Behavioral adjustments and equity effects of congestion pricing: Analysis of morning commutes during the Stockholm Trial

Transportation Research Part A 43 (2009) 283–296

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

Behavioral adjustments and equity effects of congestion pricing: Analysis of morning commutes during the Stockholm Trial q Anders Karlström *, Joel P. Franklin Transport and Economics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

a r t i c l e Keywords: Congestion pricing Equity Welfare Departure choice Mode choice Propensity score Matching estimator

i n f o

a b s t r a c t This paper assesses the horizontal and vertical equity effects of the Stockholm Trial with Congestion Pricing for morning commuters, in terms of both travel behavioral adjustments and welfare effects, as a result of the toll’s direct effects and the behavioral adjustments. We consider specifically two behavioral adjustments: mode choice and departure time choice. Initial car drivers crossing the toll cordon had a 15 percentage-points higher rate of switching to public transit as compared with those not crossing the cordon. We also find some evidence of peak spreading, in particular toward a later departure time, as a result of the charging scheme, but most people choose a departure time within 15 min both before and during the trial. In the welfare analysis, we found no clear pattern of increasing burden by either increasing income or decreasing income, and the increase in the Gini Coefficient was insignificant. We also found no significant difference in either the mode-switching behavior or the average welfare effect for women versus for men. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction This paper concerns the equity effects of Stockholm’s congestion pricing system, which was implemented on a trial basis during 2006 and restored on a permanent basis on 1 August, 2007. While congestion pricing has long been considered a social benefit in the aggregate, its Achilles Heel has also long been recognized to be its equity effects, largely because the rich or otherwise privileged are likely to be more able to cope with the toll than the poor or those who are otherwise disadvantaged, either by paying the toll or by adjusting behavior. In this paper we examine the empirical evidence from Stockholm’s congestion pricing trial in 2006 with respect to equity effects. In assessing the trial, we first examine observed changes in travel behavior, and then we estimate differences in welfare effects for different demographic groups. Following this introduction, we continue the paper with a brief background on the Stockholm Trial in Section 2, followed by a summary of the data and some initial observations in Section 3. We then start our analysis of equity effects in Section 4 by examining some of the behavioral adjustments that could be employed in response to a congestion charging scheme, and comparing those responses across genders and across income groups. There are a number of these: people can change their trip frequencies, car ownership, route choice, mode choice, departure time etc. We will consider in particular the latter two, mode choice and departure time. Mode choice is probably the most important behavioral adjustment, and we will look more closely into the question of who did switch mode, and

q This project was funded by VINNOVA, the Swedish National Road Administration, and Stockholm municipality. We acknowledge helpful comments and support by Jonas Eliasson, Lena Smidfeld Rosqvist, Annika Nilsson, Anders Levander, Muriel Beser Hugosson, and Ulf Tunberg. Computational assistance was provided by Aron Tesfaghebrel. * Corresponding author. E-mail address: [email protected] (A. Karlström).

0965-8564/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tra.2008.09.008

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what were their costs in terms of travel time increases. We also show that there was a 15% increase in travel time among car drivers who switched to public transit as the congestion charges were implemented. Departure time is also important in the context of equity analysis. It is a potential source of regressivity since, as Giuliano (1994) has argued, the poor may be less flexible in departure time than the rich. It is also interesting in its own right, since the time differentiated charging scheme was implemented with the intention of spreading the peak period. We show in this section that there is some evidence of peak spreading due to the toll, in particular to a later departure time. In Section 5, we turn to the question of total welfare effects of the congestion toll, of changes in travel time, and of other burdens that arise, given the travel behavior adjustments we observed. We estimate an average reduction in welfare of 376 SEK per year for those who drove in 2004, although those who took transit in 2004 experienced an average reduction in welfare of only 27 SEK per year. In each of these analyses, our focus is on the immediate effects, including adjustment in terms of mode choice and departure time, of the congestion charges themselves. However, we should emphasize that refunds from the collected toll revenues do matter. It has been shown by Eliasson and Mattsson (2006) and Franklin (2006) that the design of the refund scheme is of paramount importance for the equity properties of congestion charges. Still, we will ignore refunds altogether in this paper, for several reasons. First, when considering equity, any refund scheme will have to address the equity impacts of the congestion charges themselves. Second, the equity impacts of different refund schemes deserve a full-fledged analysis by itself. Third, in practice, the choice of how to redistribute revenues in the permanent implementation of Stockholm’s congestion charging system remains an open question. Another caveat is that the conclusions in the this paper are valid for the particular sample described herein. These are individuals whose situations were fairly stable between the two survey waves. In particular, people switching jobs or residential location were excluded. These individuals may have distinctly different preferences from those in our sample, for example by being more inclined than individuals in our selected sample to respond to the toll by changing mode choice. Still we believe that our sample is a interesting one, and when performing the analyses here, such as comparing the results with stated preference (SP) studies in Section 4.2 below, we believe it to be the most appropriate set of available empirical data for the task.

2. The Stockholm Trial With the stated primary objectives to ‘‘reduce congestion, increase accessibility, and improve the environment” (City of Stockholm, 2005, p. 2), the Stockholm Trial with Congestion Charging began on 3 January, 2006, and continued through 31 July, 2006. In addition, substantial public bus service enhancements and new park-and-ride lots were introduced nearly a year earlier. The toll system was set up as a cordon, where all vehicles entering or exiting the central city area across this cordon would be charged a fee, the amount of which depends on the time of day. Tolling began at 6:30 and ended at 18:30 each weekday, with a base toll level of 10 SEK per cordon crossing. During the shoulder periods and peak periods, the toll rose to 15 SEK and 20 SEK per crossing, respectively, where the shoulders were from 7:00 to 9:00 and 15:30 to 18:00 (except for the peak periods), and the peaks were from 7:30 to 8:30 and from 16:00 to 17:30. Certain types of vehicles, such as buses, taxis, motorcycles, and emergency vehicles, were exempt. After the trial ended, a referendum of City of Stockholm residents was held on the question of whether to implement the toll system on a permanent basis. The referendum passed with a yes vote of 52%, and tolls were restored on 1 August, 2007. 3. Data and initial analysis The travel survey used in this study was part of the official evaluation of the Stockholm Trial. In the first wave (October 2004), 77,000 surveys were sent to a geographically stratified sample of the population, encompassing individuals living in the Stockholm county aged 12–84. The travel survey was in the form of a travel diary. Each individual was asked to fill out a travel diary for a particular day. In the second wave (March 2006), only respondents of the first wave (36,049 individuals) were included. The response rates were 48% and 69% in the two waves, respectively. After the second wave, there were 10,088 individuals who made a work trip in both waves. The seasonal variation between fall and spring is by far the most serious problem in interpreting the results of the travel survey. During the first wave, the temperature was some 15 °C warmer than during the second wave. It is well established that there is a seasonal travel pattern in Stockholm, in particular for trip frequencies. As reported in Allström et al. (2006a), there is at the very least a 5% reduction in travel across the cordon in the spring. How this translates into trip frequencies for work trips is not clear, although it is unlikely that work trips are affected more than other trips. To partially circumvent problems with trip frequency, we will focus on a rather narrow group: those that actually made a work trip in both waves. In the total sample, there were 5294 that took a morning commute in both waves. By definition, trip frequency will not be a problem here. However, it may still be the case that mode choice and departure time exhibits a seasonal pattern. For instance, there is a huge (82%) reduction in the bicycle mode in the March second wave, compared to the October first wave. It is highly unlikely that this drop has anything to do with the congestion charges. While this is clear in the case of bike, there may be seasonal variation in other modes as well.

