How Social Norms and Menus Affect Choices:
Evidence from Tipping
Kwabena B. Donkor∗
June, 2020
Abstract
Trade-offs between personal choice versus social expectations and choosing from amenu versus computing a preferred option affect decision-making. I use changes in thetip menus used in New York City taxis to analyze these trade-offs. I nonparametricallyestimate that the cost of computing a tip when passengers deviate from the menu is$1.89 (15.53% of the average taxi fare of $12.17) on average. I then estimate a modelwhere tipping choices depend on perceptions of a social norm tip, the shame from givenless (norm-deviation cost), and the difficulty of calculating a tip (cognitive cost). Thedistribution of beliefs about the social norm tip averages about 20% of the taxi fare andthe norm-deviation cost is between $0.30 and $0.38 for tipping five percentage pointsless. Cognitive costs average between $1.10 and $1.32. Compared to using no menu,taxi companies appear to have learned over time to use a nearly tip-maximizing menuthat, on average, per ride, increases tips by 14.65% and the overall welfare from tippingby $1.08. JEL Codes: D01, D22, D64, D91, L11.
∗Kwabena Donkor: Postdotoral Research Fellow at Stanford Institute of Economic Policy Research([email protected]). I thank God. I thank Jeff Perloff, Stefano DellaVigna, Miguel Villas-Boas, BenHandel, Aprajit Mahajan, and Dmitry Taubinsky for advice and guidance. I thank the students and facultyat the Stanford GSB Marketing seminar, UCB Haas Marketing seminar, UC Berkeley Psyc & Econ lunchseminar, UC Berkeley IO seminar, and the UC Berkeley ARE ERE lunch seminar for their comments anddiscussions. Last, I thank Hanan Wasse and all UC berkeley ARE and Econonics PhD students for theirsupport and contributions. All errors are mine.
1 Introduction
Trade-offs between personal choice versus social expectations and choosing from a menu ver-
sus computing a preferred option affect decision-making. However, we know little about the
mechanisms through which social norms affect behavior, and why menus influence choices.
To understand these mechanisms, we must identify the empirical relationship between peo-
ple’s preferences and their sensitivity to social norms and menus. This paper addresses these
gaps in the literature by examining passenger tipping in New York City (NYC) Yellow taxis.
Menus and defaults (pre-selected options) should have a minor effect on choices if con-
sumers are rational (Thaler and Sunstein, 2003). However, they drive consumers’ choices
in many contexts,1 and there are some proposed explanations. Consumers may see defaults
and menus as a source of information about social norms or the status quo (Beshears et al.,
2009). Customers may choose from a menu if opting out is costly (Bernheim, Fradkin, and
Popov, 2015). Some individuals delay acting if the benefits of that action are not immediate;
such individuals would opt for a default or menu option in the interim and put off deciding
to a later date (O’Donoghue and Rabin, 1999, 2001).
These complications and factors have vexed previous researchers, and thus, we do not
know the economic importance of the mechanisms that drive the menu or default effect
(Jachimowicz et al., 2019). Also, the preferences of decision-makers and their perceptions of
social norms are difficult to observe, measure, and study scientifically.
In this study, I circumvent some of these complications, identify mechanisms, and measure
the unobserved preferences of decision-makers. I use a revealed preference approach and a
model to empirically show how sensitive passengers’ unobserved tipping preferences are to
their beliefs about the social norm tip, and estimate the cost of calculating a tip versus
the benefit of choosing from a tip menu. Because the components of these trade-offs are
all connected in the context of tipping, it provides advantages for understanding how social
norms, menus, and defaults affect choices.
There are three advantages to studying tipping, especially in NYC taxis. First, taxi
passengers cannot defer tipping to a later date. Thus, self-control problems such as pro-
crastination and present bias are not explanations for the menu or default effect. Second,
Yellow taxis offered different tip menus to passengers over the study period. These changes
in tip menus help to identify the mechanisms that drive the menu or default effect. Third,
1For example, defaults affect (1) savings behavior: Madrian and Shea (2001); Choi et al. (2002, 2004);Carroll et al. (2009); DellaVigna (2009); Beshears et al. (2009); Blumenstock, Callen, and Ghani (2018), (2)organ donations: Johnson and Goldstein (2003); Abadie and Gay (2006), (3) health insurance contracts:Handel (2013), (4) contract choice in health clubs: DellaVigna and Malmendier (2006), (5) tipping behavior:Haggag and Paci (2014), (6) marketing: Brown and Krishna (2004); Johnson, Bellman, and Lohse (2002),and (7) electricity consumption: Fowlie et al. (2017).
1
tipping is a significant economic activity. Annual tips from restaurants alone are $37 billion
(Shierholz et al., 2017), 5% of the 2019 projected sales in restaurants.
NYC Yellow taxis began presenting customers with a tip menu in 2007 (Grynbaum,
2012).2 When passengers pay for a taxi ride with a credit card, a touch-screen payment
device shows the fare, suggests three tip rates and provides the option of giving a custom
tip (or no tip) instead.
To analyze how tip menus affect tipping, I use a model where passengers’ tipping choices
depend on their perception of a socially acceptable tip (social norm tip), the shame from
given less (norm-deviation cost), and the difficulty of calculating a non-menu tip (cognitive
cost).
I apply the model to study about a billion NYC Yellow taxi rides from 2010 to 2014. The
data from the taxis vary by two different touch-screen payment devices used in the taxicabs.
The two machines have different tip menus in some years, causing the share of passengers
who opt for non-menu tips and the tip revenue received by drivers to change by device and
over time.
Data on passengers who select from the tip menu identify cognitive costs, and passengers
who give non-menu tips help to identify the norm-deviation costs. As a rough explanation,
tipping is voluntary, requires effort, and is costly. Therefore, passengers who choose from a
menu avoid the cost of computing their preferred tip, and those who tip a non-menu amount
prefer to incur the effort cost of calculating a tip in order to conform with the custom of
paying a gratuity.
I use two different approaches to measure decision costs (norm-deviation cost + cognitive
cost). In the first, I use a change in the tip menu to nonparametrically estimate that the
decision cost of computing a tip instead of choosing from a tip menu is $1.89 (15.53% of the
average taxi fare of $12.17) on average. In the second approach, I use changes in the share
of passengers who choose non-menu tips as the taxi fare increases to estimate decision costs.
I also control for trip characteristics unaccounted for in the first approach, and the average
decision cost decreases to $1.64 (13.48% of the average taxi fare).
Either approach is unable to identify norm-deviation costs and cognitive costs separately.
I use a third approach that places parametric assumptions on the tipping model, allowing
me to separately estimate passengers’ beliefs about the social norm tip, the norm-deviation
2The use of tip menus is ubiquitous. In 2009, the tech company Square started providing differentestablishments with electronic credit card readers that prompt customers to choose from a tip menu. Squarehas since popularized this technology by making these electronic devices accessible to both small localbusinesses and large corporations around the United States. For example, the café chain Starbucks agreedin 2012 to invest $25 million in Square and converted all its electronic cash registers to the ones offered bySquare (Cohan, 2012). The grocery chain Whole Foods Market followed suit and announced in 2014 that itwould roll out Square registers across some of its stores (Ravindranath, 2014).
2
cost, and the cognitive cost.
Placing parametric assumptions on the model has three advantages. First, it allows me
to test whether a change in the tip menu influences passengers’ beliefs about the social norm
tip. Second, I can separately identify the norm-deviation cost and the cognitive cost, the
two components of decision costs that individually inform policy. For example, a menu that
will maximize welfare depends on whether its options reflect consumers’ preferences and
minimizes the cost of computation. Without separating decision costs into norm-deviation
cost and cognitive cost, such an exercise would be challenging. Third, I use the parametric
model to perform several counterfactual applications, such as estimating a tip-maximizing
menu or a utility-maximizing menu for passengers who tip.
With the parametric model, I estimate that the unobserved distribution of passengers’
beliefs about the social norm tip averages about 20% of the taxi fare, and the observed menu
change has a minor impact on these beliefs. The norm-deviation cost is large relative to
the taxi fare, tipping five percentage points less than the norm results in a norm-deviation
cost of between $0.30 and $0.38 (2.5% - 3.1% of the average taxi fare of $12.17). The
average cognitive cost of computing a non-menu tip is between $1.10 and $1.32 (9% - 10.8%
of the average taxi fare). In the counterfactual applications, using a tip-maximizing menu
compared to no menu increases tips from 15.83% to 18.15% of the taxi fare (14.65% increase
in tips). Also, the current tip menu in NYC taxicabs nearly maximizes tip revenue, and
the changes in the taxi tip menus over time suggest that it took a few years before settling
on the current menu. In the welfare calculations, the current tip menu increases the overall
welfare from tipping by $1.08 per taxi ride relative to presenting no menu. These findings
contribute to several pieces of literature.
In using a model to empirically estimates population tipping preferences and the distri-
bution of beliefs about the social norm tip, this paper adds to the literature on preference
identification (for example, Rubinstein and Salant (2011); Benkert and Netzer (2018); Goldin
and Reck (2019)). In fact, this paper is first to present empirical evidence from a field setting
on how unobserved social norms affect consumer preferences while remaining agnostic to how
norms form.
This study provides insights on how consumer-switching costs, the effort it takes to
switch from one choice to another, affect firm profits. Switching costs can be exploited by
competitive firms to increase profits (Beggs and Klemperer, 1992). For example, profit-
maximizing firms design contracts that introduce switching costs and back-loaded fees to
extract more profits (DellaVigna and Malmendier, 2004). In this paper, switching costs
arise from choosing a non-menu tip. Taxi drivers have an incentive to use a tip menu that
will maximize tip revenue.
