Reducing Employee Parking with Incentives and Apps:1

A Technical Report2

on the3

UC Berkeley VPPP FlexPass Study4

Authors

Raja Sengupta (Principal Investigator)Professor, Civil and Environmental Engineering

University of California, Berkeley&

Seamus WilmotDirector, Parking and TransportationUniversity of California, Berkeley

&Dounan Tang

Ph.d Candidate, Civil and Environmental EngineeringUniversity of California, Berkeley

Supported by:

FHWA VPPP Contract# 9159, NSF Award# 1136141,Regents of the University of California

5

February 4, 20176

1. ABSTRACT1

Most employers offer free or underpriced parking to employees even as they feel the pressure2

to reduce the number of employees driving alone to work. The FlexPass study described in3

this report, explores a new kind of employee parking permit, the FlexPass and an App, that4

incentivizes employees to reduce parking without significantly changing parking prices. This5

mitigates employee discontent. Most employees of the University of California, Berkeley buy6

a monthly parking permit with pre-tax dollars. The FlexPass is the same, but then refunds7

this money to the employee in proportion to the number of working days not parked each8

month. The employee communicates parking use via the Flexpass App. We also collect9

smartphone location data and engage over email. This multi-channel IT design gives us10

overlapping measurements. The causal power of the FlexPass permit and App is revealed11

by a randomized controlled trial with 392 employees, representing 10% of the university em-12

ployees driving alone and parking. We find that control group subjects, serving as baseline,13

parked 4.3 days per week.The FlexPass treatment reduced this by 4.2% with a p-value of14

0.07. The reductions have required refunds of $27 per employee over a 3 month period.15

We also find a more significant hetergeneous treatment effect. 77% of our subjects declared16

interest in the FlexPass when signing up. This sub-population reduces parking by 6% with17

a p-value of 0.017. We find that unbundling a monthly employee parking permit reduces18

parking by making employees mindful of daily parking usage.19

20

KEYWORD: Transportation Demand Management; Incentives Parking; Random-21

ized Controlled Trial; Casual Inference22

Raja Sengupta 2

2. INTRODUCTION1

We describe a randomized controlled trial executed to quantify the unbundling of monthly2

parking as a means to reduce employee parking at the University of California, Berkeley.3

Parking demand reductions would make the university more sustainable and free valuable4

land for education. Employee parking is a benefit provided by the university at reduced5

rates. Therefore we study an monthly parking permit that is price-neutral and unbundled6

with the potential to reduce parking while enhancing employee welfare.7

Employees purchase a monthly parking permit for a fixed fee, usually with pre-tax8

dollars. The fee is independent of the number of days parked during the month. Subjects9

in our trial purchase a monthly permit in exactly the same way, but also install an App10

and engage with us by email. They receive monthly rebates proportional to the number of11

days not parked, which the subject reports via the App. The proportionality is intended12

to make employees more mindful of parking usage and incentivize its reduction. This new13

permit studied is called the FlexPass. Its App is the FlexPass App. It collects continuous14

location data for the duration of the study for subjects who consent. The FlexPass system15

also emails subjects weekly. The multi-channel design gives us overlapping data. This turns16

out to be valuable.17

According to the Bureau of Transportation Statistics (11), nine out of ten Americans18

travel to work using personal vehicles. For those who drive, 95% are provided with a parking19

space free of charge (12). A number of cities and employers have realized that "free park-20

ing" is a key contributor to many negative environmental, social, economic and aesthetic21

externalities, and thus shown increasing interest in more rigorous parking management and22

pricing (13). Several studies have shown that charging for parking will lead some travelers to23

move to other commute options (2, 8, 16). UC Berkeley Parking and Transportation office24

currently prices campus parking at $98-137 per month for most faulty and staff members.25

However, it is still heavily utilized, with recent field observations finding occupancies of 85-26

90% or higher at most locations for much of the workday (4). Parking price elasticity tends27

to be quite low, in the range of -.1 to -.3 (5). Thus, even if price increases substantially, many28

travelers are likely to continue to drive and park, meaning parking lots would continue to29

occupy valuable land. In Berkeley, cost of new space is high, with construction cost penciled30

at $65,000 per space and land costs of $7M per acre (15).31

Based on the UC Berkeley survey data, Proulex et al. concluded that if parking32

demand must be reduced, both price and incentives to use different travel modes would need33

to be increased (10). In a later project, Ng conducted focus groups, interviews, a stated34

preference survey, and proposed several incentive schemes (9). Ng’s stated preference based35

results assert that an unbundled monthly permit with rebates proportional to the number of36

days not parked could reduce the Berkeley campus parking by 5%. The FlexPass study tests37

such a permit through a randomized controlled trial with 392 subjects during the Spring38

2015 semester, February 1st, 2015 to April 30th, 2015.39

The report begins with a description of the experimental design, followed by a de-40

scription of the subjects socio-economic characteristics. We then discuss the App and the41

data collected by the trial and show how we correct under-reporting and dropout biases.42

Under-reporting is corrected by processing data from email surveys through a Mixed Latent43

Factor model. Dropout biases are captured by a sample selection model. The effect size of44

FlexPass is estimated.45

Raja Sengupta 3

2.1. Experimental Design1

The FlexPass study is a Randomized Controlled Trial (1) with the FlexPass as the treat-2

ment.Most UC Berkeley employees who purchase an annual parking permit elect to pay3

through pre-tax dollars; all permits are pre-paid. In contrast, the treatment in this study4

refunds a portion of the pre-paid amount to the FlexPass holder for each day not parked.5

The treatment is intended to make the employee mindful of parking usage and incentivize6

its reduction.7

The study was advertized to all permit holders and aimed to recruit 400 subjects from8