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A. Karlström, J.P. Franklin / Transportation Research Part A 43 (2009) 283–296 Table 1 Descriptive statistics by mode choice group. Attribute summaries by toll-effect group

Number observations Share of total observations Share with dependent children in 2004 Share with dependent children in 2006 Share female Average age in 2004 Average age in 2006 Share with formal flex-time in 2004 Share with formal flex-time in 2006 Share with informal flex-time in 2004 Share with informal flex-time in 2006 Average consumption category in 2004 Average consumption category in 2006 Average income category in 2004 Average income category in 2006 Share crossing the toll cordon Average auto travel time in 2004 Average transit travel time in 2004

Toll-effect group Tolled

Untolled

Tolled-off

Tolled-on

607 0.39 0.15 0.13 0.50 48.6 50.6 0.37 0.38 0.46 0.51 3.53 3.65 6.15 6.32 0.20 22.4 48.0

794 0.51 0.13 0.13 0.70 47.7 49.7 0.44 0.44 0.53 0.53 3.64 3.73 5.71 5.82 0.49 28.2 41.3

86 0.06 0.17 0.14 0.51 48.0 50.0 0.41 0.48 0.51 0.52 3.56 3.57 5.92 6.06 0.51 25.1 42.9

63 0.04 0.38 0.33 0.57 43.8 45.8 0.40 0.44 0.56 0.59 3.68 3.84 6.33 6.47 0.44 27.9 47.0

Since bike and walk are heavily affected by seasonal variation, we will only consider the mode choice between car and public transit in this paper, further restricting the sample to include only those taking either car or public transit to work in both survey waves. Only people with employment were included. As a final consideration, we selected only those who had the same origin and destination in both waves, meaning that we exclude those who moved residences or changed job locations. In total, we have 1550 individuals in the final data set that is used in this study. While seasonal effects are a problem, it should be noted that for most of this paper our focus is on equity issues, i.e. the differences between different groups. Such difference-in-difference estimates are more robust in the sense that our conclusions would still hold as long as the seasonal patterns are similar for different groups. Another caveat is bias due to non-response. To assess potential non-response bias, a separate non-response study was made after the second wave. Two hundred individuals were selected in the response group, and 200 individuals from the non-response group (in 2004 and 2006); both groups were given a follow-up survey by telephone. The findings of this study is reported in Allström et al. (2006a), with additional detail in the Swedish language report, Allström et al. (2006b). The main finding was that the non-response group made fewer trips than the response group. Furthermore, the mode share for walk and bike was also different. However these differences do not affect the present studies since we consider commuting trips conditional on the trip occurring and on the mode being car or transit. The mode shares, conditional on car or transit, were similar in the response and non-response groups, with a slightly higher car share in the non-response group.1 Another finding was that the proportion of trips (all purposes) crossing the toll cordon was higher in the non-response group. However, given the small samples, the only statistically significant finding was that the number of trips was smaller in the non-response group. In summary, in this study we will analyze those that made a morning commute from the same origin to the same destination, both before and during the trial. We are able to afford the luxury of being rather selective, which can be attributed to the rather huge sample of 77,000 individuals. In effect, by choosing our data carefully, we try to resemble a more stable situation with as little as possible changing. Nevertheless, all individuals age by one and a half years, most earn higher incomes, some have children, existing children age by one and a half years, car ownership may change, etc. Therefore, each individual is not exactly identical before and after, although we try to select those for whom the characteristics are the most stable. We will employ different statistical methods to address some of these problems in a sequel. Descriptive statistics of the 1550-person sample are shown in Table 1, where we have decomposed the data set into four groups defined by mode choice in each survey wave: the ‘‘Tolled” who were observed to take auto in both study years, the ‘‘Untolled” who took public transit in both years, the ‘‘Tolled-Off” who switched from auto to transit, and the ‘‘Tolled-On” who switched from transit to auto. These labels for the four possible traveler responses have been widely used in congestion pricing literature (e.g. Zettel and Carll, 1964), but the last label, ‘‘Tolled-On”, perhaps requires some clarification: we do not suppose that those who switch from transit to auto are doing so for the virtue of paying a new toll itself, but rather that they are attracted to the auto alternative by some reduction in congested travel times, which for these individuals is more valuable than the amount of the new toll. Note, further, that our survey respondents’ membership in these categories is not as firm as it may sound; someone observed to have driven in 2004 and taken public transit in 2006 may simply have been caught on an unusual day. However, collectively, the respondents observed to have made these choices are our best indicators of the attributes of travelers who actually did or did not shift behaviors due to the toll. 1

The mode share for car was 57% in the response group, and 59% in the non-response group. The difference was not statistically significant.

