Fare Pricing Elasticity, Subsidies,
and Demand for Vanpool Services
Sisinnio Concas, Philip L. Winters, and Francis W. Wambalaba
the impact of fare pricing and subsidy policies to meet program goals
and requirements.
In the literature, TDM research has been concerned mostly with
evaluating the effectiveness of measures aimed at reducing solo
driving. Its focus has been on strategies geared toward penalizing
single-occupancy vehicle (SOV) use, providing incentives to use
alternative modes, or changing the time and frequency of trips. Several studies have examined the effects of incentives and disincentives
on commuters’ mode choice, concentrating their efforts mostly on
assessing the impact of pricing policies as a means of discouraging
solo driving, often with contrasting results. For example, some suggest that free parking is considered as a major barrier to many work
site ridesharing programs (3). Baldassarre, et al. however, conclude
that commuter responses to parking pricing are less marked than previously inferred, suggesting a resistance to changes in solo driving
behavior in response to higher parking costs (4 ). Using a stated preference approach, Kuppam et al. demonstrate that travel behavior is
affected by parking pricing, with trade-offs between transportation
modes related to commuter sociodemographic attributes and travel
patterns (5).
Most studies that attempt to establish measures of price responsiveness with respect to mode shifts focus on transit ridership [for a
comprehensive review of elasticity studies with a focus on transit, see
TCRP Project H-6 Synthesis (6)]. However, relatively few studies
commissioned to assess specific vanpool programs have attempted
to establish measures of price responsiveness as a means of promoting successful ridership programs (7 ). In a more generic framework,
although Ferguson demonstrates that direct incentives to employees
have the largest and most consistent impact among TDM pricing
instruments, accounting for firm cohort and size, he does not model
the impact of fares on rideshare (8).
The objective of this study is to empirically examine fare pricing
responsiveness and the impact of subsidies on vanpool ridership. By
means of a discrete choice modeling approach, the choice of vanpool
services and the effects of subsidy programs and price on vanpool
demand are investigated. By using employer and employee data
from the 1999 survey of the commute trip reduction (CTR) program of the Puget Sound region (Washington), a conditional logit
model is built to analyze vanpool choice with respect to competing
means of transportation as a function of various socioeconomic
characteristics.
Results indicate that vanpool demand is relatively inelastic with
respect to fare changes. In particular, the direct elasticity of demand
with respect to its fare is equal to −0.73, indicating a relatively low
responsiveness to fare pricing changes. For example, a fare reduction
of 10% is associated with an increase of 7.3% in demand. This is in
contrast with a reported elasticity factor of −1.16 used in a previous
study (7 ). Furthermore, the sensitivity to price fare changes declines
as the distance increases beyond 60 mi, as individuals become less
responsive to price changes.
Practitioners of transportation demand management consider pricing a
crucial determinant of vanpool market demand. Publicly sponsored programs stress the significance of fare pricing and subsidies as key tools for
increasing ridership. This paper considers the use of discrete choice modeling techniques to investigate the effects of fares and fare subsidies on
the demand for vanpool services. With the use of employer and employee
data from the 1999 survey of the commute trip reduction program of the
Puget Sound region (Washington), a conditional discrete choice model is
built to analyze the choice of vanpool services, with competing means of
transportation as a function of various socioeconomic characteristics.
The predicted value of the direct elasticity is −0.73; a 10% increase in
vanpool price is associated with a 7.3% decrease in its demand and vanpool demand is relatively inelastic with respect to fare changes. For trips
shorter than 30 mi, the individual elasticities are equivalent to the aggregate estimate. As the distance from home to work increases beyond
60 mi, individuals are less responsive to price changes. Subsidies have
a relevant impact in increasing ridesharing, controlling for firm size and
industry sector. Whenever employees are offered a subsidy, the predicted probability of choosing vanpool more than doubles. These results
show that factors other than fare pricing, such as employee profile,
industry sector, firm size, parking policies, and travel patterns, must be
taken into account when policies or designing fare schedules geared at
stimulating ridership are implemented.
Vanpooling is a travel mode that brings five to 15 commuters together
in one vehicle, typically a van. As a mode of travel, public transit
agencies report that vanpooling accounts for 0.4% of total unlinked
passenger trips, but 2.7% vehicle revenue miles (1). In metropolitan
areas with high-occupancy vehicle lanes, vanpools are touted for their
ability to bypass traffic jams, giving commuters potentially significant
time savings.
