -2916 -12987 -12841Pseudo R2 0.17 0.39 0.40

From Table 2, we can observe that credible point estimates are obtained in all models. Thevalue of time (−α/δ) is between 10.31 and 27.59 Euro/hour, the value of schedule delayearly (−β/δ) between 8.57 and 31.31 Euro/hour, and finally the value of schedule delaylate (−γ/δ) between 6.78 and 19.09 Euro/hour. We find significant differences between thelong-run and the short-run estimates.The value of time is higher in the long-run model. This is an indication that travelers attacha higher value to more permanent (repetitive) travel time changes, as these can be exploitedbetter through the rescheduling of routines. Also within the short-run model, we find that

13

the value applied to changes in travel times that affect both the FI and the PI measure isvalued approximately twice as high as an incidental travel time change in the PI regimeonly. Hence, with respect to both the long/short-run dimension as well as the informationdimension, permanent travel time changes are considered more valuable.The opposite holds true for schedule delays. Schedule delays are valued significantly higherin the short-run compared to the long-run model. This is likely to be a consequence of themore binding nature of short-run scheduling constraints, which render the re-planning ofactivities costly.The third results column in Table 2 shows the 3-domains mode. Both µ and ν are negativeand significantly different from 0, confirming the scheduling disutility from moving away fromthe APAT towards the SPAT. More specifically, we find that µ is ca. 1/2 of β, indicating thatthe scheduling costs of moving away from the APAT are higher if APAT > SPAT > t than inthe intermediate domain where APAT > t > SPAT. With respect to ν, the scheduling costsof moving away from the APAT in the intermediate domain, hence, when APAT < t < SPATare even higher than for the case that APAT < SPAT < t. This may be an indication ofnon-linear scheduling costs (of lateness) where small delays cause a disproportionately highdisutility (e.g. one might be penalized for being late regardless of the amount of lateness).

5 Robustness Checks

5.1 Heterogeneity

In order to investigate whether the results obtained above still hold if we account forunobserved heterogeneity in the model, we re-estimate both the long-run and the short-runmodel as panel latent class models (e.g. Greene and Hensher, 2003). As we found that for aconsiderable share of the participants the reward coefficient is close to 0, we estimate eachmodel with two latent classes: Class 1 with a reward coefficient fixed to 0, and Class 2 withan unrestricted reward coefficient. The coefficient θFI for the weight attached to the FItime measure as opposed to PI is assumed equal in both classes. Table 3 shows that theaccording results.Table 3 shows that also when we control for unobserved heterogeneity, the result that thevalue of time is higher in the long-run model and the values of schedule delay are higher inthe short-run model. Although for Class 1 no monetary values of time can be determinedsince the reward coefficient is fixed to 0, we find that also for this class the time coefficient ishigher in the long-run model, while the schedule delay coefficients are higher in the short-runmodel.

5.2 Robustness Checks: Long-run Models

In the first robustness check for the long-run model, we divide the observations into twogroups: the earliest 50% and the latest 50% of SPATs. This is to check that the scheduledelay cost valuations in the long-run model are not mainly due to early travelers for schedule

14 5. ROBUSTNESS CHECKS

Table 3: Estimation results: Latent classes

Long-Run Short-RunClass 1 Class 2 Class 1 Class 2

Coefficients Value t-Stats. Value t-Stats. Value t-Stats. Value t-Stats.α -4.63 -4.34 -15.28 -5.51 -3.61 -7.13 -1.34 -3.38β -3.53 -11.05 -1.31 -8.85 -7.09 -38.67 -1.89 -30.55γ -1.96 -9.54 -1.07 -7.04 -5.20 -43.64 -1.67 -30.03δ 0 – 0.31 6.43 0 – 0.14 8.70θFI – – – – 0.62 18.83 0.62 19.23θPI – – – – 0.38 17.54 0.38 11.79Class Prob. 0.64 13.10 0.36 7.23 0.57 19.87 0.43 15.02−α/δ inf 50.07 inf 9.57−β/δ inf 4.69 inf 13.50−γ/δ inf 3.52 inf 11.93Nr. Obs. 1271 7605LogLik. -2746 -12164Pseudo R2 0.22 0.43

delay early or mainly to late travelers for schedule delay late. As Table 4 shows, we obtainvalues of time and schedule delay that are very similar to the ones obtained in the standardlong-run model as presented in Table 2. First, this is an indication that also for sub-groupsof the sample we obtain very consistent estimates. Second, the results show that driverswith early SPATs and APATs are not significantly different from drivers with late SPATsand APATs in terms of their values of schedule delay.