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The variables depicted in Table 1 are used in the discussion below. The term ‘‘Dependent Children” is defined as having children of age eight years and less. The household ‘‘Income Category” classifies household income into seven income categories, while consumption level is a household income per capita taking into account household composition in terms of age of its members. ‘‘Crossing the Cordon” is the variable indicating whether the trip involved passing the toll cordon (and, in the case of car, was subject to the toll for this trip under the charging scheme). Finally, ‘‘Formal Flex-Time” and ‘‘Informal Flex-Time” indicate two different definitions of working hours flexibility and scheduling flexibility, to be further discussed in Section 4.2. Table 1 describes raw figures, with no sample weights etc. It should be emphasized that the results in the rest of the paper will be based on analyses with weights2 employed. For instance, note that about 60% in the sample are women, possibly partially due to higher response rates for women, but the weights accounted for this in our analysis in the rest of this paper. Furthermore, another important piece of data needed for our analysis is travel times. Travel times were estimated both before and during the trial using the regional travel model, and estimates were provided by the official evaluation group. For further information, see Eliasson (2006).3 4. Behavioral adjustments We start our analysis of equity effects by examining how travelers adjusted their travel behaviors once the toll was implemented, and comparing these adjustment across genders and across income groups. We focus on two dimensions of travel choice: mode choice, particularly between automobile and public transit; and departure time. The methodologies employed to examine each of these are somewhat different, and are described separately in each subsection. 4.1. Mode choice adjustment In the context of morning commutes, the most important adjustment to consider is the change of mode. Due to the problem with seasonal effects for bike and walk, we only consider the choice between car and public transit. First, from Table 1 we note that most individuals go by transit to work, both before and after the trial. It is clear that there are gender differences in terms of mode choice. In the sample, 20% of the car drivers cross the toll cordon, while 51% cross the cordon among those switching from car to transit. This suggests that we will be able to detect a mode choice switch from car to transit. However, the number of individuals switching from transit to car is not negligible. On the other hand, while 49% of those sticking with transit cross the toll cordon, only 44% cross the cordon among those that switch to car. A majority of those switching to car are women, but the majority is even greater among those staying with transit. These descriptive figures suggest that there is an overall mode choice shift away from car to transit. We will employ a matching estimator to address the impact of congestion charges on the initial car drivers. Following the programme evaluation literature, we will here use the following definition: an individual is considered to be treated when (i) being an initial car driver, (ii) passing the toll cordon, and (iii) being eligible for paying the toll according to the charging scheme. In our sample, there are two outcomes once the toll is in place: an individual chooses either car or transit. Let Y 0j denote the outcome for individual j conditional on being untreated, and Y 1j is the corresponding outcome for an individual condition on being treated. It is clear that a using a dummy variable for the treatment variable would yield a biased estimator; treatment is not random in this setting, so the explanatory variable (treatment) would be correlated with the error term.4 We will therefore employ a propensity score matching estimator, see Rosenbaum and Rubin (1983). A matching estimator tries to match each treated individual with a similar untreated individual (control group). One estimate for ai , the average treatment effect of the treated (ATT) for an individual i, is:

ai ¼

N h i 1 X Y 1j ðX j j sj ¼ 1Þ  b E½Y 0j ðX j j sj ¼ 0Þ ; N j¼1

ð1Þ

where N is the size of the treated population and X i is a vector of characteristics for individual i, b E is an expectation estimator, and sj is a binary variable equal one if the individual is treated, while zero otherwise.5 In other words, for each treated individual we compare the outcome with an estimate of the expected outcome for individuals in the untreated group that have the same observed characteristics as the treated individual. It will be difficult to match individuals that match with respect to every observed characteristic (gender, age, travel time by car, travel time by transit, etc.). Different kernel regression weighting schemes can be employed, but we will here use a simple one based on the propensity score. In our case we will use a mode choice probability as a propensity score. Let eðX i Þ denote the probability of choosing car according to the estimated mode choice model. Now, individuals will be considered

2

The weights were calculated considering gender, age, geographical area, and background, as described in Allström et al. (2006a). In this paper we need travel time for each origin–destination in the sample, and these were not time differentiated. That is, the travel time during peak hour was time invariant. 4 For a motivation and tutorial on propensity score estimators, see, e.g., d’Agostino (1998). 5 Note that Y 1j is the outcome for individual j if it were treated. The individual may be member of the treated group or the untreated group, indicated by sj ¼ 1 and sj ¼ 0, respectively. Thus, the notation allows for counterfactual situations, see Eq. 2 below. 3

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A. Karlström, J.P. Franklin / Transportation Research Part A 43 (2009) 283–296 Table 2 Mode choice model used as propensity score estimate. Attribute

Travel time

Model 1

Model 2

Value

Std. error

Value

Std. error

0.08

0.02

0.08

0.02

1.17 0.89 0.16

0.35 0.12 0.12 – 0.01

1.36 0.90

0.36 0.12 – 0.11 0.01

Transit-only variables: Constant Gender is female Formal flex-time Informal flex-time Age

– 0.01

Auto-only variables: Auto distance Auto availability Log likelihood

0.06 0.47 1823.97

0.01 0.10

– 0.20 0.01 0.06 0.48 1823.36

0.01 0.11

equal if the propensity score is equal, i.e. eðX i Þ ¼ eðX j Þ. This reduces the dimensionality, since we now only have to compare a single index, viz. a mode choice probability. In practice, two individuals will never have exactly the same mode choice probability, so we will consider people that are nearby in terms of this probability to be the same. For this estimator to be valid, we need to make the important assumption that there is no selection bias from individuals being selected into the treatment group due to unobserved heterogeneity. Suppressing individual subscript j, one sufficient condition6 is:

EðY 0 j s ¼ 1; XÞ ¼ EðY 0 j s ¼ 0; XÞ ¼ EðY 0 j s ¼ 1; eðXÞÞ ¼ EðY 0 j s ¼ 0; eðXÞÞ;

ð2Þ

where eðXÞ is a mode choice model giving the probability for the individual to choose car. In essence, this means that an individual that crosses the toll cordon will behave the same as an individual that does not cross the cordon in terms of mode choice, if they are identical in observed characteristics X. If we consider two individuals that are identical in all respects except that one crosses the cordon and the other one does not, and they have an identical choice among car and transit, their behavior would be identical in the absence of toll. Since we use the mode choice probability as a propensity score (defining what we mean by ‘‘identical”), we are assuming that we can consistently estimate the same mode choice model whether individuals cross the cordon or not. The mode choice model that is used as a propensity score is reported in Table 2. We have retained some parameters that are not statistically significant at the 95% level, since the purpose of this model is simply to capture the concept of ‘‘similar” individuals in terms of mode choice. However, it may be noted that no income variables are present. This is because household income, consumption level and imputed income (see Section 5.3) were not nearly significant in this sample. There are two different variables capturing schedule flexibility: flexibility of working start and end times (formal flexibility) and other scheduling flexibility (informal flexibility). These are further described in the next section, but we here note that neither is significant, although informal flexibility is slightly larger in magnitude. We choose to use Model 2 in Table 2 as a propensity score. The average treatment effect for the treated (ATT) is found in Table 3. In the right panel, the four closest individuals in terms of mode choice probability were considered to be a match, while the eight closest individuals were considered in the left panel. For car drivers, the effect of the toll is quite large. For those crossing the toll cordon (and eligible), about 25% switch to transit, while only 10% do so in the control group (car drivers not crossing the toll cordon). For those that initially go by transit, 8% switch to car in the control group and 7% in the treated group (transit riders not crossing the toll cordon). It can also be noted that for both initial car drivers and initial transit riders, there are about 8–11% that switch modes even though their particular routes should not have been affected by the toll (slightly larger for switching away from car). At the same time, about 90% chose the same mode one and a half years later, even though congestion charging was implemented in between. The mode choice persistence is important because it illustrates that there are other reasons to change modes besides the toll, and that many respondents may only take the same mode part of the time. This becomes especially important when we consider horizontal equity in Section 5.1, where we wish to avoid overstating the effects on those who only drive part of the time but happened to drive on the day of the 2006 survey. If there was indeed a large effect on initial car drivers, causing them to switch to transit, then exactly who were they that switched from car to transit? First, Table 1 suggests that for this group, on average, public transit was a closer substitute (in terms of travel times) for car than it was for the group who stayed with the car mode. Furthermore, there is a only a slight preponderance (51%) for women, suggesting only small gender differences, if any. However, if we decompose the travel time changes by gender (in Fig. 1), there are some differences in travel time patterns across genders. The figure suggests that