Publicly sponsored vanpooling programs have been established
since the late 1970s in response to the energy crises and have since
experienced periods of surge and abandonment (2). These programs
are now a relevant component of transportation demand management
(TDM) initiatives geared at reducing the negative impacts of congestion caused by more traditional modes of transportation, while
promoting their use as an efficient and cost-effective commuting
alternative.
Vanpool programs, in their promotional efforts, tend to overestimate the relevance of fare pricing as a means to increase ridership. At
the same time, it is imperative for these programs to objectively assess
Center for Urban Transportation Research, University of South Florida, 4202
East Fowler Avenue, CUT 100, Tampa, FL 33620-5375.
Transportation Research Record: Journal of the Transportation Research Board,
No. 1924, Transportation Research Board of the National Academies, Washington,
D.C., 2005, pp. 215–223.
215
216
Transportation Research Record 1924
•
•
•
•
•
•
•
•
•
Subsidies have a relevant effect in increasing ridesharing, accounting for firm size and controlling for employee adherence to the CTR
law and geographical heterogeneity. When a subsidy is offered, the
odds of choosing vanpool over drive-alone more than double. Firm
size influences the likelihood of choosing vanpool as an alternative
ridesharing mode. Results show that as firm size increases above
1,100 employees, the odds of choosing vanpool more than double,
everything else constant. The negative impact of free parking on mode
shift is more accentuated for employees working for large firms
(above 2,600 employees).
The rest of the paper is structured as follows. In the next section
the sample survey data set is analyzed and the proposed set of predictors is described. In the section on the econometric model the
approach to model building is outlined and the model is estimated
and checked against violations of assumptions. After the model is
validated, results are discussed. In the final section conclusions and
caveats are considered.
To focus on vanpool choice, the data set was subsequently resized
to consider a mode choice subset fit to estimate a binomial model of
choice of vanpool versus all other modes of transportation. Because
the cost of using each mode of transportation was not reported in the
employee survey, each of the cost variables was constructed based on
a set of assumptions. The cost components of each mode are described
below.
DATA DESCRIPTION AND ANALYSIS
Drive-Alone (DA_COST)
The Puget Sound region has the largest vanpool fleet in the United
States, with six local vanpool operators providing more than 40% of
the public vanpools in the country (9).
Washington State adopted the CTR law in 1991 with the objective of improving air quality, reducing congestion, and decreasing
dependence on petroleum fuels by instituting employer-based programs (10). The law applies to employers with 100 or more fulltime employees at a single work site, employees who are scheduled
to begin their workdays between 6:00 a.m. and 9:00 a.m. weekdays,
and a work site that is located in counties with populations of more
than 150,000 (Clark, King, Kitsap, Pierce, Snohomish, Spokane,
Thurston, Whatcom, and Yakima counties). The purpose of this
program is to encourage the use of alternatives to SOV for commuter trips as part of a comprehensive TDM strategy. Beginning in
1992 all employers participating in CTR programs began implementing surveys of their employees biannually to measure changes
in commuting patterns. The purpose of the survey instrument is to
track both employer programs and employee commute patterns to
establish subsequent goals and measures geared toward reaching
program goals.
The data set used to estimate the model was derived from the 1999
CTR program employee and employer surveys. The employee survey
is a survey of revealed preferences (commuters are asked what their
choice of transportation was in the week before the day being surveyed), making the data set sufficiently fit to discrete choice analysis.
The employer survey data set provided information on mode-specific
subsidy programs, as well as firm-specific descriptors. This data set
provided quantitative and qualitative information on parking services
and on subsidies to vanpool, carpool, and transit modes. Table 1 lists
the variables tested in the model, and a more detailed description of
the most relevant ones follows below.
From the employee survey, the following information was extracted
for consideration in the model-building process.
The costs components and estimates used to construct the drive-alone
variable were derived directly from the American Automobile Association (AAA) (11). According to AAA the average operating cost of
an automobile was about 13.4 cents per mile. Operating costs include
gas, oil, maintenance, and tires. The variable was created using that
estimate and the employee reported distance, as follows:
Mode Choice
Pearson correlation coefficients showed modest correlation
between DA_COST and CP_COST, but not at a point that would
cause multicollinearity issues as discussed in the section on
results.
