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Predicting NoShows to Create an Effective
Overbooking Policy for Restaurants
Madeleine Shannon
Advisor: Professor Ivan Canay
Northwestern University Mathematical Methods in the Social Sciences
2015
Table of Contents
I. Abstract…………………………………………………………………….3
II. Acknowledgments………………………………………………………….4
III. Introduction………………………………………………………………...58
IV. Literature Review…………………………………………………………..814
V. Data Description…………………………………………………………...1417
VI. Model....……………………………………………………………………1820
VII. Results……………………………………………………………………...2124
VIII. Overbooking Policy and Implications……….……………………………..2530
IX. Conclusion………….………………………………………………………3032
X. Tables and Figures………………………………………………………….3338
XI. References………………………………………………………………….3940
XII. Appendix A...………………………………………………………………4146
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I. Abstract
Customers who do not show up for their reservations are extremely costly for
restaurants—an unfilled table may be the difference between a profitable night and an
unprofitable one. Various strategies employed to reduce noshow rates are only slightly effective.
However, other industries have used overbooking to substantially mitigate the cost of a given
noshow rate. Despite the risk of jeopardizing customer satisfaction, a moderated overbooking
policy can be effective for restaurants. I estimate the probability that restaurant customers will be
noshows using a large data set of reservation and restaurantspecific variables. I use this
logistic model to inform an overbooking policy for restaurants, emulating the overbooking
strategy of airlines and healthcare clinics. Restaurant overbooking has not been extensively
studied, and to my knowledge, no suggested policy has been developed by incorporating the
predicted probability of noshows. The data I use include 74,926 observations from fifteen
restaurants over four years. I find that a customer’s previous reservationkeeping behavior at the
restaurant in question has the largest marginal effect on whether he or she will be a noshow. I
recommend an overbooking policy that uses this variable to stratify customers and find that a
sample restaurant could save over $220,000 per year.
3
II. Acknowledgments
First and foremost, I would like to thank my advisor, Professor Ivan Canay, for all of his
advice and guidance throughout this entire process. He was instrumental to the completion and
success of this thesis. I would also like to thank Chris Butler for generously providing me with
the data and helping to develop my ideas early on. Thank you to Professor Rogerson for so
enthusiastically brainstorming my topic with me and for encouraging me to tackle this empirical
project. Germán Bet was extremely helpful in answering my questions during office hours and
engaging with my results. I’d like to thank all of my family and friends who helped edit my work
and for their support in general, which is always invaluable. Finally, I’d like to thank Marc Vetri
for stimulating my interest in the world of food and for the best meal I’ve ever eaten.
4
III. Introduction
Noshows—customers who fail to show up for their reservation—are a persistent and
costly problem for restaurants. So costly, in fact, that some restaurants have resorted to
personally outing noshows on Twitter, by name (Forbes 2013). Restaurateurs know that making
money means turning tables. A night in a restaurant is a delicate dance: one must rotate the
customers in and out as quickly as possible while still giving them a personal, enjoyable
experience. Since every empty table in a restaurant is lost revenue, and restaurants operate with
slim margins (typically around 3% 5%), noshows can be the difference between a profitable
night and a costly one. The noshow problem affects almost every restaurant—some cities, such
as New York, report restaurant noshow rates of up to 20% (Reddy 2012). This means that a
restaurant with a capacity of 50 people and an average check size of $100 for a table of two,
could be losing up to $500 in revenue each hour due to noshows. Restaurants are confronted 1
with an interesting problem: customers face no cost for not showing up for their reservation, and
yet, restaurants suffer when they hold an empty table.
Due to this costly predicament, restaurants have employed various strategies to combat
noshows. First, the optimality of taking reservations has been called into question. Despite the
fact that customers value the guaranteed seating that comes with a reservation, restaurants give
them away for free. Customers make reservations in advance, without knowing how much they
will value that reservation when it comes. The customers only fix their valuation at the time they
decide whether or not to show up; thus, there is no incentive for them to honor their reservation
if they find that their current valuation is not as high as it was when they made the reservation.
1 Assuming a table turn time of one hour and a 20% noshow rate, without accounting for differences in check size or turn time due to party size.
5
Reservations are useful, however, because they allow restaurants to shift their customers
into offpeak times by informing them that onpeak times are filled. So, reservations allow
restaurants to collect more money on slow days at the risk of losing money on fast days due to
noshows. Reservations also lead to more efficient table assignments since variations in arriving
party sizes are known ahead of time. That said, as demand increases, offering reservations
becomes less and less optimal because seats can be filled with walkins (Alexandrov and
Lariviere 2007). But not every restaurant has ample demand. Three Michelin star restaurants, for
example, are typically reserved for special occasions and therefore generally do not generate
enough foot traffic to fill tables on the spot. Restaurants that do offer reservations have found
some success combating noshows in other ways: confirming reservations via text or by phone,
requiring a credit card to hold the reservation and threatening a noshow fee, or refusing to serve
customers who did not show up for their last reservation at that restaurant (McKeever 2013).
While these strategies slightly reduce the noshow rate, none are universally successful and some
are unnecessarily harsh.
Clearly, it is hard to force people to honor reservations. The next best option, then, is for
restaurants to find a way to mitigate the costs associated with noshows. One such strategy,
overbooking, has been successfully applied in other industries. Airlines, hotels, and clinical care
settings use overbooking policies to offset the cost of noshows. Airlines have profitably applied
overbooking to the extent that it is now common practice. Some airlines will overbook up to
50% of their seats (Massey n.d.). By giving vouchers to people who volunteer to take another
flight and refunding those who are bumped involuntarily, airlines employ a compensation
scheme that allows them to oversell quite frequently, potentially without damaging customer
6
loyalty (although this is debated by Wangenheim and Bayón 2007, see section IV of this paper).
Both hotels and airlines use priority stratification of customers to determine who will be
overbooked or bumped, giving loyal customers some security.
Clinical care settings have also benefitted from overbooking. Unlike airlines, however,
noshows in doctors offices are distributed throughout the day; they do not occur at one moment.
Appointment overbooking in this setting is more nuanced, yet still has been shown to be
beneficial (LaGanga and Lawrence 2007, discussed in section IV of this paper). The downside to
appointment overbooking is that customers may face increased waiting times and service
providers may work overtime, although customers are not typically “bumped” out of their
appointments.
Overbooking in restaurants has not been extensively studied. Restaurant reservation
overbooking mirrors clinical appointment overbooking because just as appointments are spread
out over the day, reservations are spread throughout the restaurant’s open hours. However, this is
an imperfect analogy. There are many important aspects of reservations that increase the
complexity of a restaurant overbooking policy, such as varying party size and the vast
importance of customer satisfaction. Customer satisfaction is more important for restaurants than
healthcare clinics because doctors are selling a necessary service, while restaurants are selling an
optional experience. Creating a restaurant overbooking policy is also difficult because of a lack
of publicly available data—especially for small, independent restaurants. These restaurants
themselves may not know the extent of their noshow problem.