4,200 parking permit holders, i.e., approximately 10% of the population. 392 permit holders9

became the study subjects by completing a sign-up process before an advertized recruitment10

deadline. Thereafter, the subjects were randomly assigned to a treatment or control group.11

The study then attempts to measure the number of working days parked by each subject12

over a 3 month period (February March, and April) within the Spring semester of 2015. Any13

difference between the treatment and control groups as measured by the average number14

of days parked per subject is hypothesized to be caused by the treatment by virtue of the15

random assignment.16

Parking usage is measured by requiring each subject to use the FlexPass app. All17

subjects are required to be either iPhone or Android users. Figure 1 illustrates the main18

app screens. The subject can tap the green box on the main screen to indicate whether she19

intends to park or not on each day. Parking can also be declared in advance using a calendar20

screen. The green box toggles when tapped between "Parked on Campus" and "I will not21

park on campus today". A subject can change her parking decisions for a certain day till22

12 noon of the day. Thereafter the statement in the green box is assumed to be the final23

parking decision by the subject for the day. Treatment group subjects indicating they will24

not park for the day are credited a rebate amount and may be cited by enforcement officers25

if observed parked. The green box is set by default to "Parked on Campus" because subjects26

have pre-paid for the right to park. Subjects toggling the default to "I will not park ..." are27

prompted to report whether they are not coming to campus or doing so by some other mode28

as shown in the second screen.29

Control group subjects receive neither rebate nor citation. Their lack of incentive to30

report and the default result in an under-reporting bias discussed and corrected in section31

3. Subjects with no app activity during a week were prompted to report at the end of the32

week. The email included a web link used to report the number of days parked or not during33

the week.34

All subjects were compensated with a $25 Amazon gift card on completion of the35

sign-up process, installation and activation of the app. All subjects completing the study36

by filling out an exit survey were also compensated the same amount. Thus most subjects37

received $50 in Amazon gift cards in two installments.38

Subjects assigned to the treatment group were required to exchange their usual permit39

hang-tags for new FlexPasss hangtags by meeting with UC Berkeley P&T personnel prior40

to February 1, 2015. Control group subjects were not required to do this. Some treatment41

group subjects did not make the exchange. Our analyses includes statistical corrections to42

correct the resulting bias (see section 3).43

The enforcement function was executed by UC Berkeley’s P&T Enforcement Officers.44

The study team emailed a list of FlexPass permit numbers not parked at 12 PM each day45

Raja Sengupta 4

FIGURE 1 : FlexPass smartphone app interface. From left to right, (a) Main Screen,(b)Mode Reporting, (c) Calendar

to the enforcement officers. Any FlexPass permit with a number on the list could be cited.1

This study treatment targets the current annual Central Campus C Permit and Fac-2

ulty/Staff F Permit holders who constitute the vast majority of the regular users of campus3

parking. These parking permits allow holders to seek a parking space in parking garages or4

surface lots by the permit type. C permits are available only to faculty and senior staff, F5

permits to other staff. During the study, the pre-pay price for F permit was $95 per month6

while $131 per month for C permit. Subjects were recruited from the 4272 employees who7

had already purchased a C or F permit for the entire 2015 Spring semester.8

Rebates to subjects in the treatment group are based on their permit types and the9

number of working days (Mon. to Fri.) they park on campus in a given month. Rebate10

amounts are calculated as equation 1 below.11

T = max{Θ−Dδ, 0}

where D is the number of working days a certain subject parks on campus in a certain12

month and T is the total rebates for the month. The maximum monthly rebate is $Θ (Θ=9513

for F permit holders while 131 for C permit holders). For each day parked on campus,14

a subject is charged $δ (δ =6 for F permit holder while 8 for C permit) until the entire15

pre-paid amount for the month has been used up. For example, an F permit holder parking16

12 workdays on campus (approximately 3 work days a week) receives a rebate of $23.117

1Detail description of the rebate calculation and a table of all possible rebate values can be found in thehomepage of our study website https://gogreen.berkeley.edu/flexpass/.

Raja Sengupta 5

2.2. Sample Characteristics1

Among the 4272 C&F permit holders at UC Berkeley we reached through emails and post-2

cards, 392 respondents finished the sign-up process to become subjects. They were equally3

divided into the treatment group and the control group. Table 1 summarizes their demo-4

graphic and socio-economic information. UC Berkeley staff make up the bulk of the sample.5

Females account for 71 percent of staff subjects and 57 percent of faculty. Most subjects are6

over 25 and under 65 years old. 30 percent of the subjects have at least one bike while 357

percent have a Clipper card which is a reloadable contactless card used for electronic tran-8

sit fare payment in the San Francisco Bay Area. These provide them potential alternative9

commute modes when not parking on campus. 77 percent of the subjects felt interested in10

the potential rebates. The remaining 33 percent would like to support the research while11

not interested in the rebates. 71 people wrote down reasons for not being interested in the12

rebates. Typical reasons include "must park each work day", "I need to get to my children13

from time to time" and "No alternatives for me other than driving my car". Subjects were14

asked about their weekday commute modes in the week prior to the sign-up. 76 percent of15

subjects came to campus all five weekdays. 79 percent of subjects drove alone and parked16

on campus more than 4 working days.17

3. CAUSAL ANALYSIS OF THE FLEXPASS STUDY18

We infer the treatment effect of the FlexPass using a box model as shown in figure 2(a). 39219

samples are drawn from a box of 4272 C&F permit holders and assigned into treatment and20

control groups randomly. Given the group assignment T , and subjects indexed by i, Y Ti ,21

and Y Ci denote the potential outcomes given FlexPass treatment, Ti = 1, and non-treatment,22