Table 4: Long-run model: early vs. late SPAT drivers

Values Early SPAT Late SPAT−α/δ 30.41 26.05−β/δ 8.15 8.68−γ/δ 7.80 6.59

In the second robustness check for the long-run model, we seek further confirmation thatthe SPAT provided by the respondents is indeed a valid measure and therefore explainsAPATs better than other measures of SPAT. As a simple check, we alter the SPAT forall respondents by [±5,±10,±15,±20,±25,±30] minutes. Figure 3 shows that indeed thelog-likelihood peaks very near the model where the SPAT is left unchanged, confirming thatthe SPAT, although drawn from a questionnaire, indeed seems to represent the drivers’ mostdesired arrival time from a long-run perspective.

5.3. ROBUSTNESS CHECKS: SHORT-RUN MODELS 15

Figure 3: SPAT ± x minutes

−30 −20 −10 0 10 20 30−3060

−3040

−3020

−3000

−2980

−2960

−2940

−2920

−2900

Deviations from the SPAT in minutes

Lo

g−

Lik

elih

oo

d

5.3 Robustness Checks: Short-run Models

As discussed above, the APAT is defined as median (observed) arrival time, whereas thedependent variable in the short-run model are the actual departure times. So, for thoseobservations that identify the median, the schedule delays in the PI regime are 0 by definition.This might potentially introduce endogeneity in the model. In order to investigate whetherthis affects the results, we re-define the median such that always one observation (perrespondent and per weekday) can be identified as median (also in the case of an even numberof observations). In the short-run model, these observations that were identified as themedian observations when calculating the APATs are left out. We find that the resultingestimates are not significantly different from those found in the standard short-run model(see the columns for ’Test 1’ in Table 5). So, we can conclude that endogeneity does notaffect our results.We presented the 3-domains model as a method to verify whether the APAT indeed drivesshort-run departure time decisions more strongly than the SPAT does. Table 5 provides theresults of two alternative models that address the same issue. First, we re-run the short-runmodel using the SPAT instead of the APAT. The columns titled ’Test 2’ in Table 5 showthat this model performs considerably worse in terms of predicting departure time decisionsthan the standard short-run model (it has a loglikelihood of -17919 compared to -12987 inthe standard model), and that the coefficient estimates are similar to those obtained in thelong-run model. Moreover, it is consistent with the long-run character of the SPAT that wefind a higher weight attached to the FI regime, θFI , than in the standard short-run model.Second, a model is estimated where both schedule delays with respect to the APAT andwith respect to the SPAT are included. PAT-type specific weights are attached to them:

16 5. ROBUSTNESS CHECKS

θAPAT and θSPAT (they sum up to 1). We find that the estimated weight attached to theSPAT related schedule delays is not significantly different from 0 (see the columns for ’Test3’ in Table 5), which further confirms that the scheduling costs with respect to the SPATare not very relevant for short-run departure time decisions.Finally, we test whether the particular shape of the APAT distribution over the time of theday, with a large share of drivers departing before the peak (Figure 2d), drives the outcomeof the short-run model. For this purpose, we re-estimate the short-run model applyingweights to the observations that are defined as inversely proportional to the density of theAPAT distribution7. The corresponding results are presented in the columns headed by’Test 4’ in Table 5. We find that the results of this weighted model are close to those ofthe standard short-run model. Therefore, we can conclude that the differences between theshort-run and the long-run values of time and schedule delay are not due to the unusualshape of the APAT distribution.