The following means of transportation constitute the mode choice set
available to commuters:
Drive-alone,
Carpool,
Vanpool,
Bus and transit,
Bicycle,
Motorcycle,
Walk,
Telecommute, and
Other.
DA_COST = DIST ⴱ COST + PARKING
where
DIST = distance (reported daily round-trip distance as per
employee survey),
COST = daily average operating cost (AAA estimates),
PARKING = average reported daily parking cost as per employee
survey (obtained from employer survey).
Assuming an average of 22 working days per month, this cost
variable was translated into a daily cost.
Carpool Cost (CP_COST)
To account for the cost of carpooling, the general guidelines of commuter reduction programs were considered. For example, according
to the Spokane County Commute Trip Reduction Office (12), the
guidelines for charging passengers suggest the use of the auto cost
estimates as derived above, divided by the number of passengers carpooling. The cost of carpooling is equal to the cost of driving alone
adjusted by the reported vehicle occupancy. In the employee survey,
all respondents who chose a mode alternative to auto were asked to
report vehicle occupancy.
CP_COST = (DIST ⴱ COST + PARKING) OCCUPANCY
Concas, Winters, and Wambalaba
TABLE 1
217
Predictors of Vanpool Mode Choice
Variable
Mean
S.D.
Description
Mode
0.01
—
DIST
14.54
11.55
DA_COST
VP_COST
CP_COST
TR_COST
2.64
2.26
1.96
2.12
2.74
1.75
2.04
0.48
VP_SUB
CP_SUB
TR_SUB
0.40
0.20
0.47
—
—
—
Vanpool subsidy: 1 if yes, 0 if otherwise
Carpool subsidy: 1 if yes, 0 if otherwise
Transit subsidy: 1 if yes, 0 if otherwise
WDUM1
WDUM2
WDUM3
WDUM4
WDUM5
WDUM6
0.14
0.14
0.12
0.04
0.08
0.34
—
—
—
—
—
—
Work status: 1 if administrative, 0 if otherwise
Work status: 1 if craft/production/labor, 0 if otherwise
Work status: 1 if management, 0 if otherwise
Work status: 1 if sales/marketing, 0 if otherwise
Work status: 1 if customer services, 0 if otherwise
Work status: 1 if professional/technical, 0 if otherwise
CDUM1
CDUM2
CDUM3
CDUM4
CDUM5
CDUM6
CDUM7
0.01
0.02
0.12
0.08
0.08
0.02
0.58
—
—
—
—
—
—
—
County: 1 if Yakima, 0 if otherwise
County: 1 if Thurston, 0 if otherwise
County: 1 if Spokane, 0 if otherwise
County: 1 if Snohomish, 0 if otherwise
County: 1 if Pierce, 0 if otherwise
County: 1 if Kitsap, 0 if otherwise
County: 1 if King, 0 if otherwise
FDUM1
0.01
—
FDUM2
0.24
—
FDUM3
0.24
—
FDUM4
0.25
—
FDUM5
0.19
—
Firm size (employees): 1 if firm size greater than 1 and less than or equal
to 100, 0 if greater than 2600
Firm size (employees): 1 if firm size greater than 100 and less than or
equal to 280, 0 if greater than 2600
Firm size (employees): 1 if firm size greater than 280 and less than or
equal to 550, 0 if greater than 2600
Firm size (employees): 1 if firm size greater than 550 and less than or
equal to 1100, 0 if greater than 2600
Firm size (employees): 1 if firm size greater than 1100 and less than or
equal to 2600, 0 if greater than 2600
AFFECTED
0.92
—
Dummy variable indicating whether employee is affected by CTR law
(1 if yes, 0 if otherwise)
FPARKING1
—
—
Dummy interaction variables between firm size and free parking offered
by employers (1 if yes, 0 if otherwise)
FPARKING2
FPARKING3
FPARKING4
FPARKING5
—
—
—
—
—
—
—
—
1 if vanpool, 0 if otherwise
Distance (one way) from home to work
Driving cost: $ per day
Vanpool cost: $ per day
Carpool cost: $ per day
Transit cost: $ per day
Vanpool Cost (VP_COST)
The vanpool cost variable was constructed using information from
both the employer and the employee surveys. By using the reported
response identification code number, each survey respondent in the
employee survey was matched to each respective firm in the employer
survey. By applying this matching procedure, the fare schedules of
each vanpool company serving the employers’ county were used.