Ti = 0, respectively. For each subject, one or other of the potential outcomes in counter-23

factual. The observed outcome is Yi = TiYTi + (1 − Ti)Y C

i . Yi is a 64-dimension binary24

vector, where Yij is subject i’s parking choice on day j. Yij equals 1 if he or she did not park25

on campus on day j and 0 otherwise. Subjects’ social economic characteristics, denoted as26

Xi on the ticket, were measured in the entry survey. The total number of days parked on27

campus by subject i during the study is then yi = ∑jYij.28

29

If all the data Yij were observed, then the statistic E(yi|Ti = 1) − E(yi|Ti = 0)30

would be an unbiased estimator of the treatment effect. However, some treatment group31

subjects dropped out after recruitment, and not all of the Yij are observed, i.e, we have32

missing reports. Moreover, dropouts and missing reports are correlated with the assignment33

of subjects into treatment and control. This would render the naive estimator biased. This34

section describes the methods we use to correct these two biases. Subsection 3.1 shows the35

biases in the data, and reveals the missing report mechanism. The next subsection is about36

the method used to correct the missing report bias. Subsection 3.3 does the same for the37

dropout bias. The missing reports are imputed by a Mixed Latent Factor Model (MLFM)38

while dropout bias is compensated using a selection model. The selection model reveals the39

causal treatment effect.40

3.1. Dropouts, Missing Report Mechanism and Data Descriptions41

The app-reported parking demand reductions are shown in figure 3a. The blue line which42

represents the treatment group is always above the green line which represents the control43

Raja Sengupta 6

TABLE 1 : Sample descriptive statistics

Treatment Control Enrolled

UC Berkeley employment status (%) (%) (%)FACULTY 22.4 19.1 20.8

STAFF 77.6 80.9 79.2Age Group

TWENTY_FIVE_TO_THIRTY_FOUR 24.4 26.1 25.2THIRTY_FIVE_TO_FORTY_FOUR 30.5 25.6 28.0FORTY_FIVE_TO_FIFTY_FOUR 24.9 31.5 28.2FIFTY_FIVE_TO_SIXTY_FOUR 15.2 13.3 14.3

SIXTY_FIVE_AND_OLDER 2.5 2.0 2.3EIGHT_TEEN_TO_TWENTY_FOUR 2.5 1.6 2.0

GenderFEMALE 65.6 65.0 65.3

MALE 34.4 35.0 34.7Has Bike

FALSE 68.4 71.6 70.0TRUE 31.6 28.4 30.0

Has Clipper CardFALSE 66.3 64.2 65.3TRUE 33.7 35.8 34.7

Rank Mobile app1st 58.5 50.6 54.52nd 28.7 29.3 29.03rd 12.9 20.1 16.5

Rebate InterestingFALSE 21.4 23.0 22.2TRUE 78.6 77.0 77.8

Number of Days Commute to Campus5 73.7 77.6 75.64 13.4 12.2 12.83 8.6 5.6 7.12 2.7 4.1 3.41 1.1 0.5 0.80 0.5 0.0 0.3

Number of Days Drive Alone5 66.8 61.7 64.34 13.8 16.8 15.33 8.2 8.7 8.42 6.1 5.6 5.91 2.0 2.6 2.30 3.1 4.6 3.8

Number of Participates196 196 392

Raja Sengupta 7

FIGURE 2 : Box model for causal analysis

group. This may be a indicator for significant treatment effect at the first sight. However,1

this comparison relies on a strong assumption that when people did not report any thing2

through the app on certain days, they are considered as "Park On Campus". In fact, exit3

survey after the study showed that sometimes subjects forgot to use the app when they did4

not use campus parking. Especially for subjects in control group, there is no incentives for5

them to report daily commute modes. During the entire study period, there were 74 subjects6

in the control group who reported nothing through our smartphone app. In the treatment7

group, the number reduced to 38. Even with subjects who have reported some parking8

activities, they may still under report the number of not-park-on-campus days, which led to9

an overestimation of the treatment effect. Therefore, instead of respond Yij, we additionally10

define, for each occasion j, an indicate Raij, which equals 1 if subject i reported day j’s11

parking behavior through smartphone app and 0 if subject i didn’t use the app on day j.12

We then partition Yi into two sub-vectors such that Y oi is the vector containing those Yij13

for which Raij = 1 and Y m

i contains the remaining components. Y mi is referred to missing14

reports. To further understand the missing report process, we sent commute mode surveys15

in the 6 weeks during the study to those who had not used their smartphone app for a week16

prior to the survey. The survey asked subjects about their daily commute choices in the17

past week. The average response rate for the email survey is 62.2%. Hence for each occasion18

j, another indicator is defined as Reij, which equals 1 if subject i reported day j’s parking19

behavior through email and 0 otherwise.20

From the email survey, a hypothesis test of the missing report mechanism was con-21

ducted among three alternates: Missing Completely At Random (MCAR), Missing At Ran-22

dom (MAR), and Missing Not At Random (MNAR) [Rubin 1976, Little and Rubin 1987].23

The three mechanisms differ from each other based on the dependencies between missingness24

and observed and unobserved data. MCAR refers to the missingness is independent of both25

observed and unobserved data; MAR refers to missingness is independent of unobserved26

data; MNAR refers to missingness is independent of neither observed or unobserved data.27

The missingness process for MCAR and MAR are ignorable such that we can ignore formu-28

lating the missingness process when we are inferring the treatment effect. Otherwise, if the29

MNAR holds we should model the missingness process before conducting causal analysis. In30

Raja Sengupta 8

(a) Daily on-campus parking demand reduction for re-bate and control groups

(b) Comparison of non campus parkingdays between app reports and email re-sponses

FIGURE 3 : Measurements of parking behavior

the FlexPass study, we consider the missingness app reports to be Missing Not At Random1