In order to create an effective overbooking policy for restaurants, it is necessary first to
obtain and use this private data to understand the noshow problem. Why are customers not
7
showing up? What makes one customer more likely to be a noshow than another? To answer
these questions, I use a large data set to create a model that predicts the probability of a customer
being a noshow and then use this model to inform an overbooking policy—allowing restaurants
to decide whether or not to use reservation overbooking on a given night, and if so, by how
much. To my knowledge, this is the first time that a large data set of individual reservations and
restaurant characteristics has been used to estimate a binary choice model. In turn, the estimated
choice model provides a framework to develop an effective overbooking policy that incorporates
the predicted probability of being a noshow given observed characteristics of the customers and
restaurant.
IV. Literature Review
The existing literature mainly focuses on four topics related to restaurant overbooking:
noshows in general, restaurant reservations, overbooking in other industries, and the behavioral
consequences of overbooking. Restaurant overbooking itself is only briefly mentioned in a few
studies in these areas.
NoShows in General
Much of the previous work around noshows has been anecdotal. An article in The
Washington Post (2003) asserted that noshows not only cause restaurants to lose money on
unfilled tables, but also lead to additional costs due to wasted food. According to this article, in
order to combat noshows some restaurants only take reservations on weeknights, when they
benefit most from guaranteeing seats, and operate as walkin only restaurants on the weekends
when demand is higher. In Remarkable Service (2014), The Culinary Institute of America
offered a grim outlook for dealing with noshows; it suggests that even reconfirmed reservations
8
often lead to noshows. And, despite the fact that reservations help restaurants shift demand to
offpeak times, they warn that offering reservation times an hour or more outside of the
originally requested time will dramatically increase the chance of a noshow. The tradeoff
between filling tables effectively via overbooking and customer service is troublesome as
well—“it might be preferable to lose a table for a night rather than risk losing a valuable
customer” (Remarkable Service, page 124). Oh and Su (2012) proposed a pricing policy and
noshow penalty to deal with noshows. Their results showed that restaurants should charge a
noshow penalty as high as the price of the meal while providing a discount to customers for
their meal if they show up.
Restaurant Reservations
As mentioned earlier, the optimality of taking reservations has been addressed in
previous studies. For example, Alexandrov and Lariviere (2007) assume a single evening, with a
priori homogenous customers who all consume the same capacity, and find that reservations can
be profitable under any of the following circumstances: uncertain market size, when the evening
is divided into peak and offpeak periods, or under strong competition. Reservations are not
recommended when customers are likely to favor just one firm in the market or in a large market
where sales will be lost to noshows. Bertsimas and Shioda (2003) used a stochastic gradient
algorithm to create a model that determines how many reservations to accept for a particular day
given information on reservation requests, walkins, and noshow rates. This study differs from
the current study because it assumes a constant noshow probability of 10%, which I will show is
a limiting assumption.
9
Overbooking in Airlines
There has been a considerable amount of past research that focuses on overbooking in the
airline industry—with somewhat mixed results. Rothstein (1985) and Arenberg (1991) view
airline overbooking as an economic necessity. With reported noshow rates of 10% to 20%,
airlines allegedly must resort to overbooking to offset losses from unfilled aircrafts. Since the
writing of those articles, airline overbooking has become more prevalent and
nuanced—Coughlan (1999) proposed an improved airline overbooking model by addressing the
multiclass system that most airlines use. Suzuki (2002) took into account the negative effect of
overbooking on customer behavior and showed that despite the significant size of this effect,
airlines should not reduce overbooking because the positive gain far outweighs the negative
consequences. In a later work (Suzuki 2004), she addressed the net benefit of airline overbooking
and found it to be positive under all conditions, but far less than the reported gross benefit that
most airlines focus on.
Overbooking in Healthcare
In the healthcare world, the practice of patient overbooking has become more widespread
as well. LaGanga and Lawrence (2007) found that overbooking allows healthcare clinics to serve
more patients and improve provider productivity, but it can also lead to increased patient wait
times and provider overtime. In another study, increased provider overtime was taken into
account and overbooking was still shown to be beneficial. East Carolina University’s Student
Health Services Clinic, which had a 10.8% patient noshow rate prior to the study, employed an
overbooking model that included the effects of employee burnout and saved around $95,000 per
semester while improving healthcare access for students. They found that overbooking by
10
10%15% was the most effective. Zeng, Zhao, and Lawley (2010) showed that overbooking
positively affects showup rates by reducing appointment delay—the time between requesting an
appointment and being seen by a doctor—but negatively affects showup rates by increasing
office delay—the amount of time spent waiting in the office before being seen. Because of this,
they suggest using a selective dynamic overbooking strategy that takes into account their finding
that overbooking has different effects for patient populations with different characteristics. Both
Shonick and Klein (1977) and Dove and Schneider (1981) created models that use patient
characteristics to predict noshow rates and subsequently inform overbooking policy. Shonick
and Klein found age and sex within age to be significantly related to noshows and proposed
overbooking enough patients so that the expected number of arrivals based on the estimated
probabilities of arriving is equal to clinic capacity. Dove and Schneider found that the most
important predictor of appointment keeping is a patient’s previous appointmentkeeping pattern.
This study, too, suggested scheduling patients based on the expected number of patients who will
show up, but found that overbooking based on the average noshow rate is a simple and effective
method for clinics.
Behavioral Consequences of Overbooking
The behavioral consequences of overbooking were addressed by Wangenheim and Bayón
(2007), who found that customers who experience the negative effects of overbooking
significantly reduce their interactions with the firm, while customers who benefit from
overbooking only slightly increase their interactions, suggesting that firms who chose to
overbook should consider the longterm consequences of assuming a revenuecentric approach
over a customercentric one. In his article “The Customer is Not Always Right,” Sorrell responds
11
to this claim by asserting that when deference to the customer leads to a significant loss of
revenue (as it often does), the customer should not come first. Suzuki (2002) accounted for the
behavioral consequences of overbooking gone awry, as discussed earlier, and found overbooking
to be beneficial despite these consequences.
Overbooking in Restaurants
An overbooking policy for restaurants is mentioned briefly in Oh and Su’s work (2012).
They incorporate overbooking into their model of noshow penalty fees and meal pricing and
find that as the market size increases with respect to restaurant capacity, the optimal meal price
with overbooking increases, the optimal noshow fee decreases, and profit with overbooking
increases. See their results reproduced in Appendix A, Figure A1. Overbooking for restaurants is
also addressed by Alexandrov and Lariviere (2011)—their model assumes customers are
atomistic and they suggest overbooking by giving out K/F(T) reservations, yielding K actual
patrons (where K is capacity and F(T) is the number of customers interested in dining out on a
slow night). The overbooking policy they propose seems to suggest that overbooking is the
definitive answer to noshows, but this is oversimplified due to assumptions made in the
theoretical setting.
Advancing Existing Literature
As discussed, the negative effects of restaurant noshows and the motivation behind
taking reservations have been addressed in previous work. Overbooking in the airline and
healthcare industries has been looked at fairly extensively from both economic and behavioral
viewpoints. Patron characteristics have been used successfully to inform overbooking policy in
the clinical care setting. However, despite the rampant problem of noshows in the restaurant
12
industry, a comprehensive combination of these studies has not yet been tackled.