The fare schedules are based on distance and vehicle occupancy and
are published as a monthly cost. The vanpool cost variable was con-
structed using the employee reported distance and vehicle occupancy. By assuming an average of 22 working days per month, this
cost variable was translated into a daily cost.
Transit Cost (TR_COST)
By using the employer and employee survey matching procedure,
transit costs were derived using published fare schedules of the county
in which the employer was located.
218
Transportation Research Record 1924
Mode Subsidies
Section 132(f) of the Internal Revenue Code allows most employers to provide a tax-free benefit to employees of up to $100 per
month for transit, carpool, and vanpool fares and up to $185 per
month for parking fees. An attempt was made to model subsidies as
continuous regressors without success, because of few reported values of monthly subsidies offered by employers (only about 13,000
observations, of which 176 were identified as vanpool users). However, by using the employer–employee survey matching procedure,
it was possible to determine which firms offered a vanpool, carpool,
and transit subsidy. The presence or lack of these subsidies was
entered into the model as a set of dummy variables.
Data Analysis
Table 2 displays information on the mode choice frequencies. After the
data set was resized to account for auto, carpool, vanpool, and transit and after reporting errors were eliminated, 141,103 observations were retained. Because the modal split remained unchanged
throughout the days of the week, only 1 day of the week was taken
into consideration, specifically Tuesday. The employees who chose
vanpool as a means of transportation represent 1.76% of the sample,
with 1,565, or 63%, receiving some form of subsidy from their
employers. That provides the first indication of the relevance of subsidy programs in influencing rideshare. Sample descriptive statistics
showed that the daily cost of vanpooling ranges between $1.08 and
$8.22, with a daily average of $2.26. The sample median distance
across modes is about 12 mi, whereas for vanpool users it is about
25 mi, suggesting that vanpool users are more likely to have a longer
journey to work.
ECONOMETRIC MODEL
The objective of this study was to build a model that could ultimately
account for a set of relevant factors affecting the choice of vanpool as
a mode of transportation with respect to the other modes being considered. Given that the choice set consists of two outcomes, an econometric modeling approach in the form of a discrete choice model was
suggested.
Conditional choice models are index-based in nature. That is,
they postulate models in which choices are governed by the value of
TABLE 2
Mode Choice and Vanpool Subsidy
Vanpool Subsidy
Mode
Auto
Carpool
Vanpool
Transit
Other
Total observations
Number
Percent
Number
Percent
Number
Percent
Number
Percent
Number
Percent
Yes
No
38,351
41.29
8,571
40.16
1,565
62.98
6,210
35.41
2,422
35.35
54,538
58.71
12,769
59.84
920
37.02
11,328
64.59
4,429
64.65
Total
92,889
65.83
21,340
15.12
2,485
1.76
17,538
12.43
6,851
4.86
141,103
an index function that aggregates information contained in variables
believed to influence choice.
These models are best suited to analyze the relationship between
a discrete dependent variable representing the choice set an individual faces (the modes of transportation herein considered) and a set of
continuous and categorical predictors. It is assumed that the individual chooses the mode that provides the highest level of satisfaction
(i.e., utility), given the set of individual and mode-specific characteristics. For overviews of discrete (binomial and multinomial)
choice analysis, see Amemiya (13), McFadden (14 ), Blundell (15 ),
and Domencich and McFadden (16).
In the case of a binomial choice {Yi ∈ (0,1)}, the model of interest is a model of the form m(xij) = f [Y⎟ xij] in which the objective is
to predict the outcome:
Yi = 1
if f [Y x ji ] > 0
Yi = 0
if otherwise
[ f (Y
x ji ) > 1 − f (Y x ji )]
i, j = 1, . . . , n
where xji represents a set of mode- and individual-specific predictors.
The proposed equation is equivalent to the traditional conditional
logit model (with error term assumed independent and from a
Weibull distribution):
βx
Pr( y ji ) =
e ji
βx
1 + e ji
where Pr(yji) is the probability that individual i chooses outcome j
(vanpool) and β is the estimated parameter.
Assuming that the error terms are independent across the different options and that individuals choose the option (i.e., the mode)
that yields the highest value of this latent index function, then the
probability that person i chooses option j is given by the previous
equation. Concern is always expressed about the assumption of
independence of the error term. This assumption implies a condition
that is known as independence of irrelevant alternatives, frequently
denoted as IIA, meaning that the odds of choosing option j rather
than option k are not affected by other available options. Efforts to
relax that assumption have centered on introducing correlations
among the error terms. One way to solve this problem is to propose a nested logit model, as discussed in the concluding section
of this paper.