(MNAR). A possible evidence is that subjects were aware that the default choice on the app2

is "park on campus". Thus, they did not report via the app when they did park on campus.3

We compare the out comes from follow-up emails with app reports shown in figure 3b. It can4

be observed that the email responses of non-campus parking days is generally lower than the5

app reports. In those 6 weeks when surveys were sent, the app reports resulted, on average,6

1.92 non-campus parking days per week among the treatment group, while this number is7

0.57 for email responses. Through a two sample t-test the null hypothesis of MAR leads to8

a p-value of 0.002, which rejects MAR and also MCAR. The missing report mechanism is9

regarded as MNAR and will be modeled through a Mixed Latent Factor Model (MLFM) in10

the next section.11

To sum up, in our study, respond vector Yi is measured by both app and follow-up12

email. All possible outcomes for Yij are then illustrated in figure 2(b), where the shaded13

region means not observable. In situation (1), subject i report day j’s parking choice through14

the app, where Yij is observed and no email will be sent. In situation(2) , subject i didn’t15

use the app on day j and an email will be sent to i. The subject answered the email and16

thus Yij is observed. In situation(3), Yij is not observed as subject i didn’t answer the email.17

Situation(4) may happen when subject i dropped out from the study that neither did she/he18

use the app nor did she/he receive any email. Noticeably, all Y oi is observed in this study by19

definition and part of Y mi is measured in situation (2). If Yi only contains Yij of situation20

(3) and (4), subjects i is regarded as ’Dropout subjects’. Otherwise, complete data Yi will21

be recovered from Yij observed in situation (1) and (2).22

3.2. Recover Missing Reports23

To infer treatment effect, E[Yij|T ] needs to be estimated, which can be expressed by:24

E[Yij|T ] = E[Yij|T,Raij = 1]P (Ra

ij = 1|T ) + E[Yij|T,Raij = 0]P (Ra

ij = 0|T )

Raja Sengupta 9

Lets start with a simple case: assuming days and individuals are independent and identicallydistributed(i.i.d.). Under i.i.d., E[Yij|T,Ra

ij = 1] can be estimated directly by averaging overapp reports. P (Ra

ij = 1|T ) and P (Raij = 0|T ) can be estimated by counting the frequency

of app usage. E[Yij|T,Raij = 0] is the missing part. If all the subjects truthfully report

their not-park-on-campus days through the app, this term is 0. However, section 3.1 showsthat missing report exists and E[Yij|T,Ra

ij = 0] needs to be evaluated. Conditioning on theemail responds Re

ij:

E[Yij|T,Raij = 0] = E[Yij|T,Ra

ij = 0, Reij = 1]P (Re

ij = 1|T,Raij = 0)

+ E[Yij|T,Raij = 0, Re

ij = 0]P (Reij = 0|T,Ra

ij = 0)

Email survey is done after the end of each week, and its respond does not affect rebate calcu-1

lation. Therefore we assume parking behavior is independent of email survey reporting be-2

havior. Under this assumption of Yij being independent of Reij, E[Yij|T,Ra

ij = 0, Reij = 1]3

equals E[Yij|T,Raij = 0, Re

ij = 0], where E[Yij|T,Raij = 0, Re

ij = 1] can be estimated4

directly form the email responds. In practice, people behavior differently on different week-5

days. Population heterogeneity also exists. To relax the i.i.d. assumption, Mixed Latent6

Factor Model is introduced.7

The Latent Factor Model(LFM), also called Matrix Factorization Model, is widely8

applied in recommendation systems in the search engine, movie and music industry for9

matching users and potential items that they would be interested in (3, 7). It has been10

shown that the LFM’s are superior over attribute based models, which is often used in11

transportation studies, in terms of prediction accuracy (7). The idea behind LFM is that12

preference of a user and attitudes of an item are determined by a small number of factors. The13

factors of a user or an item can be represented as vectors Ui or Vj, respectively. These latent14

factors are capable of utilizing observed user-item interactions for predicting unobserved15

interactions, Yij.16

Yij = Ui′Vj + εij (1)

applying the concept to the FlexPass study, we regard the study subjects and the17

working days during the study period as ’users’ and ’items’, while parking choice matrix Y18

as rating matrix. Denote the number of subjects as M and number of working days as N. Yi,j19

stores subject i’s parking choice on day j. To illustrate the idea of LFM, we first assume for20

all i and j, Yij is generated by from the same process described in equation 1 with U and V21

unknown. U and V is aM×L and N×L matrix respectively, where ith row of U is referred22

as subject i’s latent factor while jth row of V is referred as day j’s latent factor. When εij23

is independent and identically Gaussian distributed (i.i.d. Gaussian), the estimated parking24

respond matrix Y can be expressed by U′V. Let ‖.‖F denotes Frobenius norm, to maximize25

the prediction accuracy of rating matrix equals to solve:26

minrank(Y)6L

∥∥∥Y−Y∥∥∥F

whose solution is essentially a singular value decomposition(SVD) of Y. Optimal Y∗ and27

Raja Sengupta 10

corresponding prediction error can be expressed by:1

Y∗ =L∑i=1

σiuivi′;∥∥∥Y − Y∗

∥∥∥F

=rank(Y)∑i=L+1

σi2

where σi is known as ith singular values of Y, ui and vi is called the ith left-singular vector2

and right-singular vector, respectively. These singular vectors are often regarded as latent3

semantic factors in information retrieval. In the FlexPass study, the full dataset should4

contain 292×64 = 18688 responses, while in reality we collected 8093 app responses and 26095

email responses, which account for 57% of the full dataset size. Since the sum-square distance6

can be computed only for the observed entires of the target sparse matrix Y, as shown7

by (14), this seemingly minor modification results in a difficult non-convex optimization8

problem which cannot be solved using standard SVD. LMF is closely related to SVD but9

models directly the observed ratings while avoid overfitting through a regularized model.10