3
This study also documents how menus or defaults affect social welfare. For example,
a theoretical model can determine the optimal default 401k-enrollment policy for different
choice environments (Carroll et al., 2009). This paper provides empirical evidence on how
menus affect profits and the utility of consumers and estimate the welfare implications of
different menus.
There are two studies related to this paper that also use data from NYC taxis. First,
Haggag and Paci (2014) use a regression discontinuity design to explore whether NYC Yel-
low taxi tip menus with higher tip suggestions induce consumers to tip more. They find
that higher tip suggestions increase the amount tipped but may come at the cost of some
passengers avoiding tipping altogether. Second, Thakral and Tô (2019) uses a change in
the NYC Yellow taxi fare rate in 2012 to evaluate the dynamics of adherence to the social
norm of tipping. In contrast to these studies, this paper provides the first comprehensive
model that identifies the mechanisms involved in the decision process when passengers have
the option to choose from a menu. Also, this study estimates passengers’ unobserved beliefs
about the social norm tip, the cost of deviating from the norm, a tip-maximizing menu, and
evaluates the implications of different tip menus for societal welfare.
Next, I describe the context and data (section 2). I then present a model for tipping
(section 3). After, I use a nonparametric and a semiparametric approach to estimate decision
costs (sections 4). Next, I estimate the model parametrically and conduct counterfactual
exercises (sections 5 and 6). I discuss the results and conclusions (section 7).
2 Context and Data
NYC Yellow taxicabs use touch-screen payment devices. The device shows the trip expenses
at the end of the ride. For standard rate fares, it charges passengers $2.50 and a $0.50
Metropolitan Transportation Authority tax upon entering the cab. Then, for every fifth
of a mile or for every minute where the cab travels less than 12mph, the fare increases by
an additional $0.40 ($0.50 after September 4, 2012). There is an additional $0.50 night-
surcharge for rides between 8 pm and 6 am and a $1 surcharge for rides between 4 pm and
8 pm on weekdays.
Two vendors, Creative Mobile Technologies (CMT) and VeriFone Incorporation (VTS),
supply equal shares of the payment devices.3 Before boarding a taxi, passengers cannot tell
whether the taxicab is fitted with a CMT or VTS device. The devices show a tip menu
to passengers who pay with credit cards. Passengers can choose one of the menu options,
3I do not use data from a third vendor, Digital Dispatch Systems, because it provided less than 5% ofthe electronic transmission devices in use between 2009 and August 2010.
4
manually key in any amount (including no tip), or provide a separate cash tip.
The CMT tip menu showed 15%, 20%, and 25% between 2009 and 2010. Then, the menu
options changed to 20%, 25%, and 30% starting February 9, 2011. Before 2012, VTS offered
a tip menu of dollar amounts ($2, $3, and $4) for fares under $15, and choices of 20%, 25%,
and 30% for larger fares. From 2012 on, VTS offered only the percentage choices. Therefore,
the data contains information on four sets of menus.4
CMT tip menus calculate tips on the total fare: the sum of the base fare, the tax, the
tolls, and the surcharge. In contrast, VTS calculates tips on only the base fare and the
surcharge. I use data from CMT taxis only (except in section 7.2) for consistency.
The Taxi and Limousine Commission (TLC) compiles data on the transactions and trip
records from CMT and VTS taxis. I use data from 725,441,461 taxi rides from 2010 to
2014. Tipping information is only available for credit and debit card transactions eliminating
roughly half of the rides (427,142,274 trips).5 I limit the data for my analysis to standard
rate fares in NYC with no tolls that had a positive tip recorded (285,972,868 trips).6 The
data reports the dollar amount tipped by passengers. I convert tips into percentages. For
example, for a $10 fare and a $1 tip, the tip rate is 10%.7
Table 1 shows summary statistics from CMT taxi rides. Column (1) refers to rides from
January 2010 to February 8, 2011 when the CMT tip menu showed 15%, 20%, and 25%.
Column (2) refers to rides from February 9, 2011 to December 2011, and column (3) refers
to rides from 2014. After February 8, 2011, the CMT tip menu showed 20%, 25%, and 30%.
The TLC also increased taxi fares by about 17% after September 3, 2012.
The average tip amount was $1.77 before the menu change (column (1)) and increased to
$1.95 after (column (2)). However, the average taxi fare remained around $10. Therefore, the
average tip rate increased by 8% because of the menu change (from 17.82% to 19.19%). The
share of passengers who choose menu tips decreased by about one-fifth after the change (from
59.7% to 48.3%). In 2014, the period after the taxi fare increase, the share of passengers
who choose menu tips returned to 60.6%, and the average tip and fare amount increased to
$2.27 and 12.17 respectively. Thus, the average tip rate remained at 19.06%.
4Figure A1 in the online appendix shows a typical screen displaying menu tip options, and figure A2shows the menu options by vendor and when they changed.
5See Hoover (2019) for a comparison between cash and credit card trips.6I use positive tips only because passengers sometimes pay for the taxi fare using a credit card but give
the driver a cash tip, we cannot infer that a lack of a credit card tip is because the passenger did not tip.7I identify menu tips and account for possible rounding errors by considering any tip that falls in between
14.99% and 15.01% as the 15% menu option, tips between 19.99% and 20.01% as the 20% menu option, tipsbetween 24.99% and 25.01% as the 25% menu option, and tips that fall between 29.99% and 30.01% as the30% menu option.
5
3 Model
People tip to encourage better future services from service providers, and to conform to
social norms (Azar, 2007). Travelers in NYC hail taxis nearest to them. They have little
incentive to tip for better future services because there are about 13,500 Yellow taxis in
NYC, with most searching for fares around the clock. Thus, repeated passenger and driver
interactions are unlikely. I model how passengers tip when presented with a tip menu, leaving
out strategic tipping for better future services.8
Passenger i gives a tip of ti% at the end of her taxi ride that costs Fi. She believes the
social norm is to give Ti% (ti and Ti may differ) of the taxi fare.9 If ti is less than the social
norm tip Ti, she incurs a norm-deviation cost ν(Ti, ti)—a function that captures her dislike
for not conforming to the norm. Passenger i incurs a cognitive cost ci to compute her ideal
tip. To avoid ci, she can pick menu option dj in tip menu D, where dj is one of j = 1, 2, ..., n
menu options. The norm-deviation cost plus the cognitive cost (if any) is her total decision
cost [ν(Ti, ti) + ci].
Passenger i chooses a tip to maximize her utility represented by
Maxti U = −tiFi︸ ︷︷ ︸Tip paid
− ν (Ti, ti)︸ ︷︷ ︸Norm deviation cost
− ci × 1{ti /∈ D}︸ ︷︷ ︸Cognitive cost︸ ︷︷ ︸
Decision Costs
.(1)
The first term tiFi is passenger i’s expenditure from tipping at rate ti. The second term
ν(Ti, ti) reflects her disutility from deviating from Ti. The third term ci×1{ti /∈ D} captures
passenger i’s cost of computing her tip if she does not choose from the tip menu. Therefore,
passenger i chooses her ideal non-menu tip rate ti /∈ D if the benefit, denoted as Bi, is greater
than the cost of choosing any dj from tip menu D. That is
Bi = (dj − ti)F > ∆ν + ci,(2)
where ∆ν = ν (Ti, ti)− ν (Ti, dj).
Equation (2) implies that, all else equal, passenger i computes her preferred non-menu
tip if the taxi fare is larger than some value Fi. Therefore, passenger i, from experience, has
a sense of the threshold Fi that helps her to decide whether to compute her preferred tip or
8The decision to leave out strategic tipping is also in line with the finding that customers in restaurantdo not tip strategically, but for social or psychological reasons (Azar, 2010).
9Beliefs about the social norm tip may differ across passengers.
6
opts for a menu tip instead.10
I use both a nonparametric and semiparametric approach to place bounds on the decision
costs from tipping. The nonparametric approach uses variation in the share of passengers
who choose non-menu tips caused by a change in the tip menu. The semiparametric approach
uses variation in the share of passengers who choose non-menu tips as the taxi fare increases.
Both methodologies require weak assumptions (introduced beneath) and do not separately
identify the norm-deviation cost and the cognitive cost. In a third approach, I include
parametric assumptions to the model to help separately identify these two costs.
4 Estimating Decision Costs
4.1 A Nonparametric Approach
I use the CMT tip menu change as a natural experiment to nonparametrically estimate
bounds on the decision cost of computing a tip instead of choosing from a menu. Then, I
use the bounds to compute a distribution of decision costs. That is, estimating the levels of
decision costs and the corresponding share of passengers associated with each level.
The tip menu in CMT taxis changed from 15%, 20%, and 25% to 20%, 25%, and 30% on
February 9, 2011. Figure 1A shows the distribution of tips before and after the menu change.
Focusing on tips below 20%, more passengers choose non-menu tips after the change. The
tipping model can rationalize the increase in non-menu tips.
The intuition here is that all else equal, changing tip menu options change the values
on both sides of the inequality in equation (2), and hence the sign of the inequality may
change for passengers on the margin of choosing a non-menu tip. Thus, after the menu
change, more passengers find it beneficial to incur the costs associated with calculating their
preferred non-menu tip instead of choosing from the menu.
Therefore, the variation in the share of passengers who choose non-menu tips after the
tip menu changes helps to identify the bounds on decision costs. To compute the bounds, I
make two assumptions.
A1–People’s beliefs about the social norm tip are jointly independent of the tip menu and
the taxi fare.
10If a passenger takes the same ride each time, she may learn over time to compute her preferred tip,hence, driving down her cognitive cost to zero. However, the taxi fare is calculated based on the time spentin the taxi and the distance traveled. Thus, the taxi fare depends on traffic conditions and the route thedriver takes. People will find it more difficult to compute their ideal tip for different taxi ride lengths anddurations than to use the stated fare threshold rule of thumb. This may not hold for passengers who aretourists or do not often take taxis. However, this concern should be mitigated given that I exclude data onairport rides to and from JFK.