Perhaps overbooking in restaurants has not been extensively studied due to a lack of
sufficient data in the restaurant industry, especially relative to the wealth of available data from
airlines and healthcare clinics. Both the airline and healthcare industries heavily depend on data.
These industries consist of huge, publicly owned corporations that must use data to operate
efficiently. The restaurant industry, however, is mostly made up of many small, private, and
highly competitive singular units. Large restaurant groups and hotel restaurants are the
exception; they are financially supported by the overarching company and therefore have the
capacity to collect and analyze their data, although certainly not all of them do. Only 12% of
restaurants in the U.S. have over 50 employees, while 46% of restaurants in the U.S. have under
10 employees. These singular, oneoff restaurants are usually the ones who are hit hardest by 2
noshows. They typically do not even collect data, let alone use it to their advantage. OpenTable
has played a big role in giving restaurants the opportunity to own their data. Restaurants paying
for the OpenTable service can track their customers, view their noshow rates, and start
marketing campaigns. It certainly is important that restaurants know and keep track of these
statistics, but it is more important that this information is actually analyzed and used to make
changes.
Using customer data collected from many restaurants, I will advance the existing
literature by proposing an overbooking policy for restaurants that is informed by a predictive
noshow model based on customer and restaurant characteristics. I will also attend to restaurants’
unique need for superior customer service by suggesting compensation schemes in the event that
2 Business Data from the US Census Bureau http://censtats.census.gov/cgibin/cbpnaic/cbpcomp.pl
13
overbooking goes awry. To my knowledge, this analysis has never been done.
V. Description of Data
I worked with three categories of variables: the first is restaurantspecific data that
include demographic information about the restaurants in my data set; the second is Yelp
information (price and rating) for each restaurant, which I manually collected from Yelp; and the
third is reservationspecific data that include information about each reservation in every
restaurant.
Manipulating the Data Set
I received the restaurantspecific and reservationspecific data from Chris Butler (see
acknowledgments), founder of Complete Seating, “a reservation, waitlist, and seating
management service,” similar to OpenTable. The data span from February 27, 2011 through the 3
end of 2014. My first challenge was converting this rich data into a workable form. I planned to
conduct my analysis in STATA, but the data set was in the form of a MySQL dump, which is
unreadable by STATA. To understand why, it is helpful to understand what MySQL and STATA
are. MySQL is a specialized database software that allows users to store and retrieve data
efficiently. SQL is a computer language used to access data from MySQL. STATA is a data
analysis program—not a database. In order to move the data from MySQL, where it was stored,
and into STATA, I first created a local SQL server and connected to it via Sequel Pro. Then, I
created a new database and imported the MySQL dump file. This allowed me to export the data
as a .csv file, thereby converting the MySQL dump into a file type readable by STATA.
3 www.completeseating.com
14
In order to create my final data set, I manually appended the restaurant data set with the
Yelp information that I collected by searching for each restaurant on Yelp.com. Yelp information
is missing for three out of the fifteen restaurants. I merged the restaurant and Yelp information
data set onto the reservationlevel data set using the restaurant ID number that was included in
both data sets. The final reservationlevel data set includes 74,926 observations.
Category 1: Restaurantspecific Variables
The first category of variables comprises the restaurantlevel data set which has
information about the fifteen restaurants that used the Complete Seating service to collect
reservations and acquired enough reservations to be included in the final data set (at least 100).
Three restaurants were dropped under these conditions: two because they had gathered less than
ten reservations each and another because all 117 of its observations were generated by walkins.
The retained restaurants are located in the following cities in California: San Francisco (10
restaurants), Burlingame (1), Novato (1), Oakland (1), Sonoma (1), and Winnipeg in Canada (1).
The data include choices the restaurant has made about reservations and guest communication.
For instance, restaurants chose how far in advance reservations can be made (ten out of sixteen
restaurants allow reservations 30 days in advance), the minimum and maximum party size for
reservations (minimum is one person for all but one restaurant, which has a two person
minimum, and the maximum varies between four and sixteen people), whether or not to restrict
large parties, and the number of people that constitutes a large party. Regarding guest
communication, the restaurant may or may not have allowed automated communication with the
guest through text, email, and/or phone, and may or may not allow waitlist requests via text,
phone, and/or widget (via the Complete Seating application). Finally, the restaurant chose how
15
many days in advance it would confirm the reservation with the guest: 1 day in advance (for
thirteen of the restaurants), 2 days (for one restaurant), or 7 days (for one restaurant).
Category 2: ManuallyInputted Variables
To this data, I appended the second category of variables: Yelp rating and Yelp price. It
should be noted that the Yelp information was collected in 2015 and therefore may not match the
Yelp ratings or prices at the time of many reservations in the data set—it is treated as a proxy.
Yelp information is missing for three restaurants, as mentioned, which were not listed on Yelp.
This is likely due to restaurant closure or name change. These three restaurants account for 1,176
observations. The Yelp rating is 3.5 out of five stars for eight of the restaurants. The Yelp price
is two out of four (with four being the most expensive) for seven restaurants.
Category 3: Reservationspecific Variables
The third category of variables is reservationspecific. This data set initially included
information about seatings that originated from walkins via the waitlist, cancellations, and from
reservations that were made in advance. For my purpose of predicting noshows, only
reservations that were made in advance and cancellations within one hour of the reservation time
were kept. An unidentifiable guest id, which is missing for 4,384 reservations, is used to note if
the guest is a repeat customer or a firsttime guest, and if that guest has been a noshow in the
past at this restaurant. Additionally, a “guest record” can be gleaned from this by tracking the
ratio of the number of noshows to the number of total reservations throughout the guest’s
history with the restaurant. Variables related to guest ID have 70,542 observations. Also included
in this data set are: the time of the requested reservation, the party size, the origin of the
reservation (whether it was made over the phone or from the restaurant website), the guest’s area
16
code, and guest notes. Party size is one or two people almost half the time. Guest notes include
birthday and anniversary notes, requests for special tables, and notifications about allergies or
vegetarian diets—28% of the reservations have guest notes of some kind. The guest’s area code
was matched to the restaurant’s area code to create an approximate indicator for whether or not
the guest is located nearby the restaurant. After the reservation has been made, it is noted
whether or not the guest was contacted to confirm their reservation (80% were) and if so, how
this was done (via email, phone, or text). Finally, cancellations and noshows are recorded at the
time they occur. Summary statistics for the variables included in my data can be found in Table
1, section X.
The Dependent Variable
The response variable of interest is a noshow indicator. I defined noshows as those
customers who either did not show up or cancelled within an hour of the reservation time, under
the assumption that it would not be reasonable for the restaurant to acquire a new reservation to
replace the canceled reservation within an hour. Of course, walkins may act as a replacement in
these cases, but having enough walkins to make up for noshows is not certain, and walkins are
not included in the data set. Restaurant hosts can indicate noshows either by recording a
noshow datetime or marking the “state” of the party as a noshow. With variation in the use of
the application, some hosts did one or the other and perhaps some noshows went unrecorded
entirely. Labeling cancellations within an hour of the reservation time as “noshows” will also
act as a buffer for these cases. The final noshow rate in the data is 10.9%.