6

In fact, the first equality is ensures Eq. 1 to be a consistent estimator of ATT. The condition is known as the conditional independence assumption (CIA).

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Table 3 Average treatment effect on the treated (ATT) estimates Route group

Average treatment effect on the treated Bandwidth* = 8

Not crossing the toll crdon Crossing the toll cordon Number of observations

Bandwidth* = 4

Tolled-off

Tolled-on

Tolled-off

Tolled-on

0.102 0.250 590

0.080 0.068 857

0.115 0.250 515

0.081 0.072 836

*

= thresholds used for determining which individuals are considered a ‘‘match” in terms of propensity score. In the left panel the threshold is the 8 closest individuals, it is 4 in the right panel.

15.4 Male

(b) By Income

20

40

60

80

1st/3rd Quartiles Outliers

0

Change in Travel Time (min/day)

20

40

60

80

Weighted Mean (also printed below) Median Value

0

Change in Travel Time (min/day)

(a) By Gender

24.3

26.8

Female

<25

Gender

20.1

16.1 40−55

25.3

15.9 >70

Income Group (1000 SEK/m)

Fig. 1. Travel time changes for individuals switching from car to transit.

public transit was a rather close substitute, in terms of travel times, for many men, while women who switched always suffered a significant travel time increase. It seems that those women whose travel times between car and transit were similar were in fact already transit riders in 2004. On average, the travel time increase for those switching away from transit was higher for women than for men, although some men also have considerable travel time increases as a consequence of the mode choice. 4.2. Departure time adjustment Another adjustment that is available to the commuters in our sample is to change departure time. Since the charging scheme during the Stockholm Trial was time differentiated, as opposed to other schemes such as London’s, it is interesting to see whether we can detect any changes in the departure times among the morning commuters. For example, can we detect any peak spreading? Moreover, changes in departure time are important in the context of equity and redistribution analysis, since it is a potential source of regressivity. Consider that in our sample, working hours flexibility is strongly correlated with household income and consumption level. The share of individuals reporting to have flexible working hours increases monotonically from 20% in the second lowest income group to 61% in the highest income group. If this also were to reflect a real ability to switch departure time, people in high income households would be able to avoid the toll to a greater extent than people in low income households. Indeed, this is exactly what has been suggested in literature (Richardson, 1977; Giuliano, 1994). Departure time choice has been analyzed before, both with stated preference (SP) data and revealed-preference (RP) data.7 Our RP panel data allows us to analyze what happened with departure time after a time differentiated congestion scheme was implemented. It is therefore interesting to compare the results in this study with other studies, which either use SP data or

7

We recommend Saleh and Farrell (2005) and references cited therein.

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A. Karlström, J.P. Franklin / Transportation Research Part A 43 (2009) 283–296 Table 4 Departure time changes between 2004 and 2006 Consumption category

Change in departure time Zero change

Same period

Earlier

Later

15-Minute threshold for same period 1 (Poorest) 2 3 4 5 (Richest)

0.27 0.28 0.20 0.21 0.21

0.41 0.38 0.47 0.47 0.48

0.14 0.15 0.16 0.16 0.18

0.18 0.20 0.18 0.16 0.13

30-Minute threshold for same period 1 (Poorest) 2 3 4 5 (Richest)

0.27 0.28 0.20 0.21 0.21

0.52 0.57 0.64 0.60 0.67

0.11 0.07 0.07 0.10 0.08

0.11 0.08 0.09 0.09 0.04

Table 5 Estimates for departure time model Attribute

Value

Constant (earlier) Constant (later) Formal flex-time (earlier) Cross the toll cordon (earlier) Cross the toll cordon (later) Start time (earlier) Start time (earlier) Dependent children (earlier) Dependent children (later)

1.78 3.91 0.74 0.43 0.55 0.82 4.02 0.73 0.81

Number of observations Log likelihood at convergence Log likelihood with alternative specific constants Log likelihood at zero

Std. error 0.35 0.49 0.31 0.33 0.33 0.60 0.78 0.43 0.39 607 440.04 486.21 641.20

do not involve a before-and-after study. In particular, we will here see to what extent we can replicate some of the results of Saleh and Farrell (2005) (henceforth referred to as SF). To this end, starting with the sample described in Section 2, we take a subsample of individuals traveling by car both before and after the toll scheme was implemented. The remaining sample consists of 607 individuals, which have rather stable characteristics. The departure time choices were quite persistent. Table 4 shows the distribution of departure time changes across consumption level categories (1 being the lowest and 5 being the highest). Fully 20–30% reported departing at exactly the same time. We also note that this persistence is slightly stronger among households with lower consumption level. Overall, 65% change their departure times by less than 15 min or not at all. To examine whether we can attribute these changes to the congestion charges, we will follow the procedure used by SF and estimate a simple departure time switching model. Hence, we estimate a multinomial logit (MNL) model with three alternatives. The first alternative is to not change departure time. We have chosen to interpret this as having a departure time that is the same within 15 min. The other two alternatives are to switch to an earlier and a later departure time. It should be noted that we do not have access to the exact same variables that were available in SF. In particular, we are lacking many variables with respect to scheduling flexibility, especially due to non-work related reasons. Indeed, this is a special feature of the SF study. However, we do have two sets of variables from the travel survey. The first set (‘‘Formal Flex-Time” in Table 1) reflects traditional working hour flexibility, while the second set of questions were much more complex. The purpose of this second set of questions (coded into ‘‘Informal Flex-Time” in Table 1) was to reflect whether there were other constraints, either to leave home before a certain time, having to be at work before a certain time, or other scheduling constraints. It was evident that this latter set of questions did slightly better to explain mode choice, as indicated earlier. However, it turns out that the simpler variable on work hour flexibility, Formal Flex-Time, had more explanatory power in the context of departure time choice. The estimated MNL departure time model is reported in Table 5.8 First, note that gender was not significant. We have tested various models, and it seemed that there are only very small changes between the genders with respect to departure time changes. Furthermore, income variables turn out to be insignificant. We have tried household income itself, consumption 8 We also tested a nested logit model, as well as an error component mixed logit model, to relax the i.i.d. assumption of the MNL model. More specifically, it is possible that the utilities for the alternatives for changing departure time (the second and third alternatives) are more correlated with each other than with the alternative of not switching. However, the MNL model could not be rejected against the nested logit, nor against the mixed logit model.