7
A2–Decision costs are independent of the tip menu and constant over time.
Assumption A1 suggests that the differences in the observed tipping choices under the
two menus are due to the change in menu options and not differences in the passengers
observed under the two menus. I partly relax this assumption in section 5 and provide some
empirical support in the online appendix (section A2).
Assumption A2 suggests that decision costs are uncorrelated to the tip menu and remain
stable over time. The frame of the tip menus used in this analysis follows the same structure–
both menus present percentage tip options. Therefore, a passenger’s difficulty in computing
her preferred non-menu tip should not change because a menu option is added or removed.
I present more support for this assumptions in the online appendix (section A2).
Constructing Nonparametric Bounds
I use tips at or below 20% to compute bounds for decision costs. This is because, by
inspecting non-menu tips before and after the CMT menu change (figure 1A), the main
changes occur at tip rates below 20%.11 The relevant tip menu options are 15% and 20%
before the menu change, and only 20% after. The following instructing example presents the
insight for the nonparametric estimation of bounds on decision costs.
Suppose there are two menus, old and new, each with a single menu tip: 15% and 20% of
the taxi fare respectively. A passenger has a preferred tip different from the menu options,
but to pick this tip, she must pay the decision cost to switch from the menu. For either
menu, the passenger has a choice between either paying the difference between the available
menu tip and her preferred tip or incur the decision cost of switching from the menu.
For example, for a fare of $10, suppose we observe a passenger picking the menu option
15% when the old menu is presented, but then switches to her preferred tip, say 10%, when
presented with the new menu (20%). I conclude that the decision cost to switch is more
than $0.50 (the difference between the old menu tip 15% and the preferred tip 10%), and less
than $1 (the difference between the new menu tip 20% and the preferred tip 10%). Thus,
the passenger’s decision cost is bounded between $0.50 and $1. We can rewrite these bounds
following equation (2), that is (0.15−0.10)×$10 = $0.50 < ∆ν+ci < $1 = (0.20−0.10)×$10.
I assume that passengers who choose non-menu tips reveal their preferred tip. Therefore,
11After the menu change, there were significant increases in the share of passengers who tip at the menuoptions that remained unchanged (20% and 25%). A possible explanation for the increase at 20% is thatsome passengers who chose the 15% menu option now choose 20%. For the increase at 25%, the compromiseeffect may be a possible explanation. That is, consumers are more likely to choose the middle option ratherthan the low or high option. The nonparametric method of computing bounds on decision costs cannot beapplied to the changes in the share of passengers at the menu options. Thus, I do not include them in ourcalculations.
8
for a given fare Fi, the lower and upper bound for the decision cost of switching from the
15% menu option to a preferred non-menu tip ti is given by [ |0.15− ti|Fi, |0.20− ti|Fi ].
Estimates of Nonparametric Bounds
The goal is to estimate bounds on decision costs for passengers who switch from menu options
to actively compute a preferred non-menu tip. Because the tip menu change occurred in CMT
cabs on February 9, 2011, I use rides in CMT cabs between 2010 and 2011 for this exercise.
I focus on passengers who tip 20% of the taxi fare or less, which reduces the sample by one
fifth.12
Let ∆S(t,F ) represent the increase in the share of passengers who choose a non-menu tip
t for a taxi fare F after 15% is removed from the tip menu. For each ∆S(t,F ), I compute the
corresponding bounds as [ |0.15− t|F, |0.20− t|F ].
Passengers should find it more beneficial to choose the 20% menu tip rather than calcu-
lating a non-menu tip above 17.5%. Thus, we should observe no significant changes in the
share of passengers who choose tips above 17.5% after the menu change, which holds in the
data after dropping taxi rides where passengers give round dollar tip amounts. However, our
estimates are unaffected without excluding such rides.
I compute the bounds of decision costs in three steps. First, I group taxi fares into 29 non-
overlapping bins of width $2: [$3, $5], ($5, $7], ($7, $9]. . . ($59, $61],13 and then categorize
tips into 20 non-overlapping tip rate bins of width one percent: 1%, 2%, 3%. . . 20%. For
example, the 1% bin is the share of all passengers whose tips fall within [0.5%, 1.5%] of the
taxi fare, 2% is the share whose tips fall within (1.5%, 2.5%] of the taxi fare, and so forth.
Second, I compute the difference in the share of tips for each tip and fare bin before and
after the menu change ∆S(t,F ). Figure A5 in the online appendix shows the distribution of
tips for different levels of the taxi fare. Third, I use the midpoint of each fare bin to compute
the relevant bounds. For example, for all taxi fares that fall within fare bin ($9, $11], $10 is
used to compute the relevant bounds.
For each tip rate, I summarize the estimated bounds on decision costs as follows. I
construct bounds for the CDF of decision costs by combining the shares ∆S(t,F ) and estimated
bounds [ |0.15− t|F, |0.20− t|F ]. For example, figure 1B shows the computed bounds for
the CDF of decision cost conditional on passengers who tip 10%.14
12Leaving out menu tips means that the estimates for decision costs are censored from above. This isbecause, passengers with higher decision costs are likely to choose menu options.
13I group fares into bins because the data is sparse for taxi fares above $50.14Figure A6 in the online appendix shows the computed bounds for all other other tip rates.
9
Nonparametric Distribution of Decision Costs
I take the midpoints of each estimated bound, within each conditional CDF and their corre-
sponding shares of passengers to estimate an unconditional CDF of decision costs. The solid
line in figure 1C shows the unconditional CDF. In sum, the distribution of the decision cost
of making a calculated choice versus choosing a menu tip averages at $1.89 (15.53% of the
average taxi fare of $12.17).
This nonparametric estimate of decision costs does not control for trip characteristics
such as day of the week, time of day, weather conditions, etc. Thus, if any of these factors
systematically influence the choices of passengers, then the estimates are biased. Also, the
data limits us to observe the choices each passenger under only one menu, either CMT’s old
or new tip menu. In the following section, I use a semiparametric approach to address some
of these limitations.
4.2 A Semiparametric Approach
I use a semiparametric approach to estimate a distribution of decision costs among taxi
passengers. There are three innovations compared to the nonparametric approach.
First, I use changes in the share of non-menu tips as the taxi fare increases to identify
bounds on decision costs. Second, I estimate the relationship between tips and the taxi fare
using a logistic regression that controls for trip characteristics. Third, the data I use is from
CMT taxi rides in 2014, a period where all Yellow taxis presented passengers with the same
tip menu (20%, 25%, and 30%), and there were no changes in the taxi industry. In sum,
the semiparametric estimates of decision costs avoid the potential impact of changes in the
tip menu on tipping behavior and the impact of time on decision costs. This approach also
controls for observable trip characteristics. To proceed, I make an additional assumption.
A3—A passenger’s cognitive cost is jointly independent of the taxi fare and her preferred
tip.
This assumption cannot be tested because we do not observe cognitive costs. However,
I find two instances in the data consistent with this assumption. First, passengers are not
more likely to choose non-menu tip rates that are relatively easier to compute. For example,
passengers are more likely to tip at rates such as 11%,12%, and 15% compared to 10% or
15%.15
15These empirical observations are further discussed in section A2 of the online appendix.
10
Constructing Semiparametric Bounds
I compute the bounds on decision costs by using rides where passengers tip less than 20%
of the taxi fare. I assume that 20%, the lowest menu tip option, is what these passengers
would choose if they decide to select a menu option.
I use a revealed preference argument as the basis to estimate the bounds on decision costs.
If a passenger chooses a tip different from the menu options, then she reveals her preference
for a non-menu tip. From equation (2), such a passenger finds it beneficial to compute her
preferred tip instead of choosing a menu tip. Therefore, for a passenger on the margin of
choosing a menu tip, the benefit of giving her preferred non-menu tip is approximately her
decision cost for computing it. That is, Bi ≈ ∆ν + ci (follows from equation (2)).
The following instructing scenario presents how I construct the bounds on decision costs.
Suppose at the end of a taxi ride that costs Fi, there is a passenger on the margin of choosing
her preferred tip ti% of the taxi fare or the 20% menu option, such that ti% < 20%. All else
equal, if the fare increases by ∆F , an amount large enough, then she will choose to compute
her preferred non-menu tip. This is because her decision cost will be less than her cost of
choosing the menu option. That is, (0.20 − ti) × F < ∆ν + ci < (0.20 − ti) × (Fi + ∆F ).
Therefore, her decision costs is bounded between (0.20− ti)×Fi and (0.20− ti)× (Fi+∆F ).
I calculate the shares of passengers for each bound of decision cost by relying on the
following insight. Denote p(ti|Fi, dj = 20%, Xit) as the probability of choosing a tip ti
conditional on the taxi fare Fi , the tip menu option 20%, and a vector of observed trip
characteristics Xit . Suppose that Fi increases by ∆F , then ∆p(t,F ) = p(ti|Fi+∆F, dj, Xit)−
p(ti|Fi, dj, Xit) ≥ 0 follows from equation (2). ∆p(t,F ) is the change in the share or probability
of choosing one’s preferred tip ti relative to the menu tip when Fi increases by ∆F . When
∆F is small, a marginal increase in the fare, ∆p(t,F ) represents the share of passengers who
reveal that their benefit from giving their preferred tip is approximately their decision cost.
Estimates of Semiparametric Bounds
I implement the strategies for estimating bounds of decision costs and calculating the asso-
ciated share of passengers in three steps. First, I estimate the relationship between tips and
the taxi fare using an ordered logistic regression. In this regression, the outcome variable is
the tip rate categorized into 20 non-overlapping bins of width one percent, namely 1%, 2%,
3%. . . 20%16, and the covariates are the taxi fare, month of the year, day of the week, the
hour of the day, holidays, hourly temperature and precipitation.