17
VI. Model
Let Y denote the noshow indicator and (X, Z) be a vector of reservationspecific and
restaurantspecific covariates. The following model is used to estimate the effects of different
restaurantspecific and reservationspecific characteristics on the probability of a reserver being a
noshow:
(1) Pr( = 1 | ) = ,Y jit , ZX jit jit [βX γZ ]Λ ′ jit + ′ jit + δj
where j indexes restaurants, i indexes reservations, and t indexes time. takes three forms in [∙]Λ
this analysis: a linear function for OLS, a logistic function for Logit, or a cdf normal function for
Probit. I split the covariates into two groups. The vector includes six coreX jit
reservationspecific variables. The vector includes restaurantspecific variables, which areZ jit
only used in some specifications as controls. Finally, denotes restaurant fixed effects. δj
The six core variables are: Party Size, Same Area Code Indicator, Repeat Guest
Indicator, Confirmation Indicator, Previous NoShow Indicator, and Guest Note Indicator. Same
Area Code Indicator is used as a proxy for whether or not the customer lives nearby the
restaurant and is 1 when the restaurant and customer share the same area code. Repeat Guest
Indicator is based on an unidentifiable guest ID and is 1 when that customer has previously made
a reservation at that restaurant. Confirmation Indicator is 1 when the customer was either called
or texted to confirm the reservation sometime before the reservation time, and 0 otherwise.
Previous NoShow Indicator is 1 when the customer did not show up to a previous reservation at
that restaurant—by definition, Repeat Guest is 1 whenever Previous NoShow is 1. Guest Note
Indicator is 1 if the customer included any kind of special instructions with his/her requested
reservation, and 0 if not. These core variables are all reservationspecific and therefore are easy
18
for the restaurant to track and respond to. Additionally, they all provide potential reasons for a
guest to be more or less likely to show up. For example, if someone takes the time to enter a
guest note about a special occasion, it is reasonable to believe that that person will be more
inclined to show up for their reservation. If a customer lives in the same area code as the
restaurant he or she reserved with, that customer has a lower cost of getting to his or her
reservation and therefore may be more likely to show up. Similar lines of reasoning can be
applied to the other variables.
There are five total specifications for each form of Each specification addresses a [∙].Λ
potential problem with the estimations obtained from the simple model (specification 1), which
includes only Specification 2 includes control variables that are restaurantspecific, in.X jit ,Z jit
order to draw out bias captured in the six core reservationspecific variables. Specification 3
includes restaurant fixed effects, in order to control for heterogeneity caused by consistent,δj
unobserved differences between restaurants that affect the observed variables. For example, if
one restaurant has a host who is always rude when calling to confirm a reservation, we might
expect this to lead to an increase in noshows. This effect would not be captured by the six core
variables, but would be potentially correlated with them. Specification 4 relaxes the assumption
that are iid by using clustered standard errors at the restaurant level, therefore, X , Z ) (Y jit jit jit
allowing for arbitrary correlation between the observations corresponding to the same restaurant.
A potential problem with this specification, however, is that there are only fifteen restaurants,
which leads to a small number of clusters and may cast doubt on the asymptotic arguments
behind inference with clustered standard errors. Specification 5 includes interactions between the
most predictive variable, Previous NoShow Indicator, and some of the other core variables. It is
19
worth noting that the interpretation of the coefficients reported for specification 5 differs from
that of specifications 14.
First, let be a linear function. This gives us OLS regressions with the previous five [∙] Λ
different specifications, see Table 2. I ran OLS regressions first in order to get rough baseline
estimates of these six variables’ effects. The effects are consistent across every specification,
suggesting that the six variables chosen lead to predictable changes in the dependent variable.
However, in order to estimate probability, a linear regression is not wellsuited because it does
not account for the fact that Y is binary, and therefore may lead to predicted probabilities that are
outside (0,1).
A more suitable choice is a logistic regression which treats the dependent variable as
discrete—taking either 0 or 1—by using a function whose range lies in [0,1]. Let be a [∙]Λ [∙]Λ
logistic function to produce Logit regressions, once again with five different specifications, see
Table 3. The marginal effects in this table were estimated with all other core variables set to their
average values. Marginal effects estimated with Party Size at it’s mean and all other core
variables at 0 or at 1 can be found in Appendix A, Tables A1 and A2 respectively.
As a final robustness check, I ran a Probit model, which represents an alternative popular
parameterization of the conditional probability of noshows. The signs and magnitude of the six
core variables are consistent with Logit findings and therefore both models seem to provide a
similar approximation, see Appendix A, Table A3. Thus, the results will be based on the Logit
model for the remainder of this paper.
20
VII. Results
Estimates of equation (1) show that customer characteristics are predictive of the
probability of being a noshow. The relevant estimates can be seen in Table 3, which reports
Logit regressions with all variables at their average value, for all five specifications discussed
earlier. Estimates of all six core variables are significant in every specification (except
Confirmation Indicator in Specification 4). Since the effects are consistent across all
specifications, for the purposes of discussion, I will henceforth focus on specification 2, which
includes restaurantspecific controls. For reference, some results from specification 2 are
compared to those from specification 5 as a robustness check and are found to be consistent, see
Appendix A, Figure A3.
An increase in the following variables, or a change from 0 to 1, results in a decrease in
the probability of being a noshow: Party Size, Same Area Code Indicator, Repeat Guest
Indicator, Guest Note Indicator. Changing the following variables from 0 to 1, however, leads to
an increase in the probability of being a noshow: Confirmation Indicator and Previous NoShow
Indicator. Previous NoShow Indicator has the largest marginal effect on the probability of being
a noshow. This finding is consistent with that of Dove and Schneider (1981) in the context of
healthcare. A customer who was previously a noshow at that particular restaurant is 41% more
likely to be a noshow than a customer who was not, all else equal.
According to the model, customers who were called or texted to confirm their reservation
are also more likely to be a noshow. This is a surprising result and deserves a brief discussion. It
is a considered common knowledge in the restaurant industry that confirming reservations helps
to reduce noshows, but this finding suggests the opposite. There are two potential reasons for
21
this contradiction. First, restaurants recognize that confirming reservations with customers
reduces noshows because it allows customers who are not planning to show up to cancel their
reservation immediately, giving the restaurant a chance to rereserve that table. The customers
who cancel during the confirmation may well have been noshows if they were not contacted to
confirm their reservation. Confirmation, therefore, is effective for customers who forgot about
their reservation or who cannot show up but did not plan to call the restaurant to cancel. In this
sense, confirming does reduce noshows, but this benefit is not captured in my model since my
data only focus on customers who either did not cancel or cancelled within an hour of their
reservation time. Second, there could be measurement error in this variable that is introducing
bias. The source of the error is unknown, but summary statistics shown in Table 4 provide some
insight. Customers without guest IDs show the biggest negative effect of being contacted—their
noshow percentage is 17% when contacted and only 11% when not contacted. That said, they
are only contacted 2% of the time. Based on the guest notes, it seems that many reservations
without guest IDs are created by the restaurant staff for friends, family, or special guests
(investors, etc.). It is still hard to draw conclusions about these reservations, however, and
therefore I leave this variable noted as an inconsistency.