Noticeably, the key underlying probabilistic foundation for LFM is that the error term in11

equation 1 is i.i.d. Gaussian which implies the missing data mechanism is considered as12

MCAR.13

To model MNAR mechanism, we proposed a Mixed Latent Factor Model(MLFM),14

where Yij generated from two different processes depending on whether Yij is observed15

through app reporting, Raij = 1, or otherwise Ra

ij = 0.16

Yij = (1−Raij)αmi +Ra

ijαoi + βj + Ui

′Vj + εij; εij ∼ N (ε|0, σ2) (2)

where βj is the weekday specified constant for day j; αoi is the subject specified17

constant for subject i when app report observed, Raij = 1; and αmi is the subject specified18

constant when app report missing, Raij = 0. N (x|µ, σ2) is the probability density function19

(pdf) of the Gaussian distribution with mean µ and variance σ2. Raij is the app report20

indicator defined in section 3.1. The MNAR mechanism is modeled by two subject specific21

constant parameters. Yij depends on αoi if app report exists while depends on αmi if otherwise.22

More complicated Mixed-LMF can be created where Ui is also different for app reports and23

missing reports. However, this will add M ×L more parameters to the model which largely24

increases the computation complexity. Also, absorbing heterogeneity of app report responses25

Y oi and missing reports Y m

i by two M dimension vectors leads to more clear interpretations.26

To prevent over-fitting, we also place zero-mean spherical Gaussian priors on latent factors:27

p(αo|σαo2) =

M∏i=1N (αoi|0, σαo

2I), p(αm|σαm2) =

M∏i=1N (αmi|0, σαm

2I), p(β|σβ2) =N∏j=1N (βj|0, σβ2I)

28

p(U|σU 2) =M∏i=1N (Ui|0, σU 2I), p(V |σV 2) =

N∏j=1N (Vj|0, σV 2I)

The corresponding graphic model for Mixed Latent Factor model is shown in figure 4. The

Raja Sengupta 11

log of posterior distribution over the latent factors is given by

ln p(αo,αm, β,U,V|Y,R, σαo2, σαm

2, σβ2, σU

2, σV2) ∝

ln p(Y|R, αo,αm, β,U,V) + ln∏i,j

N (αoi|0, σαo2I)R

aij + ln

∏i,j

N (αmi|0, σαm2I)(1−Ra

ij)

+ ln p(β|σβ2) + ln p(U|σU 2) + ln p(V|σV 2)

Maximizing the log-posterior over latent factors with hyper-parameters, i.e. prior variances,kept fixed is equivalent to minimizing the sum-of-squared-errors objective function withquadratic regularization terms. Furthermore, to control the number of hyper-parameters,weset σαo=σαm= σβ and σU=σV .

min∑i,j

Iij{[Yij − (1−Raij)αmi +Ra

ijαoi + βj + Ui

′V]2

+ λαβ[Raijα

o2i + (1−Ra

ij)αm2i + βj

2] + λUV (Uij2 + Vij2)} (3)

where Iij is the indicator function of all observed data that Iij = Raij +Re

ij and λαβ = σ2/σ2β,1

λUV = σ2/σ2U . A local minimum of the objective function given by equation can be found2

by perform gradient descent in αo,αm, β,U and V.3

4

FIGURE 4 : Graphic Model for Mixed Latent Factor Model

To apply the MLFM to our data, we first removed "dropouts", which results in 3065

valid users in our MLFM, M = 306. All weekdays during the study are also included, which6

leads to N = 64. Dimension of latent factors L is set to be 10. As we penalize the norms7

of parameters, the model performance will not be sensitive to L. At the occasion i,j where8

the respond is missing, we predict that subject i will not park on campus on day j if the9

Y estimated from equation 2 is larger than 0.5. A 5-fold cross validation was conducted to10

choose optimal λUV and λαβ. The original sample is randomly partitioned into 5 equal sized11

subsamples. Every round, a single subsample is retained as the validation data for testing12

the model, and the remaining 4 subsamples are used as training data. The cross-validation13

process is then repeated 5 times and the 5 predicting errors can then be averaged to produce14

a single estimation called cross validation error. λαβ = 0.5 and λUV = 0.05 results in the best15

overall cross validation error of 20.88%. For subjects in control group, the false positive rate16

Raja Sengupta 12

p(Yij = 1|Yij = 0, Ti = 0) is 19.07% while the false negative rate p(Yij = 0|Yij = 1, Ti = 0)1

is 18.09%. For subjects in treatment group, the false positive rate p(Yij = 1|Yij = 0, Ti = 1)2

is 13.61% while the false negative rate p(Yij = 0|Yij = 1, Ti = 1) is 25.39%. Although the3

false positive and negative rate is imbalanced for treatment population, it systematically4

under-predicts the number of non-campus parking days, which will lead to a conservative5

estimation of treatment effect.6

We compare the difference between MLFM and attribute based model by building7

a random forest model. The random forest model predicts the Yij using social-economic8

features collected from the entry survey with each Yij considered independent. The random9

forest resulted overall cross-validation error of 23.66%. For subjects in treatment group,10

the false positive rate p(Yij = 1|Yij = 0, Ti = 1) is 12.78% while the false negative rate11

p(Yij = 0|Yij = 1, Ti = 1) is 50.61%. The random forest model has significantly higher false12

negative rate than the MLFM, which led to a worse overall cross-validation error. This is13

due to the disadvantage of feature based models in capturing heterogeneities in subjects’14

behavior with limited features.15

In the estimated MLFM model, there are L latent components in both factor matrix16