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level using different definitions, and imputed individual income as defined in the next section, but we cannot reject the hypothesis that departure time was independent of income, when controlling for scheduling flexibility. However, as argued earlier, scheduling flexibility is strongly collinear with income. From the statistical analysis alone we cannot determine whether departure time flexibility is due to income variable or scheduling flexibility, but for obvious reasons it seems more likely that work flexibility is the more important variable. Other studies, e.g. SF and de Palma et al. (1997), have also shown that work flexibility was an important determinant for departure time changes. Still, when addressing equity below, it is important to remember that higher income individuals are overall more flexible than low income individuals, as evidenced by the collinearity. Second, the toll variable was not significant, given the limited amount of observations. The magnitude of the variable seems to be higher for later departures, as compared with earlier departures. Third, SF found that household composition is a significant determinant, but the literature is inconclusive on the sign so far. Here, the most important variable is dependent children, which turns out to be significant for departing later; this is in contrast with the finding of SF. Whether this is a seasonal effect or due to congestion charges cannot be determined from our sample. In summary, we support the conclusion in SF in that people seem to be rather inflexible in their departure time choice. In fact, in our sample a vast majority choose departure times in 2006 that are within 15 min of their departure times in 2004. Considering the one-and-a-half year lag between survey waves, the difference in season and weather, and the introduction of the toll system in between, these results show a rather high degree of inertia in departure time. Indeed, we do see some evidence for peak spreading, but then more to the later times of day, in contrast to the shifts earlier in the day as found by SF. Finally, we confirm that individuals’ own scheduling flexibility and work hour flexibility indeed affect the ability to switch departure time. With respect to equity implications, although income itself was not significant, we suspect that it is a significant determinant of scheduling flexibility, and hence would have an indirect relationship. 5. Welfare distribution analysis We have seen in detail what adjustments were made in response to the toll, and how those adjustment were made by different subgroups of the study sample. Now using this information, we turn to estimating the welfare effects of the toll system and examining the distributions of those welfare effects with respect to vertical and horizontal equity. We focus on three specific comparisons: first, we compare welfare effects on those who initially drove to work versus those who initially took transit; second, we compared welfare effects across income levels; and third, we compared males versus females. Through the second and third analyses, we will continue to monitor the results with respect to which travel mode was originally chosen for the work trip. 5.1. Method of estimating welfare effects In our analysis, we estimated welfare effects by combining observed commute mode choices, both before and during the congestion pricing trial, with knowledge of the amount of toll paid and the estimated travel times for both the mode taken (among driving alone and taking public transit) and for the mode not taken in each case. The travel time estimates were obtained from the regional travel demand forecasting model. Note that the travel model provided only flat estimates for travel times across the entire peak period, so we have no way to differentiate between travel times at different points in time. We estimated welfare effects using the Rule of Half, a standard approximating method wherein we assume a linear demand function (Lakshmanan et al., 2001), except that whereas the typical procedure is to estimate probabilities of each travel choice, in this case we observe directly all travel choices, so we can insert instead an indicator, dsm;d , of whether an individual chose mode m and departure time d in state s, taking on a value of 0 or 1. The Rule of Half can then be stated as in Eq. (3):

DW ¼

  h X   1 X 0 dm;d þ d1m;d c0m;d  c1m;d þ d0m;d þ d1m;d t0m;d  t 1m;d ; 2 m;d 2 m;d

ð3Þ

where dsm;d is a binary indicator that mode m and departure time d were chosen in state s, csm;d is the out-of-pocket cost of mode m and departure time d in state s, h is the value of time, and tsm;d is the travel time of mode m and departure time d in state s. We can simplify Eq. (3) using several observations: first, the price of public transit does not change, so its costs are equal in both survey periods, and we need only consider cost changes for automobile; second, our travel time estimates for transit are static between scenarios, hence the travel time component for transit similarly drops out from the equation; and third, our travel time estimates for automobile are insensitive to time of day, thereby we must assume a constant travel time during the peak period automobiles. We can also restate the costs for automobile in terms of the actual toll amount. In doing this, we also include a factor representing the average vehicle occupancy; since multiple occupants would likely share the cost of the toll, we must reduce the toll’s monetary effect accordingly. We then restate the cost change for autos as c0a;d  c1a;d ¼ 

s1a;d /

, where

s1a;d is the toll level for autos during time period d, and / is a vehicle occupancy factor for sharing

the cost of the toll. As a result of all these simplifications, we can restate Eq. (3) as follows:

A. Karlström, J.P. Franklin / Transportation Research Part A 43 (2009) 283–296

DW ¼ 

 s1   1 X 0 h a;d da;d þ d1a;d þ d0a þ d1a t 0a  t 1a : 2 d 2 /

291

ð4Þ

It is useful in our case to rearrange the terms in Eq. (4) so that they more clearly distinguish between three component effects of the toll system, mirroring the procedure used by Eliasson and Mattsson (2006), resulting in the terms Eqs. (5)–(7) as follows:

DW ¼ 

X d

s1a;d /

d1a;d ðTolls PaidÞ

  þ hd1a t 0a  t1a ðTravel Time SavingsÞ " # X d0a;d  d1a;d s1a;d 0  1   h t a  t a ðAdjustment BurdenÞ; 2 / d