To fully explain the meaning of each variable's effects, it is best to consider two sample
customers—the “best case” customer and the “worst case” customer. Let the best case customer
have the lowest chance of being a noshow. In order to do this, I set each of the six core variables
to their most beneficial value (except for Party Size, which, for simplicity, is set to its average
value, 4, in both cases). For example, since changing Same Area Code Indicator from 0 to 1
decreases the probability of being a noshow, the best case customer will have Same Area Code
22
Indicator set to 1. The baseline probability of being a noshow for the best case customer is
3.4%. The worst case customer has each of the core indicator variables set to the least beneficial
value—the opposite of the best case settings. For example, Same Area Code Indicator for the
worst case customer is set to 0. The baseline probability of being a noshow for the worst case
customer is 44.3%.
Once we have the baseline settings for each indicator variable in both cases, it is
interesting to see what happens to the predicted noshow probability when one indicator variable
is switched from its base value while the others remain. This is depicted in Figure 1 (an
alternative depiction with precise probabilities can be found in the Appendix A, Figure A2) .
Switching Same Area Code Indicator from its best case baseline value of 1, depicted by , to 0,
depicted by , while leaving all other variables at their best case values, changes the probability
of noshow from 3.4% to 5.0%, an increase of 1.6 percentage points. Switching Same Area Code
Indicator from its worst case baseline value of 0, depicted by , to 1, depicted by , while
leaving all other variables at their worst case values, changes the probability of noshow from
44.3% to 35.1%, a decrease of 9.2 percentage points. From this, we can conclude that having the
same area code as the restaurant has a minimal effect on the probability of being a noshow if the
customer closely resembles a best case customer, but it has a much larger effect when he or she
closely resembles a worst case customer. A similar line of interpretation applies to all other core
variables shown in Figure 1.
Repeat Guest and Previous NoShow, however, deserve additional explanation. The best
case customer is a repeat guest who is not a previous noshow: Repeat Guest = 1, depicted by ,
23
and Previous NoShow = 0, depicted by . Switching Repeat Guest to 0, then, represents a new
customer in the best case. As seen in Figure 1, a new customer who otherwise resembles a best
case customer has a noshow probability of 7.7%. The worst case customer is a previous
noshow, and by definition, also a repeat guest: Repeat Guest = 1, Previous NoShow = 1.
However, it is not accurate to say that the worst case customer is a repeat guest, because that is
reserved for the case where Repeat Guest = 1 and Previous NoShow = 0. So, in Figure 1 there is
no worst case baseline value for Repeat Guest. When Repeat Guest = 1, depicted by , this
refers to a repeat guest who is not a previous noshow but otherwise resembles a worst case
customer. When Repeat Guest = 0, depicted by , this refers to a new customer, and is also the
value shown for Previous NoShow = 0 (even though Previous NoShow also takes 0 when
Repeat Guest = 1).
The most important takeaway from Figure 1 is that in some cases a deviation from the
worst case customer leads to a lower probability of being a noshow than a deviation from the
best case customer for the same variable. For example, if the customer resembles a best case
customer except he or she is a previous noshow, the probability of being a noshow is 27.4%. If
the customer resembles a worst case customer, but is a new customer instead of a previous
noshow, the probability of being a noshow is just 13.8%. It seems that Previous NoShow
trumps the effect of the other variables. Even if the customer has entirely beneficial
characteristics, if he or she was a previous noshow, it would be preferable to have a customer
with all the “wrong” characteristics who is not a previous noshow.
A similar phenomenon is seen with Repeat Guest—a worst case repeat guest is preferable
to a bestcase new customer. Figure 2 explains this finding further. It shows the best case and
24
worst case predicted probabilities of noshow for three categories of customers: repeat guests
who are not previous noshows, new customers, and previous noshows. Here it is evident that a
best case previous noshow is far more likely to be a noshow than a worst case new customer
and a best case new customer is more likely to be a noshow than a worst case repeat guest. Due
to these findings, this customer stratification will be used to create an overbooking policy for
restaurants.
VIII. Overbooking Policy and Implications
In order to design an overbooking policy, it is useful to quantify the results above using a
sample restaurant. Of the fifteen restaurants, Restaurant 8 is the most representative—it has
13,797 observations, a noshow rate of 11.5%, a Yelp rating of 3.5, a Yelp price of 3 dollar
signs, and a confirmation percentage of 73.2%. Restaurant 8’s best case customer has a predicted
noshow probability of 3.6%, and its worst case customer has a predicted noshow probability of
52.6%. Figure 3 shows the distribution of Restaurant 8’s customers as they are divided into the
three categories discussed earlier (Category 1: repeat guests who are not previous noshows,
Category 2: new customers, and Category 3: previous noshows). It also shows the maximum,
average, and minimum noshow probabilities for each of these customer segments. Repeat guests
make up 27% of Restaurant 8’s customers and have an average predicted probability of noshow
of 7%. New customers make up 68% of Restaurant 8’s customers and have an average predicted
probability of noshow of 11%. Previous NoShows make up just 5% of Restaurant 8’s
customers, but have an average predicted probability of noshow of 47%.
Based on these findings, there are two ways to solve for the expected percent of
customers who will show up to Restaurant 8. Equation (2) uses the customer stratification
25
discussed above and equation (3) uses the predicted probability of noshow for every reservation
at Restaurant 8,
(2) E(Percent Show Up | Restaurant 8) =
[Percent Customers in Category i (1 Average NoShow Probability for Category i)]∑3
i=1×
= (27 0.93) + (68 0.89) + (5 0.53) = 88.28%× × ×
(3) E(Percent Show Up | Restaurant 8) =
[Party Size for Reservation j (1 Predicted NoShow Probability for Reservation j)] /∑13,797
j=1×
(Party Size for Reservation j) 100% = 81.86%.∑13,797
j=1×
According to equation (2), Restaurant 8 can expect 88% of its customers to show up on a
given night (note that this prediction is consistent with Restaurant 8’s average noshow rate).
What does this prediction mean for Restaurant 8’s bottom line? The following calculations will
assume Restaurant 8 only takes reservations and cannot fill the table after a noshow. In October
of 2012, Restaurant 8 was open 25 days of the month. It had 37 reservations on average per
night. The average party size per reservation is 3 customers. So Restaurant 8 was serving 111
customers on average per night. Based on the expected percent of customers who will show up,
only 98 of those customers would arrive (111 0.88 = 98). Thus 13 people would be noshows.×
Restaurant 8 has a fixed price menu that costs $65 and an optional wine pairing that costs $49.
Assuming 50% of customers opt for the wine pairing, and everyone tips 18%, Restaurant 8’s
average check size is $105 per person. When 13 people do not show up, Restaurant 8 loses
$1,365 per night. That is a loss of $409,500 in revenue per year! But what if Restaurant 8
overbooked?
26
In order to create an efficient overbooking policy, the following variables need to be
considered:
C Restaurant capacity
N Number of customers booked
E Expected number of customers who will arrive, from equation (2) or (3)
A Number of customers who actually arrive
W Number of customers who arrive without overbooking
The goal of an overbooking policy is to find the optimal N for each night the restaurant is open.