16The outcome variable is categorized as follows; for example, 15% is defined as the share of passengerswhose tip falls within the range of 14.5% and 15.5%.
11
Second, I use the regression results to estimate the probability for choosing each tip
rate in the outcome variable as functions of the taxi fare, with all covariates set to their
sample average. Figure 2A shows the predicted probability estimates for choosing a 10%
tip as a function of the taxi fare. The probability is increasing as the fare increases. Figure
1 in the online appendix shows the estimated predicted probabilities for all the other tip
rates. In contrast, figure 2B shows that the probability of choosing the menu tip option
20% is decreasing as the fare increases, corroborating the reasoning that, as the taxi fare
increases choosing the menu option becomes more costly than the decision cost of computing
a preferred tip.
Third, for each tip rate, I compute bounds on decision costs for small increments of the
taxi fare and calculate the corresponding changes in the estimated probabilities or shares
∆p(t,F ). I use this information to construct bounds on the CDF of decision costs. For
example, figure 2C shows the empirical estimate of bounds on the CDF of decision cost for
passengers who tip 10% of the taxi fare.17
Semiparametric Distribution of Decision Costs
I use the shares of passengers and the midpoints of the estimated bound of decision costs from
all the conditional CDFs to estimate an unconditional CDF of decision costs. The dashed
line depicted in figure D shows the semiparametric CDF of decision costs. The distribution
averages at $1.64 (13.48% of the average taxi fare of $12.17). This average is $0.25 lower
than the distribution from the nonparametric approach.
Whereas the semiparametric estimate of decision costs is purged of potential biases from
trip characteristics and changes in tip menus, it has limitations. As with the nonparametric
approach, I am unable to recover the full distribution of decision costs; the sample is limited
to passengers who tip less than 20%. Second, only fares within the range of $3 - $30 are
used, and thus, the support of the distribution of decision cost is censored.18 Both the
nonparametric and the semiparametric estimates of decision costs do no distinguish between
the norm-deviation cost and cognitive cost of tipping, the two components that drive decision
costs. The following section circumvents all these limitations.
17Figure A8 in the online appendix shows the computed bounds for all other tip rates.18Because, $3 is the lowest taxi fare, and $3 - $30 is the range where the change in the predicted probabilities
(∆p(t,F )) is nonnegative, I restrict the support of the taxi fare to $3 - $30.
12
5 Social Norm Tip, Norm-Deviation Cost and Cognitive Cost
I place parametric assumptions on the tipping model in section 3 to empirically estimate pas-
sengers’ beliefs about the social norm tip, how menus affect these beliefs, and to distinguish
between norm-deviation cost and cognitive cost.
5.1 A Parametric Model
The tipping model characterizes passengers by three random variables (Ti, Fi, ci), each drawn
from some underlying population distribution. I parameterize equation (1) as follows. Pas-
senger i chooses a tip to maximize her utility represented by
Ui = −tiFi︸ ︷︷ ︸Tip paid
− θ (Ti − ti)2
︸ ︷︷ ︸Norm deviation cost
− ci × 1{ti /∈ D}︸ ︷︷ ︸Cognitive cost︸ ︷︷ ︸
Decision Costs
(3)
The first term −tiFi is her expenditure from tipping ti (a percentage of the fare). The
second term θ (Ti − ti)2 is her norm-deviation cost—disutility for not conforming to what she
believes is the social norm tip. The scalar θ is the norm-deviation cost parameter. Passenger
i avoids the norm-deviation cost if she tips Ti, however, if she deviates from tipping Ti, then
her norm-deviation cost increases with the size of the percentage point deviation.19 The
model remains agnostic to how passenger i determines Ti. Passenger i’s cognitive cost for
computing her preferred tip is ci, a fixed dollar cost. The indicator function 1{ti /∈ D} equals
one if ti is not one of the tip menu options and zero otherwise.
The utility from tipping is quasi-linear in money; the dollar tip amount enters linearly
into the utility function. This assumption is innocuous given that tips are a small amount
compared to passengers’ wealth.
The benefit to passenger i for choosing a non-menu tip ti /∈ D rather than a (higher)
menu tip is Bi = (dj − ti)Fi. However, the cost is that her norm-deviation cost rises from
19Because the norm-deviation cost of not conforming to the norm is symmetric, passenger i will nonethelessexperience a utility loss if she chooses a tip larger than Ti. However, it may be intuitive that one wouldlikely feel ashamed or experience disutility for choosing a tip that is less than Ti , but not for a tip largerthan Ti. I conduct an exercise where passenger i is assumed to face no disutility from choosing a tip that islarger than her belief about the social norm tip Ti. So, passenger i’s utility from tipping can be written as
Ui =
{−tiF − θ (Ti − ti)
2− ci1{ti /∈ D} , if ti < Ti
−tiF , if ti ≥ Ti
The estimates from equation (3) are unaffected by this parameterization. This is because the only casewhere a passenger tips above Ti is if she chooses a menu tip larger than Ti: a rare occurrence in the modelsetup.
13
θ (Ti − dj)2 to θ (Ti − ti)
2 and she incurs a cognitive cost of ci. Therefore, she tips at her
preferred non-menu tip rate if the benefit is greater than the cost. That is,
Bi = (dj − ti)Fi > θ[(Ti − ti)
2 − (Ti − dj)2]+ ci(4)
For ti < dj, it follows that dBi
dF= dj− ti > 0. That is, the benefit of computing one’s ideal
tip is larger at higher fares. Therefore, passengers will be more likely to choose non-menu
tips at higher fares; this is confirmed in the data: see figure A9A in the online appendix.
I solve for passenger i’s preferred tip by maximizing equation (3). I ignore the cognitive
cost ci because of the indicator function 1{ti /∈ D}. From the first-order condition, the
optimal tip is
t∗i = Ti −0.5
θFi.(5)
Passenger i’s preferred tip t∗i is 0.5θFi less than her belief about the social norm tip Ti. The
preferred tip rate falls as the taxi fare increases(
dt∗i
dF= −0.5
θ< 0
). This observation generally
holds in the data. Figure A9B in the online appendix shows that the average tip rate falls
as the fare increases. Therefore, when deciding on how much to tip, a passenger tries to save
by trading off the dollars lost to tipping at the social norm against the shame from being a
cheapskate.
Some passengers may use other tipping heuristics such as tipping a fixed dollar amount
or rounding off the taxi fare to a specific dollar amount. For example, a passenger facing a
fare of $9 many decide to tip $1 to round off her total trip expense to $10. I will account for
this behavior when I estimate the model.
I relax part of assumption A1 by allowing the tip menu to affect passengers’ belief about
the social norm tip. I define beliefs about the social norm tip as Ti = Ti + γkDk, where Ti
is passenger i’s belief about the social norm tip, Dk is a vector of different menus indexed
by k = 1, .., n, and γk is a vector of coefficients that denote the differential impact of each
menu on a passenger’s belief about the social norm tip. Therefore, the first-order condition
(equation (5)) can be rewritten as
t∗i = Ti + γkDk −0.5
θFi.(6)
With the above characterization of tipping behavior, I estimate the parametric model
in two steps. First, I use the first-order condition to estimate the unobserved population
distribution of beliefs about the social norm tip Ti and the norm-deviation cost parameter
θ. The advantage here is that, I need not make any distributional assumptions regarding
14
Ti. Also, θ is directly estimated in the same equation used to estimate Ti. Second, I use a
simulated method of moments algorithm to estimate the distribution of cognitive costs ci.
5.2 Estimating the Social Norm Tip and the Norm-Deviation Cost
We can estimate the first-order condition using an OLS regression. Without loss of generality,
I will focus on equation (5) and not equation (6) to describe the procedure. An empirical
analogue of equation (5) is
ti = αT + βFi + εi,(7)
where ti is the observed tip rate in the data, αT is a constant, β is the coefficient on the
taxi fare Fi, and εi is the residual.20 The link between equation (5) and (7) is that, αT is
the population average social norm tip E[Ti], β = 0.5θ
, and the residual term εi = Ti − αT .
To estimate Ti, note that εi ≡ t∗i − αT + 0.5θFi, therefore Ti = αT + εi ≡ t∗i +
0.5θFi. In other
words, the constant term plus the residual is an estimate of passenger i’s belief about the
social norm tip. The norm-deviation cost parameter can be estimated as θ = 0.5β
.
The challenge with estimating equation (7) is that, for passengers who choose menu tips,
we do not know what they would otherwise tip. However, by revealed preference, we observe
t∗i for the subsample of passengers who choose non-menu tips. Therefore, the coefficient
estimates from equation (7) are likely biased if we use all observed tips.
My approach is to estimate equation (7) using the subsample of non-menu tips and then
correct for potential sample selection bias. Using non-menu tips, we can write equation (7)
in a regression form as
E[t∗i |Fi, ci] = αT + βFi + E[εi|Fi, ci]
= αT + βFi + E[εi|ci].
The above equation follows from assumption A1, which implies that Ti⊥(Fi, Dk), and so
20We can generalize equation (7) to capture equation (6) by including dummy variables for different tipmenus.
The outcome variable in the equation is the tiptaxi fare
and the main covariate is the taxi fare. Thus, divisionbias might be a concern for estimating equation (7). However, this bias is insignificant in our setting for tworeasons. First, there is little to no measurement error in the data on tips and fares. Second, the lowest taxifare is $3—hence the outcome variable does not have a case where the numerator (tip) is divided by $0 or asmall fare.