ð5Þ ð6Þ ð7Þ

where / is the expected vehicle occupancy for automobiles. Note that since the cost of transit does not change, we can focus 1 the out-of-pocket computations on the automobile mode, a, which sees a cost increase equal to the relevant toll da . In dissecting the components of the welfare effect, term Eq. (5) represents the expected amount actually paid in tolls; the second term, (6), represents the value of travel time savings; and the last term, (7), is a simple approximator for the burden of switching modes due to the toll using the rule of half. The value of time savings, h, in the equations above, was estimated to be 65 SEK/h for the entire study sample, an assumption that has its advantages and its drawbacks. It has long been understood that the monetary value of time tends to be greater for those with higher incomes than for those with lower incomes (Moses and Williamson, 1963). This is especially important for understanding travel behavior, particularly the trade-offs that individuals in different socio-economic groups make between time and money. Hence, by making the assumption of a constant value of time, among the rich we may be underestimating the relative value of travel time savings compared to the burden of tolls paid, and among the poor we may be overestimating the same. However, in the context of a social welfare assessment, the use of an increasing value of time with income runs the risk of causing time savings for the rich to be seen as more beneficial for society as a whole than the same time savings for the poor. Indeed, an examination by Mackie et al. (2001) finds that the use of differentiated willingness-to-pay as a proxy for social value of time savings in a welfare analysis would be inappropriate, and that in the absence of grounds for social weights for different socio-economic groups, the use of a single value of time is justified. Hence, in our analysis we choose a constant value of time, and we acknowledge that the relative value of time savings versus toll costs may be biased, with the direction of that bias depending on income level. Before presenting the results, we alert the reader to several considerations regarding adjustment factors and units of measurement. First, time savings are expressed in minutes per day, while welfare effects are expressed in SEK per year, assuming 220 work days per year. Also, recall from Section 4.1 that about 8–11% of travelers who were not affected by the toll still chose a different mode in 2004 than in 2006. In other words, there are obviously other reasons, besides the toll, for people to not take the same mode on the survey day in 2004 as on the survey day in 2006. Given this evidence, we should account for the possibility that there are many travelers who vary their choice of commute mode on a regular basis. Since we do not know who, in particular, varies their mode more often than others, we simply apply an adjustment factor to the entire study sample, resulting in a scaling down of the full set of welfare results. In particular, we multiply the results by a factor of 88% (set below 90% to be conservative) to account for those who do not drive every day. As a final adjustment, we assumed an average vehicle occupancy of 1.27, so all results were divided by this number to reflect the effects on individuals, rather than on vehicles. 5.2. Overall welfare effects The average welfare effects are summarized in Table 6. The average change in welfare across the study sample, after sample weighting, was 189 SEK per year. Isolating only those who initially drove to work, the average effect was significantly higher, at 376 SEK per year. At the same time, those who initially took transit to work in 2004 nearly all continued to do so in 2006, and hence when we average the welfare effects across those who did and did not switch from transit, we obtain the small, but significant, figure of 27 SEK per year. In reality, some small additional travel time savings were likely enjoyed by bus riders as a secondary effect of reduced congestion on the roadways used by buses, but because we relied on the regional travel model to estimate transit travel times, we are not able to estimate this secondary effect. In any case, a greater proportion of the transit riders take a grade-separated rail system, rather than bus, and therefore their travel times would not be reduced by any relief in roadway congestion. Table 6 includes t-statistics that both assess the magnitudes of welfare effects in each demographic group and compare the differences between demographic groups. In the second column, the t-statistics against zero demonstrate that all demographic groups experience significant effects. Moreover, all demographic groups, when compared individually against all other groups, have significantly different welfare effects, with the exception of gender groups; men and women did not have significantly different overall welfare effects. The last two columns of Table 6 show the results of t-tests when comparing each income group to either all lower income groups, or to all higher income groups, showing mixed results.

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Table 6 Summary of welfare effects t-Stat. vs. zero

t-Stat. vs. other

t-Stat. vs. poorer

t-Stat. vs. richer

By initial commute mode All 189 Automobile 376 Public transit 27

Avg. effect (SEK/year)

83** 92** +20**

– 92** +92**

– – –

– – –

By tolled initial commute Tolled autos 1840 All others +69

227** +52**

229** +229**

– –

– –

By income group (SEK/month) <25,000 321 25–40,000 199 40–55,000 35 55–70,000 348 >70,000 219

52** 43** 22** 34** 32**

20** +4** +35** 8** 9**

– +16** +30** 9** 9**

20** 4** +27** +2 –

By gender Male Female

48** 69**

+0.8 0.8

– –

– –

175 202

t-Test significance levels: * = significant at <0.05,

**

= significant at <0.01.

As we already saw from Section 4.1, most travelers did not switch modes. Moreover, even those who drove initially may not have crossed the toll cordon, hence the averages above include some drivers who would be subject to the toll and some who would not. However, all drivers may well have benefited from reduced congestion on the roadways on which buses and untolled cars travel. Among those who initially drove but did not cross the cordon, we estimated an average welfare increase of +69 SEK per year due to these secondary travel time savings. In contrast, isolating only those drivers whose paths did cross the toll cordon, the average welfare effect was 1840 SEK per year; this reflects those who felt the full brunt of paying the tolls. Our interest in equity effects compels us to move beyond averages, to the distributions of effects, so that we can examine not only the central tendencies but also the divergence of effects across individuals, such as between winners and losers. We can examine the divergence of effects by estimating probability density functions (PDFs), which play a similar role to histograms in that they illustrate at what welfare levels and within what welfare ranges were there the greatest concentrations of individuals. We estimated these PDFs using a kernel density estimator with a consistent bandwidth across all of the results presented here. In PDF estimation, the data were weighted by their sampling weights. Consider first the probability densities in Fig. 2, starting with Panel (a). The dominant peak of the density function at zero SEK per year, which extends vertically well above the extent of the plot, indicates that the bulk of the population felt no welfare effect at all. However, for a large minority there was a noticeable effect, which was positive for some and negative for others. Moving to Panel (b), we can attribute most of the negative effects to the tolls paid; this burden could only take on one of three levels given by the toll schedule, depending on the time of day that the cordon was crossed. Travel time effects, shown in Panel (c), could be positive or negative, suggesting that the congestion relief from the toll system was not universal. Finally, the adjustment effects in Panel (d) were negligible; this is consistent with our earlier finding that only a small proportion of commuters did, in fact, adjust modes in response to the toll. The overall results in Fig. 2 (indicated by solid black lines) were strongly affected by a large number of zero-size effects, many of which were transit riders who did not switch modes, and hence had no effect. To focus more specifically on the nonzero effects, the dashed lines indicate the results for only those travelers who initially commuted by car. Now, we can see more clearly that those drivers were, by and large, negatively affected – some by nearly 20 SEK per day. A clear burden came from the toll itself, at least for those who continue to drive, but an even greater burden was carried by those who shifted from auto to transit. Meanwhile, the solid grey lines indicate that those who began by taking transit to work experienced mainly changes in travel time. 5.3. Welfare effects by income level We have now seen that the welfare effects were not uniform – some had positive effects, some negative effects. A pressing policy question is whether there was a pattern between these effects and income level. To examine this, we first compare the distributions of effects in each income category, using the reported household incomes from the travel survey, as shown in Fig. 3. The four panels (a) through (d) show, respectively, the total effect, the effect of tolls paid, the effect of travel time changes, and the effect of adjustment costs. The first finding from Fig. 3 is that no clear pattern emerges – either in the total welfare effect, or in any of the component effects. This agrees with the findings from Sections 4.1 and 4.2, in which we saw that income was not a significant determinant of mode choice or departure time choice: the result of similar travel patterns across income groups is that the welfare effects should also be similar across income groups. Even if we were to focus only on those who initially drove to work, we would see similar results to Fig. 3.