U and V. Similar to the standard SVD, we rank these components by their information17

amount, where first we calculate σl2 =M∑i=1

Uil2 +

N∑j=1

Vjl2 and sort U and V in the way that18

σ2l > σ2

l+1 for all l = 1, ..., L. lth column of the new factor matrix U and V is denoted as19

lth principal component of V. Weekday latent factor matrix V is visualized by its first and20

second principal component in figure 5a. Different weekdays are drawn with different color21

and markers. Patterns can be observed such as Fridays are mainly distributed on the upper22

part while Mondays on the lower left. Features of two holidays are captured in the model as23

their latent factors depart from the population. In order to show how MNAR mechanism is24

captured in subject specific constant parameters, a scatter-hist plot for αoi and αmi is drawn25

for every valid subject i on figure 5b. with kernel density of αo and αm projecting on x26

and y axis. It can be observed from the scatter plot that for subjects in treatment group,27

73% of the blue dots are below the 45 degree dash line, meaning that αoi > αmi , which is28

in line to with the information shown in figure 3b. From the kernel density plot for αo we29

can observe that the distribution of αo for treatment group is shifted to the right of control30

group, meaning the app reports revealed that treatment group forwent parking on campus31

more often. The kernel density plot for missing report subject-specified constant αm shows32

the opposite result. αmi for treatment group are concentrating at rather low values, meaning33

that the missing report rate of treatment subjects is rather small. αm distribution of control34

group shows similar pattern as its αo distribution, capturing control subjects often forgot to35

report when they did not park.36

3.3. Compensate Differential Dropout Bias37

For valid subjects, yi can be calculated from the recovered parking response matrix Y, such38

that yi =N∑j=1

Yij. For dropout subjects, i.e. subjects in the treatment group did not pick39

up the FlexPass hang-tag and people in control group did not report any parking choice40

during the study, their yi’s are unobservable. We denote a dropout indicator Rdi , where41

Rdi = 0 if subject i dropped out and 0 otherwise. The naive estimator using observed42

Raja Sengupta 13

(a) First and second principal component of V(b) Scatter-hist plot for subject specific con-stant parameters αo and αm

FIGURE 5 : Visualization of latent factors

outcomes, E(y|T = 1, Rd = 1)−E(y|T = 0, Rd = 1), will be biased because of the existence1

of non-random dropout as confounder. Existence of in randomized controlled trials, e.g.2

FlexPass Study, experiments of new drug impact, are not rare. Often, the subjects can decide3

themselves, whether they accept the treatment, which is not under researchers’ control. This4

problem is usually referred to as a sample selection or self-selection problem (6). Additional5

information is required to estimate the causal effect under this scenario. Popular choices6

include, pseudo-randomization, instruments and the information about the functional form7

of the selection process. As the reason for dropout is explicitly known in our study, sample8

selection model was employed.9

We first consider a homogeneous treatment effect δ which does not vary over individ-10

ual. The sample selection model with differential consists the following structural process:11

y∗i = βO′Xi

O + δTi + εiO

Rd∗i = [TiβT S + (1− Ti)βCS]′ZiS + εi

S

where Rd∗i is the realization of the latent value of the selection "tendency" for the subject i,12

and y∗i is the latent outcome of total non-campus parking days during the study. XiO are13

explanatory variables including some background characteristics of enrolled subjects. ZiS

14

are explanatory variables for the selection equation. Identification requires XiO be at most15

a strict subset of ZiS (there should be at least one variable in ZiS that is not also in XiO).16

As dropouts happened in both groups and is due to different reason, a differential dropout17

process is modeled. βT S and βCS represents parameters describes distinct dropout processes18

for treatment and control group respectively. We observe:19

Rdi =

{01

if Rd∗i < 0

otherwise

Raja Sengupta 14

1

yi ={unknown

yi∗

if Rdi = 0

otherwise

i.e. we observe the parking response only if the latent selection Rd∗i is positive, which

means the subject i did not dropout. The observed dependence between non-campus parkingfrequency yi and treatment Ti can now be written as:

E[y|T = Ti, Rd = 1, XO = XO

i] =βO′Xi

O + δTi + E[εiO|εiS > −[TiβT S + (1− Ti)βCS]′ZiS] (4)

The third term in equation 4 illustrates why the naive estimator using observed data2

gives in general biased result. E[εiO|εiS > −[TiβT S + (1 − Ti)βCS]′ZiS] 6= 0 unless εiS and3

εiO are mean independent, e.g. the dropout process is completely random. Parameters can4

be estimated effectively through maximal likelihood method by assuming the error terms5

follow a bivariate normal distribution:6 (εS

εO

)∼ N

([00

],

[1 ρρ σ2

])

where ρ describes the relationship between observed non-campus parking frequency and7

dropout process. ρ > 0 indicates a "positive selection", where subjects remained in the study8

are those who forwent campus parking more often. ρ < 0 indicates a ‘negative selection’,9

where subjects who forwent parking more often dropped out. ρ = 0 indicates that subjects’10

parking behavior is independent of the dropout process.11

The probit results for selection process in TABLE 2 offer clear insights into the value12

of different social economic features in explaining the probability of dropout in treatment13

and control groups. Subjects who stay valid in treatment group are essentially those who14

went to the P&T office in person and changed to the new hang-tag, which can be viewed as a15

extra time cost. Table 2 column (1) suggests that owning a Clipper card decreases the odds16

of dropping off in treatment group; being interested in rebates increased the probability of17

staying valid even more. Indeed, the selection process implied that there may exists a "pos-18

itive selection" that people with potential alternative commute modes and with willingness19

to collect the rebate tend to remain active in the treatment group. Control group subjects20

those who never used the app nor replied to the email survey were considered as dropped21

out. Table 2 column (2) describes the control group drop-out. We found that subjects who22

prefer to receive information through channels other than smartphone app tend to drop out23

when assigned to the control group.24

The regression result for measurement equation in sample selection model is shown in25