Table 5: Robustness checks for short-run model

Test 1 Test 2 Test 3 Test 4Coefficient Value t-Stat. Value t-Stat. Value t-Stat. Value t-Stat.α -1.23 -2.39 -6.11 -8.14 -1.55 -2.70 -0.70 -1.60β -2.98 -17.14 -1.81 -13.71 -3.62 -14.28 -3.29 -20.79γ -2.56 -20.41 -1.54 -17.97 -3.03 16.63 -2.92 -21.18δ 0.12 5.14 0.19 5.49 0.13 4.98 0.11 4.79θFI 0.53 12.24 0.88 33.71 0.56 10.28 0.53 11.89θPI 0.47 10.85 0.12 4.59 0.44 8.08 0.47 10.54θSPAT – – – – 0.05 1.36 – –θAPAT – – – – 0.95 25.84 – –−α/δ 10.41 30.79 11.95 6.14−β/δ 24.51 9.13 27.91 28.92−γ/δ 21.03 7.80 23.34 25.71−α/δ ∗ θPI 4.89 3.69 5.26 2.89−β/δ ∗ θPI 11.52 1.09 12.28 13.59−γ/δ ∗ θPI 9.88 0.94 10.27 12.08Nr. Obs. 6382 7605 7605 7605LogLik. -11609 -17919 -12982 -13470Pseudo R2 0.35 0.16 0.39 0.37

7The density of the APAT distribution is calculated using a normal kernel function with a bandwidth of0.05.

17

6 Conclusions

In this paper, we decompose scheduling decisions of travelers into long-run choices of routinesand short-run choices of departure times. Furthermore, we take into account that travelershave a less precise knowledge on travel times in the long run compared to the short run,where day-specific characteristics such as weather conditions become known to the traveler.We find that in the long run many travelers adjust their routines in order to avoid themost heavily congested periods. They trade off shorter travel times with the disutility fromdeviating from their ’structural PAT’ (SPAT), which is defined as the preferred arrival timeif no congestion occurs for sure. In the short-run model, we find that departure time choicesare more dependent on the schedule delays relative to the chosen routines, in particular the’adapted PAT’ (APAT), rather than on the schedule delays relative to the SPAT. This resultconfirms the dominance of chosen routines as determinant of short-run scheduling behavior.The values obtained for travel time and schedule delay differ considerably between long-runand short-run models. We find relatively high values of time and relatively low values ofschedule delay in the long-run model. Thus, travel time gains are valued higher if they aremore permanent, since they can be exploited better as travelers can re-adjust their routinesin order to fully benefit from these time gains. In the short run, however, routines are fixedand scheduling constraints are more binding, leading to higher values of schedule delays.Our results imply that different values of time and schedule delay should be used in theevaluation of policy options, depending on whether they lead to permanent changes in traveltimes (e.g. an increase in road capacity) or changes in travel times that occur only undercertain circumstances (e.g. incident management). As the value of travel time savingsincreases in the permanentness of travel time changes, while the value of gains in scheduledelays decreases in the permanentness, no definite conclusion can be drawn about whetherlong-run or short-run oriented policies decrease aggregate costs the most.Our results also have implications for the determination of optimal (road) pricing schemes.One question that we consider in follow-up research concerns the optimal pricing schedulefor a congestible facility when preferences take on the form suggested by this paper. Oneparticularly interesting aspect of the problem is whether a consistent application of optimalshort-run toll schedules, that optimize departure times given the APATs, lead to a long-runexpected toll schedule that optimizes the choice of APATs given the SPATs.This paper also gives some insights with respect to the costs of travel time variability. Thescheduling costs in the short-run model can be interpreted as costs that arise due to the factthat travel times are stochastic. These costs are substantial: 29.70 Euro/hour for arrivingearly and 25.08 Euro/hour for arriving late, clearly indicating significant costs of variability.Finally, the research conducted in this paper can also help explaining the substantialdispersion of the values of time and schedule delays that have been reported in the relevantliterature since we show that the results obtained from scheduling models are stronglydependent on whether the estimated models are oriented towards explaining long-runor short-run behavior. Furthermore, although our research is based on RP data, it hasimplications for SP experiments as well. So, it is likely that the phrasing of SP experiments

18 REFERENCES

affects whether respondents consider the choice alternatives as long-run or short-run decisions,which in turn can be expected to affect the results as well as their interpretation.

Acknowledgements

This study is financially supported by the Dutch Ministry of Infrastructure and the Environ-ment, as well as by the TRANSUMO foundation. Also the financial support from the ERC(Advanced Grant OPTION #246969) for the research of Paul Koster and Erik Verhoef isgratefully acknowledged. The authors would like to thank Carl Koopmans for very helpfulcomments.

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