15
(αT + εi)⊥(Fi, Dk), therefore εi⊥Fi.21
Therefore, the decision to choose a non-menu tip depends solely on a passenger’s cognitive
cost ci. Unfortunately, we do not know the relationship between εi and ci, and the concern
is the possibility that E[εi|ci] 6= 0. That is, cognitive costs systematically differ between
passengers who choose non-menu tips versus those who do.
I use an instrument to correct for sample selection bias in a two-step Heckman selection
correction model. The instrument must impact a passenger’s decision to choose a menu tip
(relevance), however, it should have no effect on her belief about the social norm tip or the
cost of computing her preferred non-menu tip (exclusion restriction).
As an instrument, I use taxi drivers’ reports of the number of passengers on the trip. The
motivation is that a passenger faces greater time pressure when traveling with co-riders, but
time pressure does not change her preferred tip or the cognitive cost for computing it.
The exclusion restriction is violated if a passenger’s preference is impacted by her co-
riders. For example, if passengers decide to split the bill, then the group’s preferred tip
may differ from each traveler’s preferred tip. Also, the number of co-riders does not affect
a passengers’ utility from tipping (equation (1)). Thus, the number of passengers is an
excluded instrument with respect to the model.
In the first step of the Heckman selection model, I use a probit regression to estimate
the probability of choosing a non-menu tip using the entire sample. The outcome variable
is a dummy variable that equals one if the passenger chooses a non-menu tip and zero
otherwise. The independent variables are the taxi fare and the taxi driver’s report of the
number of passengers on the trip. In the second step, I use rides where passengers give to
estimate equation (7) and include the estimated Inverse Mills Ratio from the first-step probit
regression to correct for sample selection bias.
Because passengers who give round dollar tips may be using a tipping heuristic different
from the model, I control for round dollar tip amounts by including an dummy variable for
round number tips in the Heckman selection correction model. The dummy variable captures
the potential impact of round-number tips on the parameters of the model.22
Results
First, I estimate the first-order condition from the parametric model using CMT taxi rides
from 2014: a period where the NYC taxi industry was likely in a steady-state. All taxis used
the same tip menu (20%, 25%, and 30%) and there were no changes in the taxi industry in
21I maintain that, assumption A1 holds independent of the cognitive cost ci.22This approach is similar to what Kleven and Waseem (2013) used to capture the effect of self-employed
workers who report round-number income amounts for tax purposes.
16
2014. Second, I use CMT taxi rides from 2010 and 2011 to analyze how different tip menus
affect passengers’ beliefs about the social norm tip by relying on a change in the tip menu
during this period.
Table A2 column (1) in the online appendix presents the first-stage probit estimate of the
Heckman selection correction model and panel A of table 2 column (1) presents estimates
of the first-order condition; the second-stage estimates of the Heckman selection correction
model. All the estimates are statistically significant at the one percent level and precisely
estimated.
The first-stage shows that passengers are more likely to choose a menu tip when there are
co-riders in the cab, corroborating the claim that passengers face more time pressure when
traveling with other passengers. The second stage estimates show that the distribution of
beliefs about the social norm tip averages at 19.8% of the taxi fare. Figure 3A shows the
distribution of passengers’ beliefs about the social norm tip that I estimate by adding the
regression residuals to the constant term.
The norm-deviation cost parameter θ is 0.5 divided by the coefficient on the taxi fare.
Therefore, the norm-deviation cost is calculated as θ times the squared percentage point
deviation of a passenger’s tip from her belief about the social norm tip. The coefficient on
the taxi fare is −0.00328, therefore, the norm-deviation cost parameter is 152.24. Hence,
the cost of a five percentage point deviation from one’s belief of the social norm tip is $0.38
(= 152.24× 0.52): 3.1% of the average taxi fare of $12.17.
I now analyze the impact of menus on passengers’ beliefs about the social norm tip. I
use CMT rides from 2010 to 2011, the period where CMT changed its’ tip menu from 15%,
20%, and 25% to 20%, 25%, and 30%. I test for the impact of the menu change by adding
a dummy variable to the regression equation (equation (7)) that equals one for the period
after the menu change and zero otherwise. The coefficient on the dummy variable measures
the impact of the new tip menu on passengers’ beliefs about the social norm tip.
Panel A of Table 2 column (2) shows that the average of passengers’ beliefs about the
social norm tip is 20.22% of the taxi fare when the menu shows 15%, 20%, and 25%, and
19.56% when the menu changes to 20%, 25%, and 30%. Whereas the difference between the
averages is statistically significant, it is not economically significant.23 Figure 3B shows the
similarities between passengers’ beliefs about the social norm tip before and after the menu
change. Also, beliefs about the social norm tip remained similar between 2010 and 2014;
on average, 20.22% in 2010 before menu change and after menu change19.56% in 2011 and
19.8% in 2014. Therefore, the CMT tip menu change had little impact on passengers’ beliefs
about the social norm tip.
23The difference is only three-hundredths of the average norm before the change.
17
On the other hand, the norm-deviation cost is lower in 2010–2011 compared to 2014. The
coefficient on the taxi fare in 2010-2011 is −0.00423, so the norm-deviation cost parameter
is 118.3. Therefore, the norm-deviation cost for tipping five-percentage points less than the
norm is $0.30, $0.08 less than the estimate from using rides in 2014. Thus, between 2010
and 2014, the norm-deviation cost increased by 21%.
I find similar results when I exclude the Inverse Mills Ratio in the second step of the
Heckman selection model.24 This implies that sample selection bias is inconsequential when
using non-menu tips to estimate the population distribution of beliefs about the social norm
tip and the norm-deviation cost.
In sum, I find that the distribution of beliefs about the social norm tip averages around
20% of the taxi fare. The CMT tip menu change had little impact on passengers’ beliefs
about the social norm tip. The norm-deviation cost of tipping five percentage points less
than the norm is between $0.30 and $0.38 (2.5% and 3.1% of the average taxi fare of $12.17).
5.3 Estimating Cognitive Cost
5.3.1 An Upper Bound of Cognitive Cost for Non-Menu Tips
For passengers who give non-menu tips, I use their estimated beliefs about the social norm
tip Ti and the norm-deviation cost parameter θ to compute an upper bound of their cognitive
cost and their norm-deviation cost. For a passenger who gives a non-menu tip rate ti for a
taxi fare Fi, we can compute their belief about the social norm tip using equation (5). We
can then compute a level of cognitive cost above which the passenger would opt for a menu
tip (using equation (4)). That is,
ci = (dj − ti)Fi + θ[(Ti − ti)
2 − (Ti − dj)2] .
I use the higher menu option near each non-menu tip as the applicable menu option for
computing ci. For example, for a non-menu tip rate of 17%, the applicable menu option is
20%, and for a non-menu tip rate of 22%, the menu option is 25%, and so forth. I drop
non-menu tips above 30% of the taxi fare as there is no menu option greater than 30%. Also,
I calculate the norm-deviation cost for each non-menu tip as θ × (Ti − ti)2.
I use data from CMT taxi rides with non-menu tips in 2014 and parameter estimates from
table 2 (Panel A, column (1)), for this exercise. Figure 4 shows both the distribution of the
computed upper bounds of the cognitive costs and the norm-deviation cost for passengers
who give non-menu tips. The averages of these distributions are $0.95 for cognitive cost and
24Table A3 in the online appendix present OLS estimates analogous to table 2 Panel A.
18
$0.33 for the norm-deviation cost. Passengers who choose menu options possibly have higher
decision costs compared to those we observe giving non-menu tips.
5.3.2 A Simulated Method of Moments Estimate of Cognitive Cost
I estimate the population distribution of cognitive costs for taxi passengers using a simu-
lated method of moments approach and by assuming that cognitive costs are exponentially
distributed with rate parameter λ. I choose an exponential distribution because the esti-
mated upper bound of cognitive costs (figure 4) approximates an exponential distribution.
Also, both the nonparametric and semiparametric estimates of decision cost approximate
exponential distributions (figure 2D).
There is no analytical solution to equation (3), hence, no corresponding closed-form
expression to estimate cognitive cost ci. This is because the derivative of the indicator
function 1{ti /∈ Dk} is not well defined. I circumvent this problem by using a Monte Carlo
algorithm that follows these steps:
1. For each observed taxi fare Fi, the algorithm draw at random a value of Ti from the
estimated distribution of passenger beliefs about the social norm tip, and a value of
cognitive cost ci from an exponential distribution with rate parameter λ.
2. The algorithm computes the preferred tip t∗i , as defined in equation (5), using the
values of Fi, Ti, and the estimated norm-deviation cost parameter θ.
3. Using equation (3), the algorithm computes the level of utility for choosing the non-
menu tips U t∗i and the three menu tips Ud1, Ud2, and Ud3.
4. The algorithm then chooses the tip that results in the highest level of utility.
With this algorithm, I use a simulated method of moments approach to estimate λ such
that the model predicts a realization of tips that matches the observed data as closely as
possible. The simulated method of moments approach matches a vector of model predicted
moments to those computed from the observed data. Henceforth, symbols with the carets
atop denotes estimates of population statistics.
I describe the simulated method of moments approach. Let g(λ|Ti, θ) = [m−m(λ|Ti, θ)]
be a vector of moment conditions, where m is the vector of sample statistics (empirical
moments from the data) and m(λ|Ti, θ) is the model analogue of m. The simulated method
of moments algorithm minimizes the criterion function Q(λ|Ti, θ) = g′Wg, where W is some
positive-definite weight matrix that is a function of the realized data. When minimizing
the criterion function Q(λ|Ti, θ), I match the sample statistics to their simulated analogues
under the model.
19
I use a two-step procedure to compute model parameters. In the first step, I use an
identity matrix (W1 = I) as a preliminary weight matrix to estimate λ. Then, I use the
estimated λ (denoted as λ1) to predict a set of realized tips via equation (3). Next, I use the
predicted tips to compute m(λ1|Ti, θ)—the model analogue of the empirical moments m. I
then calculate the vector of moment conditions as g(λ1|Ti, θ) = [m−m(λ1|Ti, θ)].