TABLE 2. Two ordinary least squares (OLS) regressions were also conducted directly based26

on 306 observed parking responses as baseline. All four models gave similar estimations for27

the effect of being UC Berkeley staff members. Staff significantly parked about 4 days more28

than faculty. This may be caused by their more restricted working schedules. The regression29

also showed that subjects owning bikes parked on campus less often. First considering model30

(1) and (3), where the homogeneous treatment effect was estimated. The selection model31

suggested a barely significant average treatment effect of 2.295 days reduction of on cam-32

pus parking per subject during 3 months. The correction between selection and observation33

Raja Sengupta 15

process ρ was highly significantly positive. We interpret this as an indicator for "positive1

selection". The OLS estimated a larger and more significant treatment effect, which, how-2

ever, biased. We further consider the existence of heterogeneous treatment effect, where3

FlexPass’ treatment effect varied among different types of individuals. This is captured by4

an interaction term in model (2) and (4). In the sample selection model with interaction5

term, model (4), there is no significant treatment effect for people who had reported not6

interested in the rebate when signed up. According to the entry survey, before the study7

non-rebate-interested subjects parked on campus for 4.6±1.1 days, while rebate-interested8

subjects parked on campus 4.1± 1.3 days. Non-rebate-interested subjects generally have a9

hard demand for driving and parking on campus, with small price elasticities. The size of10

treatment effect on rebate-interested subjects was 3.372 days with standard error 1.436 (The11

covariance between the coefficients of interaction term and treatment T was -8.024). This12

results in a p-value of 0.017, which is considered as significant effect. FlexPass’ treatment13

effect also varied by weekday. We run model (3) in TABLE 2 on different weekdays, includ-14

ing Monday, Tuesday, Wednesday, Thursday and Friday. In the worst case, Monday, the15

reduction is 0.31 days per subject on all Mondays during the study. Compared to control16

group baseline, it is a 1.8 % reduction, with p-value 0.19.17

As mentioned before, MFLM underestimated number of non-campus parking days for18

treatment group. Compared with OLS, the sample selection model produced conservative19

estimator of the treatment effect. Although our estimation of treatment effect may still20

be biased, it is in the safe direction . Therefore we concluded that FlexPass did changed21

subjects’ parking behavior. On the population level, the treatment effect of FlexPass was22

2.23 days per subjects, which is a 0.18 day reduction per week. This 4.2% demand reduction23

is close to the 5% Ng inferred from the focus group and stated preference survey (9), but24

slightly smaller. There is no significant treatment effect for people who were regular drivers.25

For subjects reported interested in the incentives, which is 77.8 percent of the population,26

FlexPass induced a 3.372 days on campus parking demand reduction per subject, which is a27

0.26 day reduction per week, a 6.0% demand reduction. This reduction was achieved with28

an average rebate of nearly $27 per subject over a 3 month period. The study suggests that29

the unbundling of monthly parking and moderate incentive payments can reduce employee30

parking.31

4. CONCLUSION32

Employee parking is a benefit provided by the university at below market rates. Large33

employers like the University of California, Berkeley, nevertheless need to increase greener34

travel for economic and sustainability goals. To this end, the FlexPass study has explored35

reducing the number of employees who drive alone and park by testing a pay back scheme36

that unbundles monthly parking permit. UC Berkeley employees usually pre-pay for monthly37

parking by buying a permit with pre-tax dollars. The FlexPass treatment rebates some or38

all of this amount in proportion to the number of days not parked.39

We designed the FlexPass study as a randomized controlled trial to learn if daily40

rebates can reduce employee parking. The trial measures the number of days parked or not41

parked by requiring subjects to report parking each day using an app. The same information42

was solicited in weekly emails from subjects not using the app. The causal effect of the43

FlexPass is quantified by estimating the average number of days parked per subject in the44

Raja Sengupta 16

TABLE 2 : Casual Inference Results from Sample Selection Model-Selection equation

Dependent variable:TreatmentValid ControlValid

(1) (2)Age Group.SENIOR 0.116 −0.666∗∗

(0.314) (0.297)

Gender.MALE 0.307 0.027(0.265) (0.222)

Has Bike.TRUE 0.420 0.241(0.270) (0.236)

Has Clipper Card.TRUE 0.541∗∗ 0.030(0.257) (0.218)

Berkeley Staff.TRUE 0.665∗∗ 0.251(0.271) (0.270)

Days Not Commute 0.159∗ 0.204∗∗(0.089) (0.092)

Rank Mobile app 0.084 −0.191∗(0.132) (0.114)

Rebate Interesting.TRUE 0.793∗∗∗ −0.340(0.251) (0.262)

Constant −0.977∗∗ 0.674(0.449) (0.428)

Observations 196 196Log Likelihood -83.604 -101.530Akaike Inf. Crit. 185.208 221.061

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Raja Sengupta 17

TABLE 3 : Casual Inference Results from Sample Selection Model-Observation equation

Dependent variable:

noPark

OLS selection

(1) (2) (3) (4)Rebate 2.841∗∗ −2.836 2.295∗ −1.978

(1.257) (2.792) (1.279) (2.814)

Berkeley Staff −4.010∗∗∗ −3.907∗∗ −4.430∗∗∗ −4.300∗∗∗(1.532) (1.522) (1.551) (1.535)

Age Group.Senior 0.969 1.308 1.650 1.812(1.942) (1.934) (1.967) (1.949)