The vector of explanatory variables for the initial model contained the following predictors:
• Choice-specific
– Mode costs
– Mode subsidies
– Free parking
• Individual-specific
– Work status
– County of destination
– Firm size
– CTR law affected
RESULTS
Parameter estimates are shown in Table 3. The table displays the
results of the first model with all regressors included, the relative
standard errors, and Wald chi-square statistics. [Before estimating
Concas, Winters, and Wambalaba
TABLE 3
219
Complete Main Effect Model of Vanpool Mode Choice
Parameter
Estimate
Standard
Error
Wald
Chi-Square
P > Chi-Sq
Exponent (Est.)
Intercept
DIST
VP_COST
DA_COST
CP_COST
VP_SUB
CP_SUB
TR_SUB
CDUM1
CDUM2
CDUM3
CDUM4
CDUM5
CDUM6
CDUM7
WDUM1
WDUM2
WDUM3
WDUM4
WDUM5
WDUM6
AFFECTED
FDUM1
FDUM2
FDUM3
FDUM4
FDUM5
FPARKING1
FPARKING2
FPARKING3
FPARKING4
−6.4270
0.1248
−0.5714
1.4262
−5.1168
0.9439
0.2793
−0.6645
2.0513
1.9616
0.8720
1.2906
2.3428
1.8698
2.5141
0.0766
−0.0584
−0.2025
−0.0914
−0.1664
0.1592
0.3947
−0.5739
0.3743
0.7437
0.9671
1.1498
−8.6110
−13.2214
0.7367
0.2776
0.7833
0.0096
0.1143
0.0407
0.1021
0.0838
0.0794
0.0844
0.8743
0.7732
0.7548
0.7517
0.7388
0.7600
0.7327
0.1658
0.1777
0.1744
0.2191
0.1937
0.1503
0.0677
0.9455
0.2277
0.2141
0.2183
0.2100
988.6000
218.6000
0.9114
0.2672
67.3173
169.9274
25.0059
1228.7266
2511.9438
127.0056
12.3891
62.0520
5.5041
6.4358
1.3349
2.9475
10.0562
6.0534
11.7749
0.2134
0.1082
1.3476
0.1741
0.7381
1.1214
34.0212
0.3684
2.7026
12.0644
19.6242
29.9683
0.0001
0.0037
0.6534
1.0796
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0004
<.0001
0.0190
0.0112
0.2479
0.0860
0.0015
0.0139
0.0006
0.6441
0.7422
0.2457
0.6765
0.3903
0.2896
<.0001
0.5439
0.1002
0.0005
<.0001
<.0001
0.9931
0.9518
0.4189
0.2988
0.0020
1.1330
0.5650
4.1630
0.0060
2.5700
1.3220
0.5150
7.7780
7.1110
2.3920
3.6350
10.4100
6.4870
12.3550
1.0800
0.9430
0.8170
0.9130
0.8470
1.1730
1.4840
0.5630
1.4540
2.1040
2.6300
3.1580
0.0000
0.0000
2.0890
1.3200
FPARKING5
−10.4449
347.9000
0.0009
0.9761
0.0000
the model and making any inferences, a regular regression model
was run to investigate the presence of multicollinearity. Variance
inflation factors (VIF) were used as indicators of the presence of
multicollinearity. Given that the VIF ranged between 1.5 and 5.7
(well below the usual threshold of 7), it was concluded that the
model does not suffer any relevant multicollinearity. This approach
is preferred to the more simplistic analysis of Pearson correlation
coefficients and graphical analysis of outliers. Indeed, multicollinearity is a property of the explanatory variables, not the
dependent variable, thus running regular regression to spot this
problem suffices (15). All explanatory variables were retained for
model building.]
Table 3 also reports the global tests for the effects of each variable
on the outcome variable (mode choice), controlling for the other variables in the model. (In the final model, the dummy variables depicting job occupation were removed because they were all statistically
insignificant at any alpha level. One explanation could be that the
original survey question was designed in a somewhat broad format,
which allowed assessing only the industry of occupation but not the
employee-specific occupation.) The reported chi-square statistics test
the null hypothesis that the explanatory variables have no effect on the
outcome variable. The adjusted R2 shows that the model explains
about 64% of the sample variation in the dependent value (mode
choice) after adjusting for the sample size and number of independent
variables in the model.