An ideal overbooking policy would have N such that: N > A = C > W. The risk with any
overbooking policy is that too many customers show up as a result of overbooking and there is
not enough room in the restaurant to accommodate them: N > A > C > W. The practical
implications of taking this risk are costly—a bad Yelp review or an angry customer can damage
a restaurant’s reputation. With this in mind, my goal is not to find an optimal booking policy,
necessarily, but instead an efficient one, so that: N > C ≥ A > W. This overbooking policy must
be clearly communicated to busy restaurant owners and therefore should also be simple.
Restaurant 8 could overbook based on expected value, so that: N > E = C > W. This is
suggested by Dove and Schneider (1981) and Shonick and Klein (1977) for overbooking patients
in healthcare settings. There are two ways to implement overbooking using expected value. The
first, based on equation (2) above, involves dividing customers into three categories and using
the average predicted probability of each category to find the expected number of customers who
will show up. The second way, based on equation (3) above, involves calculating the expected
number of people who will show up based on the noshow probability for each reservation.
27
Due to the high risk of overbooking, mentioned earlier, it is important to know the
accuracy of the predicted expected values produced by my model before using those predictions
to overbook. In order to do this, I randomly divided the data into two groups. First, I ran the
logistic model on group 1. Then I divided the customers in group 2 into three categories, repeat
guests, new customers, and previous noshows, and used the estimates generated from the model
to find the average predicted probability of noshow for each category. Using equation (2), I
calculated the total expected number of arrivals, E, for group 2. I compared this value to the
actual number of customers who arrived from group 2, A, and found that my model predicts A
with 95% accuracy,
(4) = 0.95.AE
I used the same method to find the accuracy of the expected value predictions based on equation
(3), and found that predictions from that model are 94% accurate. Therefore, I will focus on
equation (2) since it is slightly more accurate. Overbooking based on expected value is ideal
when arrivals are predicted with 100% accuracy. Since this is nearly impossible due to
unobservable random variation in human behavior, I suggest restaurants employ an overbooking
policy based on modified expected values. Instead of overbooking so that the number of
expected arrivals equals restaurant capacity: N > E = C > W, restaurants should overbook with a
buffer so that the number of expected arrivals equals 95% of restaurant capacity: N > E =
(0.95)C > W.
Let Restaurant 8’s capacity be its average number of reservations per night, 37,
multiplied by its average party size per reservation, 3: (37 3 = 111). As shown previously,×
28
equation (2) predicts that 88.28% of reservations will show up on a given night. This means 98
seats are expected to be filled out of the 111 available. Using the suggested policy, Restaurant 8
should overbook until 95% of its capacity is expected to be filled, or until 105 seats are filled.
This means Restaurant 8 should book enough customers, N, so that 88.28% of N equals 105.
Restaurant 8 must solve for N in the following equation:
(5) (N = Number of booked customers) (Percent of customers expected to show up)× = (0.95) (C = Capacity)×
N(0.8828) = (0.95)(111)
N = 119
(N C) = (119 111) = 8.
Restaurant 8 should book 8 customers over capacity. In doing so, Restaurant 8 can expect
E = 105 customers to show up. Without overbooking, Restaurant 8 was expected to fill only W =
98 seats. The additional 7 seats that could be filled by implementing an overbooking policy could
save Restaurant 8 $220,500 per year. 4
Alternative overbooking policies suggested by previously mentioned studies are more
complex. Bertsimas and Shioda (2003) and Oh and Su (2012) incorporate additional factors into
their models such as walkin demand or the effect of noshow penalties. However, neither study
incorporates the distribution of noshow probabilities based on a customer stratification. In fact,
Bertsimas and Shioda (2003), assume that the probability of noshows is independent and
identically distributed across parties of the same size, which I have shown is not the case.
Therefore, the findings of the current study can help advance the work of nonempirical previous
studies that have depended on simplifying assumptions. To create a more thorough overbooking
4 7 additional customers/night x $105/customer x 25 nights open/month x 12 months/year = $220,500 saved/year
29
policy, one would need to employ a structural model that describes the behavior of consumers
and restaurants, and how the market operates. This would likely be more accurate than the
reduced form model suggested here and future work could address this.
An effective overbooking policy must also take into account the potential downside of
overbooking discussed by The Culinary Institute of America (2014), Wangenheim and Bayón
(2007), and Hirschman (1970). As noted earlier, the risk with overbooking lies in the nonzero
probability that the number of customers who arrive will exceed restaurant capacity: N > A > C >
W. The restaurant has two choices in this case: increase the wait time of every customer in order
to accommodate additional arrivals or refuse service to a few customers with reservations. There
are costs associated with either choice. Let’s assume the restaurant chooses to turn some
customers away. In this case the restaurant would have to provide enough compensation to avoid
a damaging loss in customer loyalty or restaurant reputation. I suggest a voucher equal to the
price of a meal—for Restaurant 8 this would be a $65 voucher per person. An analogous strategy
is successfully employed by airlines, however there are many important market differences
between airlines and restaurants that must be addressed.
First, unlike airlines, restaurants do not typically overbook and they certainly do not often
bump customers. Therefore the public response to a restaurant’s compensation scheme is
untested. Second, the airline industry is an oligopoly—there are huge barriers to entry and few
dominant firms. Customers therefore do not have much choice between firms nor the power to
significantly damage a firm’s reputation. This is contrasted with the nearly perfect competition of
the restaurant market. Here, customers can easily switch between firms and in doing so they have
the power to affect a firm’s profits. That said, the offer of a free meal is likely ample
30
compensation for the cost of a lost reservation. If this is the case, then the benefits of
overbooking will outweigh the costs of compensation doled out in the infrequent event of
overbooking gone awry. Further research should address optimal compensation schemes for
restaurants.
IX. Conclusion
Using a large data set of restaurant and reservationspecific variables, I predicted the
probability of a restaurant customer being a noshow and found that whether a customer showed
up for his or her previous reservation is the most important predictor of future behavior. Using
this variable, I divided customers into three categories: repeat guests who are not previous
noshows, new customers, and previous noshows. I suggested an overbooking policy for
restaurants by calculating the expected number of customers who will arrive based on the
distribution of customers in this stratification and the average predicted probability of noshow
for each category. Due to the 95% accuracy of my model, I recommended overbooking until the
expected number of arrivals equals 95% of the restaurant’s capacity. Despite the risks associated
with overbooking in the case where it goes awry, the benefits of decreasing the high costs
associated with noshows very likely outweigh the necessary increase in costs of compensation.
Therefore, overbooking may help lead to a long overdue power shift in the restaurant industry
from customers to restaurants themselves. Further studies could be done to increase the
complexity of the suggested overbooking policy by addressing complications such as: customer
response to increased wait times or compensation, the effect of an overbooking policy on the
noshow rate itself, and importantly, further empirical experiments could be done using
31
overbooking in some restaurants and comparing the effects to similar counterpart restaurants
without overbooking policies.