In step two, I take the diagonal of the inverted variance-covariance matrix of the moment
conditions from step one and use it as a weight matrix (i.e., W2 = [diag{gg′}]−1) to compute
the final parameter estimates.25 Using W2 implies that moment conditions are independent
of each other. Therefore, the algorithm in the second step minimizes the squared distance
between the empirical and the model predicted moments with a metric determined by the
weight matrix W2.
The rate parameter λ of the exponential distribution is identified by the share of passen-
gers who choose menu tips. If there is no cognitive cost for computing one’s preferred tip,
then we should find a few passengers choosing from the menu relative to other non-menu tip
rates. Thus, the large shares of passengers who choose menu tips identify λ and hence ci.
The moments I use to estimate λ are the shares of passengers whose tip fall in one of 35
non-overlapping one percent bins, namely 1%, 2%, 3%...35%. For example, the estimated
moment for passengers who tip 10% of the taxi fare is defined as the share of passengers who
give a tip that is between 9.5% and 10.5% of their taxi fare. Also, the change in the CMT
tip menu in 2011 provides an extra source of variation that helps to identify λ. That is, the
menu change presents variation in menu options providing extra moments to identify λ.26
I use the numerical optimization algorithm “optim” that is implemented in the R statis-
tical software to compute λ. This algorithm finds the parameter estimate that minimize the
criterion function Q(λ|Ti, θ). To avoid selecting a local minimum, I search for the param-
eter estimate over 500 iterations of the algorithm and choose the estimate that results in
the smallest minimized value of Q(λ|Ti, θ). I compute standard errors using a bootstrapped
procedure where 1000 independent draws of tips are constructed by a random resampling of
tips generated via equation (3). The standard error is defined as the standard deviation of
the distribution of parameter estimates computed from all 1000 bootstrap samples.
Estimates
Table 2 panel B presents the simulated method of moments estimate of the average cognitive
cost 1λ
separately for the CMT taxi rides in 2014 (column (1)) and for those in 2010-2011
25The theory suggests that the best choice of a weight matrix is the inverse of the covariance of the momentconditions.
26I use 70 moments when using data from rides in the period when the menu change: thirty-five momentsfrom the period before and 35 after the change.
20
(column (2)) when the tip menu changed. Because of the large size data, I select five
million taxi rides at random for each period (2014 and 2010-2011), to reduce the time for
computation. The table reports both the first and second step estimates of λ from the
simulated method of moments approach.
The first and second step estimates of the average cognitive cost are similar. Therefore,
estimates from the model are not driven by the choice of weighting matrix. Focusing on the
second step, the estimate of the average cognitive cost is $1.34 (11% of the average taxi fare
of $12.17) when using rides from 2014 and reduces to $1.14 (9.4% of the average taxi fare)
when using rides from 2010-2011.
5.4 Model Performance
The parametric model performs best in periods where the tip menu shows 20%, 25%, and
30% instead of 15%, 20%, and 25%. Between 2011 and 2014, when the CMT tip menu
was 20%, 25%, and 30%, figures 5A and 5B show that the model mimics both the share
of passengers at all three menu options and at most of the non-menu tip rates. Figure 5C
shows that the model does not performs as well in predicting tips in 2010 when the tip menu
showed 15%, 20%, and 25%.27
Estimates from the parametric model are comparable to the nonparametric and semipara-
metric estimates. For example, adding the norm-deviation costs of tipping five percentage
points less than the norm ($0.30 - $0.38)28 and the cognitive cost of computing a non-menu
tip ($1.14 - $1.34), the average decision cost is between $1.44 and $1.72 (i.e., between 11.83%
and 14.13% of the average taxi fare $12.17). These magnitude of the semiparametric and
parametric estimates of the average decision cost is $1.64, and $1.89 respectively (13.48%
and 15.53% of the taxi fare).
6 Counterfactual Applications and Welfare
6.1 A Tip-Maximizing Menu
What tip menu will maximize tip revenue? The answer to this question is of interest beyond
tipping in taxis because the use of tip menus is ubiquitous across restaurants, bars, hotels,
27A χ2 goodness of fit test suggests that the model predictions of passenger tipping under the two CMTtip menus are significantly different from the observed tips. The test results are presented in the notes offigure 5.
28I choose a five-percentage point deviation because, $0.33, the average norm-deviation cost among pas-sengers who give non-menu tips, is roughly the cost of tipping five percentage points less than ones’ beliefof the social norm tip.
21
delivery services, and the service sector at large. Increasing tip revenue raises the earnings of
workers who receive tipped wages or depend on tips to supplement their income. For firms
where tips are a direct source of revenue, a menu that maximizes tips maximizes profits.
These reasons are identical for taxi drivers because they keep all the earnings (taxi fares +
tips) from driving.
The goal is to find the number of menu options to show passengers and the corresponding
tip rate for each option. I set the model parameters to the estimates from column (1) of table
2 and the tip menu options as the free parameters to be evaluated for values that maximize
tips. I focus on tip menus that will present passengers with suggestions of tips as a percent
of the taxi fare, which is not a full characterization of the tip-maximizing menu.29
To start, I first consider the case where drivers are restricted to show passengers a one-
option menu. Using data from CMT taxi rides in 2014, I search over a grid of tip rates
between 0% and 100% to find the tip rate that the model predicts as increasing the average
tip the most. Figure 6A shows the results from the grid search and that tips are highest
when passengers are shown 22% as the menu option. Tips increase by 12.76%, an increase
from 15.83% on average when using no menu to 17.85% when using the 22% tip menu.
From one menu option, I continue to add more options until the model predicts that tip
revenue cannot be increased further. Figure 6B shows results from the grid search for two
menu options, and the model predicts that showing 20% and 27% maximizes tips. Figure
6C plots the predicted average tip rate as the number of menu tip options increase. The
average tip increases no further after showing three or more tip-maximizing menu options. I
conclude that using three menu options is tip-maximizing, and the model predicts showing
20%, 26%, and 32% as menu options.30 With this menu, the average tip rate increases to
18.15%, a 14.65% increase in the average tip relative to using no menu. Also, the estimated
tip-maximizing menu (20%, 26%, and 32%) is similar to the current tip menu (20%, 25%,
and 30%) in NYC Yellow taxis.
Both figures 6A and 6B show that using some values as menu options can either have
a positive or negative effect on tip revenue. For example, in figure 6A, showing a tip rate
below 13% of the taxi fare depresses tips compared to using no tip menu.
6.2 How Different Tip Menus Impact Tipping
CMT and VTS, vendors of the touch screen payment devices in NYC Yellow taxis, use four
sets of tip menus between 2010 and 2014. I examine how the different tip menus affect
29This may include but not be limited to presenting some combination of dollar tip amounts and percent-ages.
30Figure 6D shows the model predicted distribution of tips for the tip maximizing menu.
22
passenger tips.
CMT’s tip menu showed 15%, 20%, and 25% in 2010. Then, it changed these rates to
20%, 25%, and 30% starting February 9, 2011. Before 2012, VTS offered a tip menu of dollar
amounts ($2, $3, and $4) for fares under $15, and percentages 20%, 25%, and 30% for larger
fares. From 2012 on, VTS only used the percentage options. Thus, after 2011, both CMT
and VTS use the same tip menu (20%, 25%, and 30%) for all fares. Table 3 reports the
average tip per each menu used by the two vendors, column (1) for CMT and column (2)
for VTS.
In 2010, when CMT taxis used 15%, 20%, and 25% as a tip menu, the average tip was
17.81% of the taxi fare. After the CMT tip menu changed to 20%, 25%, and 30% and the
average tip increased to 19.16% in 2011 and 19.07% in 2013-2014.
From 2010-2011, the average tip was 20.68% of the taxi fare in VTS taxis when the tip
menu that showed dollars amounts ($2, $3, and $4) for taxi fares under $15, and percentages
(20%, 25%, and 30%) for larger taxi fares. In 2013-2014, when VTS used 20%, 25%, and
30% as the tip menu for all taxi fares, the average tip fell to 18.55%. VTS stopped using the
tip menu that showed dollar amounts because of customer complaints that lead the TLC to
order its removal.
The current tip menu, 20%, 25%, and 30%, increases tip revenue compared to showing
15%, 20%, and 25%. Also, the current menu is close to the model predicted tip-maximizing
menu (20%, 26%, and 32%). Concerning using a tip menu that shows percentages, the
convergence in tip menus across the two vendors over time is consistent with taxi companies
learning overtime to us a menu that maximizes tips.
6.3 Welfare
How do different tip menus affect revenues from tips and passengers’ utility from tipping?
To answer this question, I evaluate how four tip menus compare to using no tip menu. The
first menu is 15%, 20%, and 25%, the second is 20%, 25%, and 30%, and the third is the
estimated tip-maximizing menu 20%, 26%, and 32%. For the fourth tip menu, I estimate a
menu that maximizes the utility of tippers and evaluates how it impacts the revenue from
tips.
The welfare from tipping is the sum of the dollar value of utility that consumers get from
tipping and the tip revenue that drivers receive. The utility from tipping (equation (3)) is
quasi-linear in money. Therefore, I use the parameter estimates from Table 2 column (1) to
compute the dollar value of passengers’ utility from tipping.
The utility from tipping is always less than zero, even for the case where the passenger
23
decides not to leave a tip. This is because the tip is an expense, and the passenger incurs
a decision cost (norm-deviation cost + cognitive cost) for tipping. Thus, the sum of tip
revenue and the utility from tipping is at most zero.