Vanpool Cost (VP_COST)
The estimated parameter associated with the cost variable has a value
of −0.7168; its sign agrees with the theory of demand. Figure 1 shows
the plots of the estimated cumulative distribution function (CDF) and
the individual marginal effects interpreted at the means of the regressors. The graph depicts the probability function (probability vanpool = 1) as a function of vanpool cost. The plot was constructed at
the sample mean distance using King County and a firm size of 2,600
employees and greater (in the sample this corresponds to the most
recurring profile of individuals that choose vanpool) as a reference
220
Transportation Research Record 1924
0.002
CDF
Marginal Effect
0.0015
Density
0.001
0.0005
0
-0.0005
-0.001
-0.0015
0
1
2
3
4
5
6
7
8
9
Vanpool Cost
FIGURE 1
Demand for and price sensitivity of vanpools.
and can be interpreted as the demand for vanpool services with respect
to price. The marginal effect, or gradient, shows that the demand
(e.g., the probability) is more sensitive to price changes for fares
below $3 (daily).
The marginal effect is of direct interest to applied researchers,
because it tells how choice probabilities change due to changes in the
variables affecting choice. The marginal effects model the response
of f [Y⎟ xij] due to changes in xij, which is defined as follows:
∂f (Y x ji )
∂x ji
∇ x ji f (Y x ji ) =
This paper makes use of marginal effects as well as the interpretation of estimated parameters of interest.
Elasticity of Vanpool Cost
To understand how responsive the demand is to changes in fares, it
is useful to employ the concept of demand elasticity.
The direct elasticity (E) formulas for the logit model are as follows:
Ei = (1 − Pi )β k z kji
∑ (1 − P )β z
∑P
i
E =
(individual elasticity)
i
i
i
k
ji
k
(aggregate elasticity, over individuals)
where the elasticity measures the percentage change in the frequency
of making a given choice, in response to a 1% change in a given
predictor zji, for attribute k and alternative j.
That can be defined as the percentage change in the number of trips
demanded, associated with a 1% change in the cost variable. An estimate of the direct elasticity of mode choice with respect to price was
obtained using the cost parameter estimate, by evaluating the price
elasticity at each sample observation and then taking a weighted
average with respect to the predicted individual probabilities.
[This addresses the limitation due to the fact that elasticities are
linear functions of the observed data, and there is no guarantee that
the logit function will pass through that point defined by the sample
averages (the sample mean of vanpool cost). Furthermore, the elasticity evaluated at the sample means of the predictors tends to overestimate the probability response to a change in an explanatory
variable (16)].
The predicted value of the aggregate elasticity is equal to −0.73,
meaning that a 10% increase in vanpool price is associated with a
7.3% decrease in its demand. This result indicates that vanpool choice
is relatively inelastic to fare changes.
Figure 2 shows the predicted individual elasticities plotted versus
the distance traveled by respondents. Results corroborate what was
suggested by the rideshare literature (3, 5, 17 ); the belief that individuals are more likely to use vanpool services the longer the distance from home to work. Clearly, it is evident that for trips below
30 mi, the individual elasticities are equivalent to the aggregate estimate. As the distance increases beyond 60 mi, individuals are less
responsive to price changes, providing some insight in designing
effective fare schedules.
Concas, Winters, and Wambalaba
221
0
Individual Elasticity
-0.1
-0.2
Elasticity
-0.3
-0.4
-0.5
-0.6
-0.7
-0.8
0
FIGURE 2
10
20
30
40
50
Distance
60
70
80
90
100
Price responsiveness and distance traveled.
Vanpool Subsidy (VP_SUB) Marginal Effect
The impact of vanpool subsidies is represented by a dummy variable
indicating the presence of a vanpool subsidy when VP_SUB = 1, and
its absence when VP_SUB = 0. The estimated parameter is 0.8707.
Figure 3 shows the two probability functions plotted over VP_COST.
The marginal effect is the difference between the two functions. [Marginal effects can also be generated when dealing with a qualitative
predictor by analyzing the effect of the dummy variable on the whole
distribution by computing prob(vanpool = 1) over the range of βkz kji
(using the sample estimates) employing the two values of the binary
variable.] Figure 3 shows that the probability that an individual
chooses vanpool decreases as its price increases, and that such effect
is far greater for those employees who are not offered a subsidy. The
difference is substantial at the sample mean value of VP_COST,
where the predicted probability of choosing vanpool more than doubles when the employee is offered a subsidy, suggesting a relatively
strong effect on ridership.