Has Bike 2.750∗∗ 2.960∗∗ 2.253 2.484∗(1.370) (1.363) (1.393) (1.383)

Rebate Interesting.TRUE 3.279∗∗ 0.149 2.758∗ 0.414(1.594) (2.098) (1.611) (2.107)

Rebate:Rebate Interesting.TRUE 7.089∗∗ 5.435∗(3.118) (3.193)

Constant 8.481∗∗∗ 10.653∗∗∗ 7.182∗∗∗ 9.501∗∗∗(2.055) (2.254) (2.241) (2.386)

Observations 306 306 400 400R2 0.085 0.101Adjusted R2 0.070 0.083Log Likelihood -1,354.243 -1,352.815rho 0.405∗∗∗ 0.356∗∗

(0.122) (0.141)

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Raja Sengupta 18

treatment and control groups.1

The causal analysis of the treatment effect uses the longitudinal parking usage data2

produced by the app using the box model. There are two biases estimated using the Mixed3

Latent Factor Model (MLFM) and the selection model. Under-reporting in the app is quan-4

tified as Missing Not At Random (MNAR), and estimated by using the email surveys. We5

proposed the MLFM for modeling the under-reporting and for recovering the missing data.6

The MLFM resulted in a 20.88% cross-validation error rate, which outperforms the best7

feature-based model we tried. Dropout biases are estimated by a sample selection model.8

We present both the OLS and selection model. The selection model has a conservative re-9

sult. We estimate the FlexPass causes a 4.2% reduction in parking consumption (2.23 days10

over the 3 month study period) with a p-value of 0.07. The 77% of the subjects reporting11

interest in the incentives a priori show a greater and more significant demand reduction.12

FlexPass induced a 3.372 days on campus parking demand reduction per subject in this13

sub-population, which is a 0.26 day reduction per week, a 6.0% demand reduction, with a14

p-value of 0.017. The FlexPass treatment effect varies by weekday. The smallest treatment15

effect is on Monday. There is only a 1.8 % reduction with p-value 0.19.16

These reductions required a total rebate of $4256 to the 158 valid subjects in the17

treatment group. Each subject received $26.94 on average over the entire study period.18

The highest rebate for an individual is $285 with most rebates being under $20. We find19

that unbundling a monthly employee parking permit reduces parking by making employees20

mindful of daily parking usage.21

REFERENCES22

[1] Thomas C Chalmers, Harry Smith, Bradley Blackburn, Bernard Silverman, Biruta23

Schroeder, Dinah Reitman, and Alexander Ambroz. A method for assessing the quality24

of a randomized control trial. Controlled clinical trials, 2(1):31–49, 1981.25

[2] Bhuvanachithra Chidambaram, Marco A Janssen, Jens Rommel, and Dimitrios Zikos.26

CommutersâĂŹ mode choice as a coordination problem: A framed field experiment on27

traffic policy in hyderabad, india. Transportation research part A: policy and practice,28

65:9–22, 2014.29

[3] James Davidson, Benjamin Liebald, Junning Liu, Palash Nandy, Taylor Van Vleet, Ullas30

Gargi, Sujoy Gupta, Yu He, Mike Lambert, Blake Livingston, et al. The youtube video31

recommendation system. In Proceedings of the fourth ACM conference on Recommender32

systems, pages 293–296. ACM, 2010.33

[4] Miller R. Pincus-Roth E. Wickland T. Sen A. Shirgaokar M. Liu Q. Deakin, E. Campus34

parking demand: Results from baseline data collection and analysis. Technical report,35

2013.36

[5] IV Evans, KU Bhatt, KF Turnbull, et al. Traveler Response to Transportation System37

Changes. Chapter 14-Road Value Pricing. Number Project B-12A FY’99. 2003.38

[6] James J Heckman. Sample selection bias as a specification error (with an application39

to the estimation of labor supply functions), 1977.40

Raja Sengupta 19

[7] Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix factorization techniques for1

recommender systems. Computer, (8):30–37, 2009.2

[8] Adeel Lari, Frank Douma, Kate Lang Yang, Kathryn Caskey, and Colin Cureton. In-3

novative parking pricing demonstration in the twin cities: Introducing flexibility and4

incentives to parking contracts. Technical report, 2014.5

[9] Wei-Shiuen Ng. Assessing the Impact of Parking Pricing on Transportation Mode Choice6

and Behavior. PhD thesis, University of California, Berkeley, 2014.7

[10] Frank Roland Proulx, Brian Cavagnolo, and Mariana Torres-Montoya. The impact of8

parking pricing and transit fares on mode choice to a major university campus. In9

Transportation Research Board 93rd Annual Meeting, number 14-5236, 2014.10

[11] Adella Santos, Nancy McGuckin, Hikari Yukiko Nakamoto, Danielle Gray, and Susan11

Liss. Summary of travel trends: 2009 national household travel survey. Technical report,12

2011.13

[12] Donald C Shoup, American Planning Association, et al. The high cost of free parking,14

volume 206. Planners Press Chicago, 2005.15

[13] Dani Simons. Sfpark: San francisco knows how to park it. Sustainable Transport, (23),16

2012.17

[14] Nathan Srebro, Tommi Jaakkola, et al. Weighted low-rank approximations. In ICML,18

volume 3, pages 720–727, 2003.19

[15] Aldo Tudela Rivadeneyra, Manish Shirgaokar, Elizabeth Deakin, and William Riggs.20

The cost versus price for parking spaces at major employment centers: Findings from21

uc berkeley. In Transportation Research Board 94th Annual Meeting, number 15-3640,22

2015.23

[16] Richard WWillson and Donald C Shoup. Parking subsidies and travel choices: assessing24

the evidence. Transportation, 17(2):141–157, 1990.25