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All (−189.5) Initial Drivers (−376.0) Initial Transit Riders (−27.3)

−2500

−1500

−500

0

500 1000

0.0000 0.0010 0.0020

(b) Toll Costs

Density

0.0000 0.0010 0.0020

Density

(a) Total Effect

All (−240.6) Initial Drivers (−446.8) Initial Transit Riders (−61.3)

−2500

Change in Welfare (SEK/year)

0

500 1000

Change in Welfare (SEK/year)

0.0000 0.0010 0.0020

Density

0.0000 0.0010 0.0020

Density

Initial Drivers (101.9) Initial Transit Riders (6.74)

−500

0

500 1000

(d) Adjustment Costs

All (51.0)

−1500

−500

Change in Welfare (SEK/year)

(c) Travel Time Savings

−2500

−1500

All (0.0982) Initial Drivers (−31.1) Initial Transit Riders (27.3)

−2500

−1500

−500

0

500 1000

Change in Welfare (SEK/year)

Fig. 2. Densities of welfare effects. Mean effects for each mode group are shown in parentheses.

Despite the absence of an overall pattern, a sequence of t-tests for each household income group against all higher income individuals and against all lower income individuals shows that there were some more subtle significant differences. The results of these t-tests are shown in Table 6. In particular, the evidence indicates that those in the center income group lost the least, while those in the two highest groups lost much more. Most concerning is that those in the lowest income group appear to have received the second largest burden of the five income groups, second only to the next-to-highest income group. The irregular pattern here stems from a variety of differences between these groups’ travel patterns, with the most prominent being the proportion of travelers in each household income group who drove and whose paths crossed the toll cordon. The center income group had the lowest proportion driving across the cordon, 6.3%, while the lowest group and the two highest groups had 17.1%, 17.4%, and 17.8%, respectively. This does not entirely explain the large burden carried by the lowest income group, however. Another contributing factor was that the lowest income drivers received the lowest auto travel time reductions of all income groups, with an average savings of 0.08 min per morning commute compared to an average savings 0.30 min among all other income groups. In other words, it appears that there was a tendency for those in the lowest income group to have a ‘‘worst of both worlds” effect, whereby they had a high propensity to cross the toll cordon, but their overall routes did not take advantage of the toll system’s congestion relief. What can these results tell us about the congestion pricing system’s total equity effects? From both academic literature and in popular thought, there is a commonly held perception that while congestion pricing may be progressive across all travelers, because the poor would tend not be driving in the first place, it would yet be regressive among auto drivers themselves. Yet, the absence of a consistent trend across household income levels in our findings makes it difficult to come to any conclusions. Another approach is to summarize the progressivity or regressivity of the toll system’s welfare effects using a unified equity measure. To do this, we must treat the welfare effect as directly altering one’s income level, even if only slightly. This approach enables us to examine the effect that the toll would have on the distribution of total welfare levels, as indicated by daily individual income. We can then compute Gini Coefficients, a common measure of inequality with several desirable properties (Cowell, 1977), to summarize the progressivity or regressivity of the toll system. Unfortunately, exact individual incomes were not available, since only the household income category was reported in the travel survey. Instead, we have imputed exact incomes. In short, we used the characteristics of the household (age,

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(b) Toll Costs

−2500

−1500

−500

Density

<25k (−320.7) 25−40k (−199.1) 40−55k (−35.0) 55−70k (−348.4) >70k (−218.7)

0

500 1000

0.0000 0.0010 0.0020

0.0000 0.0010 0.0020

Density

(a) Total Effect

<25k (−327.4) 25−40k (−239.8) 40−55k (−70.9) 55−70k (−503.9) >70k (−273.7)

−2500

Change in Welfare (SEK/year)

−500

Density

<25k (14.3) 25−40k (29.9) 40−55k (47.8) 55−70k (133.2) >70k (62.4)

−1500

0

−500

0

500 1000

(d) Adjustment Costs

500 1000

0.0000 0.0010 0.0020

0.0000 0.0010 0.0020

Density

(c) Travel Time Savings

−2500

−1500

Change in Welfare (SEK/year)

<25k (−7.58) 25−40k (10.8) 40−55k (−11.9) 55−70k (22.3) >70k (−7.41)

−2500

Change in Welfare (SEK/year)

−1500

−500

0

500 1000

Change in Welfare (SEK/year)

Fig. 3. Densities of welfare effects, by household income group. Mean effects for each income group are shown in parentheses.

Male (−175.4) Female (−201.7)

−2500

−1500

−500

0

500 1000

0.0000 0.0010 0.0020

(b) Toll Costs

Density

0.0000 0.0010 0.0020

Density

(a) Total Effect

Male (−235.5) Female (−245.0)

−2500

Change in Welfare (SEK/year)

0

500 1000

Change in Welfare (SEK/year)

0.0000 0.0010 0.0020

Density

Density

0.0000 0.0010 0.0020

−500

0

500 1000

(d) Adjustment Costs

Male (64.6) Female (39.3)

−1500

−500

Change in Welfare (SEK/year)

(c) Travel Time Savings

−2500

−1500

Male (−4.43) Female (4.0)

−2500

−1500

−500

0

500 1000

Change in Welfare (SEK/year)

Fig. 4. Densities of welfare effects, by gender. Mean effects for each gender group are shown in parentheses.