Firm Size and Parking Policy
On the basis of results showing a significant positive relationship
between employer-sponsored ridesharing programs choice and firm
size, Ferguson concludes that public policy on ridesharing should
focus on larger firms (17 ). Results of this model tend to confirm that
firm size plays a major role in influencing the choice of vanpool services over SOV. The impact of firm size is statistically significant
when the firm size is above the 280 threshold and becomes more
substantial for firms with 2,600 employees and above as shown in
Figure 4, which plots the probability functions of the statistically significant firm-size dummies over the distance traveled. Although the
interaction between firm size and parking policies (by introducing an
interaction term between firm size and free parking) resulted in estimated parameters that were not statistically significant, the signs
agreed with what is generally concluded by the current literature.
These results provide some indication of a negative relationship
between free parking and vanpool use and firm size, in particular for
those firms with 1,100 employees and above.
CONCLUSIONS
It has been demonstrated that employer-sponsored programs, such as
vanpool services, could have a dramatic impact on ridesharing alternatives to driving alone (17 ). Given that the maximum amount an
employee can apply toward the current tax benefit program is $100 per
month for transit and vanpooling, it can be argued that employees who
collect such a benefit from their employers could be receiving services
at a very low cost or even free of charge and, therefore, ridership should
be significantly higher. Additional research on price elasticity of vanpool fares and subsidies becomes essential to determine the potential
impact of such programs.
This paper considered the use of logistic regression modeling techniques to investigate the effects of fare pricing and subsidies on vanpool demand. By using employer and employee data from the 1999
CTR program surveys of the state of Washington, a conditional discrete choice model was built to analyze the choice of vanpool services
with respect to competing means of transportation as a function of
various socioeconomic characteristics.
Results indicate that employer subsidies to vanpool users influence
the choice of this mode of transportation with respect to using auto
as a means of transportation, providing evidence of a strong positive
impact in stimulating ridership.
222
Transportation Research Record 1924
0.002
VP_SUB = 1
VP_SUB = 0
0.0018
0.0016
Prob(Vanpool = 1)
0.0014
0.0012
0.001
0.0008
0.0006
0.0004
0.0002
0
FIGURE 3
0
1
2
3
4
5
Vanpool Cost
6
7
8
9
90
100
Subsidies and demand for vanpool services.
0.35
FDUM3
FDUM4
FDUM5
0.3
Prob(Vanpool = 1)
0.25
0.2
0.15
0.1
0.05
0
0
FIGURE 4
10
20
30
40
Impact of firm size on vanpool demand.
50
Distance
60
70
80
Concas, Winters, and Wambalaba
A weighted average price elasticity value was estimated; the value
is equal to −0.73, indicating that vanpool demand is relatively inelastic to fare pricing changes. Furthermore, the sensitivity to price fare
changes declines as the distance increases beyond 60 mi, as individuals become less responsive to price changes. When considered in the
context of subsidies, these results support the evidence that policies
other than those intended to affect fare pricing could play a more
important role. The analysis also showed that firm size plays a major
role in influencing the choice of vanpool services over SOV. To focus
on the magnitude of the direct price elasticity, the model controlled
for its influence across sampled individuals.
The analysis presented in this study is increasingly relevant because
vanpool employer-based ridesharing program initiatives are based
largely on policies that either penalize SOV use or create incentives
in the form of fare pricing strategies and subsidies. In conclusion, an
enhancement on the model could be represented by a nested logit
model, which allows the existence of different competitive relationships between groups of alternatives in a common nest (thus relaxing
the IIA assumption). A next step in the analysis would be to include
examining the impacts of programs offering vanpool users guaranteed
emergency rides home, providing the assurance and flexibility most
typical of SOV.
ACKNOWLEDGMENTS
The authors thank Janet L. Davis, Stephen L. Reich, and Gary L.
Brosch for their help and editorial suggestions; Marlo Chavarria for
his help and support in the preliminary steps of data analysis and
variable design; and Edward Hillsman and Brian Lagerberg with
Washington State Department of Transportation for providing the data.
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The Transportation Demand Management Committee sponsored publication of
this paper.