32
X. Tables and Figures
Table 1: Descriptive Statistics
Variables
Total Show Noshow Difference
Mean SD Mean SD Mean SD mshowmnoshow
Category 1: Restaurantspecific
Booking days in advance 29.89 6.84 29.94 6.92 29.47 6.18 0.47
Minimum Party Size 1.02 0.13 1.02 0.13 1.02 0.14 0.00
Maximum Party Size 6.81 2.93 6.78 2.90 7.09 3.11 0.30
Restricts Large Parties 0.08 0.27 0.08 0.27 0.04 0.20 0.04
Large Party Threshold 5.85 0.53 5.84 0.55 5.92 0.39 0.08
First Confirmation Days in Advance 1.65 1.60 1.67 1.64 1.43 1.20 0.24
Automated Communication via Text 0.94 0.25 0.94 0.24 0.92 0.27 0.02
Automated Communication via Email 0.93 0.26 0.93 0.25 0.92 0.27 0.01
Automated Communication via Phone 0.02 0.13 0.02 0.13 0.02 0.14 0.00
Allows Waitlist Requests Via Text 0.34 0.47 0.35 0.48 0.20 0.40 0.16
Allows Waitlist Requests Via Phone 0.02 0.13 0.02 0.13 0.02 0.14 0.00
Allows Waitlist Requests Via Widget 0.10 0.30 0.11 0.31 0.06 0.23 0.05
Category 3: Reservationspecific
Party Size 3.93 3.62 4.01 3.74 3.26 2.36 0.75
Same Area Code Indicator 0.50 0.50 0.51 0.50 0.42 0.49 0.10
Guest Note Indicator 0.28 0.45 0.29 0.45 0.21 0.41 0.08
Reservation Made via Phone 0.58 0.49 0.59 0.49 0.49 0.50 0.10
Reservation Made via Website 0.42 0.49 0.41 0.49 0.51 0.50 0.10
Confirmation Indicator 0.76 0.43 0.76 0.43 0.77 0.42 0.01
Confirmation via Phone Indicator 0.45 0.50 0.46 0.50 0.42 0.49 0.04
Confirmation via Text Indicator 0.30 0.46 0.30 0.46 0.35 0.48 0.05
Number of observations for variables above 74,926 66,759 8,167 —
Repeat Guest Indicator 0.33 0.47 0.33 0.47 0.31 0.46 0.03
Previous NoShow Indicator 0.05 0.22 0.04 0.19 0.18 0.38 0.14
Number of observations for variables above 70,542 62,864 7,678 —
Category 2: Manually Inputted
Yelp Rating 3.32 0.50 3.31 0.51 3.41 0.41 0.10
Yelp Price 2.73 0.44 2.74 0.44 2.68 0.47 0.06
Number of Observations for Category 2 73,750 65,654 8,096 —
33
Table 2: Estimates from OLS Regressions
OLS Regressions Specification
Variables 1 2 3 4 5
Party Size 0.004 (0.000)
0.004 (0.000)
0.004 (0.000)
0.004 (0.001)
0.004 (0.000)
Same Area Code Indicator 0.037 (0.002)
0.030 (0.003)
0.031 (0.003)
0.037 (0.010)
0.034 (0.002)
Repeat Guest Indicator 0.055 (0.002)
0.047 (0.002)
0.046 (0.002)
0.055 (0.008)
0.056 (0.002)
Confirmation Indicator 0.007 (0.003)
0.010 (0.003)
0.009 (0.003)
0.007 (0.007)
0.007 (0.003)
Previous NoShow Indicator 0.317 (0.008)
0.318 (0.008)
0.311 (0.008)
0.317 (0.018)
0.394 (0.024)
Guest Note Indicator 0.022 (0.003)
0.013 (0.003)
0.014 (0.003)
0.022 (0.010)
0.020 (0.002)
Other Controls No Yes No No No
Restaurant Fixed Effects No No Yes No No
Cluster s.e. No No No Yes No
Interactions No No No No Yes
Note: Dependent variable is NoShow Indicator. Other controls in specification 2 include: First Confirmation Days in Advance, Yelp Rating, Yelp Price. The interactions in specification 5 are Previous NoShow Indicator interacted with Party Size, Same Area Code Indicator, Confirmation Indicator, and Guest Note Indicator. Robust standard error in parentheses.
34
Table 3: Estimates from Logit Regressions
All variables evaluated at avg.
Specification
Variables 1 2 3 4 5
Party Size Marginal Effect (Marginal s.e.)
[Beta from Logit]
0.007 (0.001) [0.083]
0.006 (0.001) [0.077]
0.007 (0.001) [0.081]
0.007 (0.001) [0.083]
0.008 (0.001) [0.090]
Same Area Code Indicator 0.035 (0.002) [0.407]
0.025 (0.002) [0.297]
0.025 (0.002) [0.300]
0.035 (0.009) [0.407]
0.034 (0.002) [0.402]
Repeat Guest Indicator 0.061 (0.002) [0.780]
0.054 (0.002) [0.709]
0.052 (0.002) [0.696]
0.061 (0.009) [0.800]
0.061 (0.002) [0.801]
Confirmation Indicator 0.007 (0.003) [0.088]
0.009 (0.003) [0.117]
0.009 (0.003) [0.114]
0.007ª (0.006) [0.088]
0.007 (0.003) [0.082]
Previous NoShow Indicator 0.415 (0.011) [2.396]
0.406 (0.011) [2.368]
0.398 (0.011) [2.351]
0.415 (0.031) [2.396]
0.358 (0.022) [2.160]
Guest Note Indicator 0.020 (0.002) [0.245]
0.012 (0.003) [0.153]
0.014 (0.002) [0.173]
0.020 (0.009) [0.245]
0.020 (0.003) [0.251]
Other Controls No Yes No No No
Restaurant Fixed Effects No No Yes No No
Cluster No No No Yes No
Interactions No No No No Yes
Note: Dependent variable is NoShow Indicator. Other controls in specification 2 include: First Confirmation Days in Advance, Yelp Rating, Yelp Price. The interactions in specification 5 are Previous NoShow Indicator interacted with Party Size, Same Area Code Indicator, Confirmation Indicator, and Guest Note Indicator. Robust standard error in parentheses. ªInsignificant results.
35
Table 4: Summary Statistics Related to Confirmation Indicator
Percent Show
Percent NoShow
Number of Observations
Confirmation | Total 89% 11% 56,839
Confirmation | Repeat Guest who is not a Previous NoShow 95% 5% 15,192
Confirmation | New Customer 89% 11% 37,818
Confirmation | Previous NoShow 63% 37% 3,032
Confirmation | No Guest ID = unknown customer category 83% 17% 77
No Confirmation | Total 90% 10% 18,087
No Confirmation | Repeat Guest who is not a Previous NoShow 95% 5% 3,704
No Confirmation | New Customer 90% 10% 9,444
No Confirmation | Previous NoShow 62% 38% 632
No Confirmation | No Guest ID = unknown customer category 89% 11% 4,307
36
Figure 1: Probability of NoShow When Indicators are Switched— Deviations from Best and Worst Case Baselines Specification 2
37
Figure 2: The Best Case and Worst Case Predicted NoShow Probabilities for Three Categories of Customers
Figure 3: Distribution of Restaurant 8’s Customers by Probability of NoShow as Compared to Distribution by Customer Type
38
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40
XII. Appendix A Figure A1: Reallocation Price and Profit from Oh and Su (2012) Overbooking Analysis
Note: Λ = Market size, µ = Restaurant capacity
41
Table A1: Estimates from Logit Regressions
Party size evaluated at avg. Other variables at 0
Specification
Variables 1 2 3 4 5
Party Size Marginal Effect (Marginal s.e.)