Using data from CMT taxi rides in 2014, table 4 presents the welfare calculations at the
taxi trip level. Columns (1) reports the utility from tipping, column (2) the tip revenue
received by drivers, and column (3) the welfare from tipping (the sum of columns (1) and
(2)). Panel A shows that with no tip menu, the utility from tipping is -$3.429 (26.68% of the
average taxi fare of $12.17), and the tip received by drivers is $1.924 (15.8% of the average
taxi fare). Therefore, on average, the welfare from tipping in a taxi trip with no tip menu is
-$3.429 + $1.924 = -$1.504 (12.35% of the average taxi fare).
I compute changes in welfare under the four tip menus relative to using no tip menu.
Panel B shows the results. Using CMT’s previous tip menu, 15%, 20%, and 25%, increases
overall welfare by $1.265—an 84% increase relative to using no tip menu. The increment is
from a $1.097 increase in the utility from tipping and a $0.167 increase in tip revenue. The
current tip menu 20%, 25%, and 30% increases overall welfare by $1.081, an $0.80 increase
in the utility from tipping and a $0.281 increase in tip revenue. Comparing the current menu
to the previous, passengers lose $0.297 in utility. This loss comes from a transfer of $0.114 to
drivers and a deadweight loss of $0.183. The estimated tip-maximizing menu yields similar
results as the current tip-menu.31
I follow the procedure in subsection 6.1 to estimate a three-option tip menu that maxi-
mizes the utility from tipping. I find that using 9%, 15%, and 25% as a tip menu maximizes
the utility of passengers. The increase in consumer utility is highest under this menu ($1.212)
compared to the other menus. However, tipping remains the same as in the no-menu case.
The overall welfare under the utility-maximizing menu increases by $1.217 relative to the
no-menu case.32
The welfare estimates do not account for a passenger’s utility from the whole taxi ride
experience. Therefore, these estimates assume that all unobserved aspects of the taxi ride
are similar on average.
31The 2014 Taxi fact book reports that there are about 175 million taxi rides annually. To put the ride levelwelfare estimates in perspective, we can rescale all the estimates in table 4, by multiplying by 175 million.For example, the current taxi menu increases the welfare from tipping by about $190 million annually relativeto the no-menu case.
32Forcing passengers not to tip does not maximize the utility from tipping. For example, using theestimated social norm tip of 20%, the welfare from not tipping at all is −θ×(d−t)2 = −152.24×(0.20−0)2 =−$6.01, four times worse than the no-menu case.
24
7 Conclusions
Studies posit that social norms matter for decision-making. Policymakers and firms find that
menus and defaults are powerful tools that influence choices. However, we know little about
the mechanisms through which social norms affect decisions, and why menus or defaults
impact choices.
By studying tipping in NYC Yellow taxis, this paper documents an empirical relationship
between personal preferences and social norms and choosing from a menu versus actively
calculating a preferred choice. The advantage here is that NYC taxis used different tip
menus that change over time, and the context helps to avoid several complications that vexed
previous researchers. For example, at the end of a ride, customers cannot defer tipping to a
later period. Thus, procrastination and present bias do not affect the analysis.
In this study, I develop a model that captures how consumers tip when they are presented
with a tip menu. In the model, passengers have beliefs about the social norm tip, they incur
a cost for not conforming to the norm (norm-deviation cost), and an effort cost of calculating
a non-menu tip (cognitive cost). I use three approaches to analyze tipping behavior and they
all provide consistent results.
In the first approach, I use changes in the tip menu to nonparametrically estimate that
the cost of computing a tip when passengers deviate from the tip menu is about $1.89
(15.53% of the average taxi fare of $12.17) on average. In the second approach, the average
decision cost decreases to $1.64 after I control for observable trip characteristics. In the
third approach, I use a parameterization of the tipping model to estimate the distribution
of passengers’ unobserved beliefs about the social norm tip and to identify norm-deviation
costs and cognitive costs separately. The average social norm tip is 20% of the taxi fare. The
norm-deviation cost varies with the size of the deviation, for example, the norm-deviation
cost is between $0.30 and $0.38 when passengers tip five percentage points less than the norm.
The cognitive cost of calculating a non-menu tip ranges from $1.10 to $1.32 on average.
I use the model to investigate several what-if questions. For example, compared to using
no tip menu on a taxi trip, the current tip menu increases tips by 14.65%, and the overall
welfare from tipping by $1.08. Also, I find that the current tip menu in NYC Yellow taxicabs
nearly maximizes tips. The two vendors who provide the touch-screen payment devices in
taxicabs appear to have converged over time to use the current menu.
The findings from this study are not limited to tipping in taxis. It applies to other service
industries such as restaurants, delivery services, bars, and hotels. The result that the size
of norm-deviation costs and cognitive costs are relatively large may be useful in considering
more general nudges such as those that are widely used by businesses and policymakers.
25
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28
Figures & Tables
Figure 1: (A) Distribution of Tips (% of Taxi Fare) Before and After Menu Change, (B) Non-parametric Bounds of CDF of Decision Cost (Tip = 10%), (C) Nonparametric UnconditionalCDF of Decision Costs
A
0.0
0.1
0.2
0.3
0.4
0 5 10 15 20 25 30 35 Tip (% of Fare)
Sh
are
After Menu Change
Before Menu Change
B C
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Mean = $1.89
0.0
0.2
0.4
0.6
0.8
1.0
0 1 1.89 3 4 5 6 7 8 9 10 11 Decision Cost ($)
Sh
are
Panel A shows the distribution of tips in CMT Yellow taxis before and after the menu of tipspresented to passengers changed from showing15%, 20%, and 25% to show 20%, 25%, and 30%.The bars in Panel A are non-overlapping bins of width 1% for tips between 0.5% and 35.5% of thetaxi fare. The tips rates are truncated at 35.5% because the share becomes essentially zero. PanelB shows the lower and upper bounds for the CDF of decision costs computed nonparametricallyfor passengers who tip 10% of the taxi fare (tips rates between 9.5% and 10.5%). Panel C showsthe nonparametric estimate of the unconditional CDF of decision costs. The sample restriction arestandard rate taxi trips, with no tolls, paid for via a CMT credit card machine along with a positivetip. 29
Figure 2: (A) Predicted Probability of Tipping 10% (B) Predicted Probability of Tipping20% (C) Semiparametric Bounds of CDF of Decision Cost (Tip = 10%), (D) Semiparametricand Nonparametric Unconditional CDF of Decision Costs
A B
10%
5 10
15
20
25
30
0.00
0.02
0.04
Fare ($)
Pre
dic
ted P
robabili
ty
20%
5 10
15
20
25
30
0.0
0.2
0.4
0.6
Fare ($)P
red
icte
d P
rob
ab
ility
C D
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Nonparametric Approach: Mean = $1.89Semiparametric Approach: Mean = $1.64
Panels A and B show the predicted probabilities for tipping 10% and choosing the menu tip rate of20% respectively as functions of the taxi fare. The range of fares are between $3 and $30. Panel Cshows the lower and upper bounds for the CDF of decision costs computed semiparametrically forpassengers who tip 10% of the taxi fare (tips rates between 9.5% and 10.5%). Panel D shows theboth the semiparametric and nonparametric estimate of the unconditional CDF of decision costs.The sample restriction are standard rate taxi trips, with no tolls, paid for via a CMT credit cardmachine along with a positive tip.
30
Figure 3: Distribution of Beliefs about social norm tip
A B0
.00
00
.02
50
.05
00
.07
50
.10
0
0 5 10 15 20 25 30 35 40 45 50Tip (% of Fare)
Sh
are
Tipping Norm [ T ]
0.0
00
0.0
25
0.0
50
0.0
75
0.1
00
0 5 10 15 20 25 30 35 40 45 50 Tipping Norm (% of Fare)
Sh
are
After Menu ChangeBefore Menu Change
Panel A shows the estimated distribution of passengers’ beliefs about the social norm tip in CMTtaxis in 2014. Panel B shows the estimated distribution of passengers’ beliefs about the social normtip before and after the menu of tips presented to passengers changed from showing15%, 20%, and25% to show 20%, 25%, and 30% in CMT taxis over the period of 2010-2011. For the left panel, achi-square goodness of fit test between the distribution of beliefs about the social norm tips beforeand after the menu change yields a χ2 statistic of = 362900 and a P-value < 2.2e-16. The samplerestriction are standard rate taxi trips, with no tolls, paid for via a CMT credit card machine alongwith a positive non-menu tip.
Figure 4: CDF of (1) Upper Bound of Cognitive Costs and (2) The norm-deviation Cost forNon-Menu Tips
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7$ Cognitive Cost | Norm Deviation Cost
Sh
are
Mean Cognitive Cost = $0.95Mean Norm Deviation Cost = $0.33
This figure shows the distribution of upper bounds of cognitive costs for passengers who choosenon-menu options and the distribution of their norm-deviation cost. The sample restriction arestandard rate taxi trips, with no tolls, paid for via a CMT credit card machine along with a positivenon-menu tip.