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household composition, and residential zone) to match each individual with similar individuals in a registry of income data. For instance, for an individual living in a certain residential zone, from registry data we have sampled those individuals in the same zone that have the same gender, age, and household income category. For some individuals, we used different ‘bandwidths’ in terms of allowed spans of ages and income categories. In the median, this resulted in a sample of 20 matched individuals for each individual in the data set. Using the imputed individual incomes, we can estimate a probability density function for welfares both before the toll and during the toll, taking the welfare effect from the Rule of Half to be an increment on daily income during the toll. Using the imputed individual income levels as baseline 2004 welfare estimates, we computed Gini Coefficients for both before the tolls and, by adding together the welfare effects, for during the toll trial. The Gini Coefficient for the imputed individual income levels, representing 2004, is 0.2778. When we introduce the toll system, the overall equity effect is to raise the Gini Coefficient to 0.2785 – an increase of +0.0007. This suggests that the toll is regressive, but the change is very small. Indeed, using the bootstrap method as described by Hesterberg et al. (2005), with 10,000 repetitions, we can only say with an estimated 74.7% confidence that this is significant. Hence, although we did see some differentiation in welfare effects among the five income groups, we cannot confirm that there is an overall trend of either regressivity or progressivity. 5.4. Welfare effects by gender In our final examination we consider the welfare effects on men versus women. Men, on average, experience a loss of 175 SEK per year, while women experience an average loss of 202 SEK per year. While this is a noticeable difference, it is not statistically significant; indeed, the variations within each gender group are considerably greater than the variations between them. In Fig. 4 we look more closely at the distribution of welfare effects for each gender. Panel (a) shows the total effect, while Panels (b) through (d) show the component effects. As expected, we see that women have a greater number of zero-values for cost burdens and adjustment burdens, owing to less overall use of automobile than for men. 6. Conclusions In this paper we have examined the behavioral responses of a rather inflexible group, namely those that travel from the same home location to the same work location during morning rush hours both before and after the toll was implemented. Commuters as a group of particular interest, since it is a major goal of congestion pricing to reduce morning traffic congestion. We have focused on behavioral adjustment with respect to mode choice and time departure. First, both mode choice and departure time choice is highly persistent in this group. Most individuals do not change behavior, or only slightly so. Still, we are able to detect changes in both mode choice and departure time. It is shown that initial car drivers crossing the toll cordon had a 15 percentage-points higher rate of switching to public transit as compared with those not crossing the cordon. Also, we can detect a weak effect on time departure due to the congestion pricing, in particular to an earlier departure time. The results of the welfare analysis detected some regressive effects, similar to those cited in previous literature, but they did not do so conclusively. The toll policy appears regressive overall according to the Gini Coefficient, but the magnitude of the overall effect is not significant. Nevertheless, we did find that some income groups do significantly worse than others: specifically, the lowest income group and the two highest income groups were the worst-off. The situation may in fact be even worse than it seems here: in this study, we assumed a constant value of time, but it is more likely that lower income individuals value time less than higher income individuals. We also implicitly assumed a constant marginal utility of money. The consequence of these choices is that the estimates of travel time benefits or burdens may have been skewed, favoring effects on the well-off rather than effects on the worse-off. With respect to gender, the comparison of males and females suggested that males, in general, might fare better than females – even though they are more likely to drive – because they tend to benefit from larger travel time savings, but that the difference are too small to be considered significant, especially compared to the differentiation in welfare effects within each gender group. A final note is that we have completely disregarded any effects that may arise from using the toll revenues. In the trial, revenues were used mainly to support public transit, but in the permanent installation this is an open question. It is certain that the final equity effects will be profoundly affected by the choice of how to use these revenues. References Allström, A., Bengtsson, L., Neergaard, K., Nilsson, A., Smidfelt Rosqvist, L., Ström, L., Viklund, L., 2006a. Changes in Travel Habits in Stockholm County: Effects of the Stockholm Trial. Rapport 2006:67. Trivector Traffic AB, Stockholm. Allström, A., Bengtsson, L., Neergaard, K., Nilsson, A., Smidfelt Rosqvist, L., Ström, L., Viklund, L., 2006b. Resvanor i Stockholms län: bortfallsundersökningar. Rapport 2006:21. Trivector Traffic AB, Stockholm. City of Stockholm, 2005. Information Brochure: On Stockholm’s Trial, English Version. Cowell, F.A., 1977. Measuring Inequality. Philip Allan, Oxford, UK. d’Agostino, R.B., 1998. Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group. Statistics in Medicine 17, 2265–2281. de Palma, A., Khattak, A.J., Gupta, D., 1997. Commuters’ departure time decisions in Brussels, Belgium. Transportation Research Record 1607, 139–146.

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Eliasson, J., 2006. Cost-benefit analysis of the Stockholm congestion charging system. Report No. 31. Transek, Solna, Sweden. Eliasson, J., Mattsson, L.-G., 2006. Equity effects of congestion pricing. Transportation Research Part A 40, 602–620. Franklin, J., 2006. Decomposing the distributional effects of roadway tolls. In: Paper Presented at the Transportation Research Board 86th Annual Meeting, Washington, DC, January 21–25. Giuliano, G., 1994. Equity and fairness considerations of congestion pricing. In: Special Report 242: Curbing Gridlock: Peak-Period Fees to Relieve Traffic Congestion, vol. 2. Transportation Research Board, Washington, DC. Hesterberg, T., Moore, D.S., Monaghan, S., Clipson, A., Epstein, R., 2005. Bootstrap Methods and Permutation Tests, second ed. W.H. Freeman, New York. Lakshmanan, T.R., Nijkamp, P., Rietveld, P., Verhoef, E.T., 2001. Benefits and costs of transport: classification, methodologies and policies. Papers in Regional Science 80, 139–164. Mackie, P.J., Jara-Diáz, S., Fowkes, A.S., 2001. The value of travel time savings in evaluation. Transportation Research Part E 37, 91–106. Moses, L.N., Williamson Jr, H.F., 1963. Value of time, choice of mode, and the subsidy issue in urban transportation. The Journal of the Political Economy 71, 247–264. Richardson, H., 1977. A note on the redistributional effects of road pricing. Journal of Transport Economics and Policy 8, 82–85. Rosenbaum, P.M., Rubin, D.B., 1983. The central role of the propensity score in observational studies for casual effects. Biometrika 70, 41–55. Saleh, W., Farrell, S., 2005. Implications for congestion charging for departure time choice: work and non-work schedule flexibility. Transportation Research Part A 39, 773–791. Zettel, R.M., Carll, R.R., 1964. The basic theory of efficiency tolls: the tolled, the tolled-off, and the un-tolled. Traffic Congestion as a Factor in Road-User Taxation, Highway Research Record 47, 46–65.