[Beta from Logit]
0.009 (0.001) [0.083]
0.008 (0.001) [0.077]
0.008 (0.001) [0.081]
0.009 (0.001) [0.083]
0.010 (0.001) [0.090]
Same Area Code Indicator 0.039 (0.003) [0.407]
0.026 (0.003) [0.297]
0.027 (0.003) [0.300]
0.039 (0.009) [0.407]
0.039 (0.003) [0.402]
Repeat Guest Indicator 0.065 (0.003) [0.780]
0.054 (0.003) [0.709]
0.053 (0.003) [0.696]
0.065 (0.012) [0.800]
0.066 (0.003) [0.801]
Confirmation Indicator 0.010 (0.004) [0.088]
0.012 (0.003) [0.117]
0.012 (0.003) [0.114]
0.010 (0.008) [0.088]
0.009 (0.004) [0.082]
Previous NoShow Indicator 0.487 (0.012) [2.396]
0.456 (0.013) [2.368]
0.450 (0.013) [2.351]
0.487 (0.043) [2.396]
0.432 (0.022) [2.160]
Guest Note Indicator 0.025 (0.003) [0.245]
0.014 (0.003) [0.153]
0.016 (0.003) [0.173]
0.025 (0.010) [0.245]
0.026 (0.003) [0.251]
Other Controls No Yes No No No
Restaurant Fixed Effects No No Yes No No
Cluster s.e. No No No Yes No
Interactions No No No No Yes
Note: Dependent variable is NoShow Indicator. Other controls in specification 2 include: First Confirmation Days in Advance, Yelp Rating, Yelp Price. The interactions in specification 5 are Previous NoShow Indicator interacted with Party Size, Same Area Code Indicator, Confirmation Indicator, and Guest Note Indicator. Robust standard error in parentheses.
42
Table A2: Estimates from Logit Regressions
Party size evaluated at avg. Other variables at 1
Specification
Variables 1 2 3 4 5
Party Size Marginal Effect (Marginal s.e.)
[Beta from Logit]
0.017 (0.001) [0.083]
0.017 (0.001) [0.077]
0.017 (0.001) [0.081]
0.017 (0.003) [0.083]
0.017 (0.001) [0.090]
Same Area Code Indicator 0.090 (0.006) [0.407]
0.067 (0.007) [0.297]
0.067 (0.007) [0.300]
0.090 (0.029) [0.407]
0.081 (0.006) [0.402]
Repeat Guest Indicator 0.186 (0.009) [0.780]
0.166 (0.009) [0.709]
0.161 (0.009) [0.696]
0.186 (0.035) [0.800]
0.174 (0.011) [0.801]
Confirmation Indicator 0.018 (0.006) [0.088]
0.025 (0.007) [0.117]
0.024 (0.007) [0.114]
0.018ª (0.014) [0.088]
0.015 (0.006) [0.082]
Previous NoShow Indicator 0.254 (0.008) [2.396]
0.278 (0.009) [2.368]
0.272 (0.009) [2.351]
0.254 (0.022) [2.396]
0.208 (0.016) [2.160]
Guest Note Indicator 0.053 (0.007) [0.245]
0.034 (0.007) [0.153]
0.038 (0.007) [0.173]
0.053 (0.023) [0.245]
0.049 (0.007) [0.251]
Other Controls No Yes No No No
Restaurant Fixed Effects No No Yes No No
Cluster No No No Yes No
Interactions No No No No Yes
Note: Dependent variable is NoShow Indicator. Other controls in specification 2 include: First Confirmation Days in Advance, Yelp Rating, Yelp Price. The interactions in specification 5 are Previous NoShow Indicator interacted with Party Size, Same Area Code Indicator, Confirmation Indicator, and Guest Note Indicator. Robust standard error in parentheses. ªInsignificant results.
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Figure A2: Probability of NoShow When Indicators are Switched—Deviations from Best and Worst Case Baselines with Probability Values and Magnitude of Deviation Specified
Same Area Code
Repeat Guest Confirmation Previous
NoShow Guest Note Probability of NoShow
Magnitude of Deviation
Best Case: 1 1 0 0 1 3% ∅
Deviations from Best Case
0 1 0 0 1 5% 2
1 0 0 0 1 8% 5
1 1 1 0 1 4% 1
1 1 0 1 1 27% 24
1 1 0 0 0 4% 1
Same Area Code
Repeat Guest Confirmation Previous
NoShow Guest Note Probability of NoShow
Magnitude of Deviation
Worst Case: 0 1 1 1 0 44% ∅
Deviations from Worst Case
1 1 1 1 0 35% 9
0 1 1 0 0 7% 37
0 1 0 1 0 44% 0
0 0 1 0 0 14% 30
0 1 1 0 1 35% 9
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Figure A3: Absolute Difference in Probability—Switching Indicators—Specification 2 vs. 5
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Table A3: Estimates from Probit Regressions
All variables evaluated at avg.
Specification
Variables 1 2 3 4 5
Party Size Marginal Effect (Marginal s.e.)
[Beta from Logit]
0.007 (0.001) [0.040]
0.006 (0.001) [0.037]
0.006 (0.001) [0.039]
0.007 (0.001) [0.040]
0.007 (0.001) [0.042]
Same Area Code Indicator 0.036 (0.002) [0.212]
0.026 (0.003) [0.155]
0.026 (0.003) [0.157]
0.036 (0.010) [0.212]
0.035 (0.002) [0.207]
Repeat Guest Indicator 0.061 (0.002) [0.394]
0.055 (0.002) [0.351]
0.053 (0.002) [0.346]
0.061 (0.008) [0394]
0.062 (0.002) [0.395]
Confirmation Indicator 0.008 (0.003) [0.046]
0.010 (0.003) [0.061]
0.010 (0.003) [0.059]
0.008ª (0.006) [0.046]
0.007 (0.003) [0.043]
Previous NoShow Indicator 0.389 (0.010) [1.309]
0.384 (0.010) [1.302]
0.378 (0.010) [1.293]
0.389 (0.025) [1.309]
0.361 (0.020) [1.238]
Guest Note Indicator 0.021 (0.003) [0.978]
0.013 (0.003) [0.078]
0.014 (0.003) [0.087]
0.021 (0.009) [0.127]
0.021 (0.003) [0.127]
Other Controls No Yes No No No
Restaurant Fixed Effects No No Yes No No
Cluster No No No Yes No
Interactions No No No No Yes
Note: Dependent variable is NoShow Indicator. Other controls in specification 2 include: First Confirmation Days in Advance, Yelp Rating, Yelp Price. The interactions in specification 5 are Previous NoShow Indicator interacted with Party Size, Same Area Code Indicator, Confirmation Indicator, and Guest Note Indicator. Robust standard error in parentheses. ªInsignificant results.
46