31
Figure 5: Model Fit
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20 25 30 35
Tip (% of Fare)
Sh
are
Model Predicted Tips Observed Tips
0.0
0.1
0.2
0.3
0.4
0 5 10 15 20 25 30 35 Tip (% of Fare)
Sh
are
� � � � � � � � � � � � �
Observed tip
0.0
0.2
0.4
0.6
0 5 10 15 20 25 3 3 �
� � � � � � � � � � �
S���
�
� � � � ! " # � � $ % & $ � '
Observed tip
These figures illustrate how the parametric model fits the observed data by showing the observed distribution of tips against the modelpredicted distribution of tips. The left panel shows the fit of the model for passenger tips in CMT taxis in 2014 when the tip menu showed20%, 25%, 30%. A chi-square goodness of fit test between the model and the observed data yields a chi2 statistic of = 1726300 and aP-value < 2.2e-16. The middle panel shows the fit of the model for passenger tips in CMT taxis in 2011 right after the tip menu changedfrom showing 15%, 20%, and 25% to show 20%, 25%, 30%. A chi-square goodness of fit test between the model and the observed datayields a χ2 statistic of = 1860100 and a P-value < 2.2e-16. The right panel shows the fit of the model for passenger tips in CMT taxis in2010 when the tip menu showed 15%, 20%, and 25%. A chi-square goodness of fit test between the model and the observed data yields aχ2 statistic of = 1692300 and a P-value < 2.2e-16. The bars in this all the panels are non-overlapping bins of width 1% for tips between0.5% and 35.5% of the taxi fare. The tips rates are truncated at 35.5% where the share becomes essentially zero. The sample restrictionare standard rate taxi trips, with no tolls, paid for via a CMT credit card machine along with a positive tip.
32
Figure 6: Grid Search for Tip-Maximizing Menu
A B
14
15
16
1 (1 )
5 10 15 22 25 * + * , 4 + 4 , 50
M - . / 0 2 5 6 5 7 2 8 . 9 : ;
T<=
>?@
AT
BC
<D
BEF
G
H I J K L N J O P Q R U V W J X Y Z
H I J K L N J O P Q R [ P \ ] W J X Y Z Menu Option 2 (%)
0 1020
3040
50 Menu Option 1 (%)
010
2030
4050
Tip
(% o
f Taxi F
are
)
10
12
14
16
18
C D
15.5
16.0
16.5
^ _ ` a^ _ ` b
^ c ` a^ c ` b
d e
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16
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h i j k l m n o p l q i r s t u t v s n q w
xyz
{|}
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¨ © ª « ¬ ® ¯ ° ¹ ± ¯ ¨ © « ± ² ³ ´ · ¶ µ º ¸
» ® ¼ ½ ® ¯ ° ¨ © « ± ³ ¾ º ¿ ¸ À º Á ¸ À Â º ¸ Ã
» ® ¼ ½ ® ¯ ° ¹ ± ¯ ¨ © « ±
Panels A and B plot the results from a grid search for a one-option menu and a two-option menu respectively that will maximize theaverage tip received from passengers. Panel C plots the average tip from a grid search of the tip-maximizing menu as a function of thenumber of menu options. Panel D shows the model prediction of the distribution of tips for a three-option menu that maximizes tips.The bars in Panel D are non-overlapping bins of width 1% for tips between 0.5% and 35.5% of the taxi fare. The sample restriction arestandard rate taxi trips, with no tolls, paid for via a CMT credit card machine along with a positive tip.
33
Table 1: Taxi Trip Characteristics
Before Menu Change After Menu Change
1/2010 − 2/8/2011 2/9/2011 − 12/2011 2014
(1) (2) (3)
Menu of Tips [15%, 20%, 25%] [20%, 25%, 30%]
Tip ($) 1.77 1.95 2.27
(1.88) (1.23) (1.51)
Taxi Fare ($) 10.22 10.42 12.17
(5.33) (5.24) (6.69)
Tip Rate (% of Taxi Fare) 17.82% 19.19% 19.06%
(7.77%) (8.59%) (7.01%)
Menu Tip (%) 18.22% 21.64% 21.40%
(3.38%) (2.96%) ((2.93%)
Non-Menu Tip (%) 17.22% 16.70% 15.75%
(11.40%) (11.12%) (17.46%)
Share of Menu Tips 59.7% 48.3% 60.6%
Observations 28,305,969 31,227,439 41,620,454
Notes: This table presents means (standard deviation) across different trip characteristics. Column(1) presents trip characteristics one year before the CMT menu change, and column (2) presentstrip characteristics about a year after the change. Column (3) presents trip characteristics fouryears after CMT’s menu change. The data used are standard rate NYC Yellow taxi trips, with notolls, paid for via a CMT credit card machine along with a positive tip.
34
Table 2: Estimates of Model Parameters
2014 2010− 2011(1) (2)
Panel A: Heckman Selection Estimates of αT and θDependent Variable: Tip Rate
Taxi Fare −0.00328∗∗∗(0.00001) −0.00423∗∗∗(0.00001)
Inverse Mills Ratio 0.00481∗∗∗(0.00034) 0.00320∗∗∗(0.00020)
1(Post Menu Change) −0.00640∗∗∗(0.00005)
Constant 0.19801∗∗∗(0.00051) 0.20220∗∗∗(0.00027)
norm-deviation Cost Parameter θ(= −0.5
β
)152.2359∗∗∗(0.68173) 118.298∗∗∗(0.52862)
1st-Stage Instrument Number of Passengers Number of Passengers1(Round Number Tip) Yes YesObservations with Non-Menu Tips 16,394,917 25,206,358R2 0.01641 0.04198
Panel B: Simulated Method of Moments Estimates of ciMean Cognitive Cost ($): ci = 1/λ
1st-Step Estimate (weight matrix: W = I) 1.38021∗∗∗(0.00522) 1.1073∗∗∗(0.00262)
2nd-Step Estimate (weight matrix: W = [diag{gg′}]−1) 1.33586∗∗∗(0.00531) 1.13705∗∗∗(0.00873)Observations 5,000,000 5,000,000
Notes: This table reports estimates of the primitives in the structural model. In column (1), we use CMT taxi rides from 2014, andin column (2), we use CMT taxi trips from 2010-2011. Panel A reports estimates of the social norm tip Ti and the norm-deviation costparameter θ from the second step of the 2-step Heckman selection correction model. I use the delta method to compute the standard errors
for the estimates of θ. Using a simulated method of moments algorithm, Panel B reports estimates of the two-step procedure of estimatingthe cognitive costs incurred by passengers when they opt to compute their preferred non-menu tip. We use the whole analysis samplein Panel A. However, in Panel B, we randomly sample five million observations each from 2014 and 2010-2011 respectively to reduce thecomputational burden of the simulated method of moments algorithm. The sample restriction are standard rate taxi trips, with no tolls,paid for via a CMT credit card machine along with a positive tip. The standard errors in Panel A are robust white standard errors andin Panel B, the standard errors are computed as the standard deviation of the distribution of parameter estimates computed from 1000bootstrap samples. *p<0.1, **p<0.05, ***p<0.001.
35
Table 3: How Different Tip Menus Impact Tipping
CMT VTS(1) (2)
Panel A: Rides from Jan 2010 - Jan 2011
Tip menu for taxi fare < $15[15%, 20%, 25%]
[$2, $3, $4]
Tip menu for taxi fare ≥ $15 [20%, 25%, 30%]
Average tip for all fares 17.81% 20.68%Average tip for fare < $15 18.00% 21.19%Average tip for fare ≥ $15 17.51% 16.61%
Observations 27,574,410 28,658,477Panel B: Rides from Feb 2011 - Dec 2011
Tip menu for taxi fare < $15[20%, 25%, 30%]
[$2, $3, $4]
Tip menu for taxi fare ≥ $15 [20%, 25%, 30%]
Average tip for all fares 19.16% 20.66%Average tip for fare < $15 19.37% 21.21%Average tip for fare ≥ $15 18.00% 17.66%
Observations 31,960,044 30,339,659Panel C: Rides from 2013 - 2014
Tip menu for all taxi fares [20%, 25%, 30%] [20%, 25%, 30%]
Average tip for all fares 19.07% 18.55%Average tip for fare < $15 19.42% 18.74%Average tip for fare ≥ $15 17.96% 17.93%
Observations 83,107,354 84,332,924
Notes: This table reports the average tip rate across the different menus of tips presented topassengers in NYC Yellow taxis over time. Panels A through C correspond to one of three periodswhere at least one of the two Yellow tax credit card machine providers (CMT and VTS) changed themenu of tips presented to passengers. Column (1) shows the average tip rate offered by passengersin CMT cabs. Column (2) is analogous to column (1) but for passengers in VTS cabs. Each panelalso reports the average tip rate separately for trips where the taxi fare is less than $15. Onlystandard rate taxi trips, with no tolls, paid for for via a credit card machine where passengers leavea positive tip are used in this table. The sample restriction are standard rate taxi trips paid via aCMT or VTS credit card machine along with a positive tip.
36
Table 4: Welfare Estimates (Trip Level)
Utility (Loss)Tip Revenue Welfare
from TippingConsumer Surplus (CS) Producer Surplus (PS) CS + PS
(1) (2) (3)
Panel A: Baseline
No tip menu -$3.429 $1.924 -$1.504
Panel B: Change relative to no tip menu
Previous tip menu $1.097 $0.167 $1.265[15%, 20%, 25%]
Current tip menu $0.800 $0.281 $1.081[20%, 25%, 30%]
Tip-maximizing menu $0.802 $0.282 $1.084[20%, 26%, 32%]
Consumer utility-maximizing menu $1.212 $0.005 $1.217[9%, 15%, 25%]
Notes: This table reports estimates of the effect of different tip menus on social welfare at the taxi ride level. In column (1), we use theparametric estimates to compute the dollar value of a passenger’s utility from tipping. In column (2), we compute the tip revenue thatdrivers receive. Social welfare is calculated in column (3) as the sum of the utility that consumers get from tipping and the tip revenuesthat drivers receive. The utility from tipping is always less than zero, even for the case where the passenger decides not to leave a tip.This is because, in addition to the payment of the tip to the driver, the consumer incurs decision costs (norm-deviation or cognitive costs).
37
Online Appendix: Not for Publication
How Social Norms and Menus Affect Choices: Evidence from Tipping
Kwabena Donkor
1
Online Appendix Donkor
A1 New York City Yellow Taxi Tipping Systems
Figure A1: NYC Yellow Taxi Payment Screen with Menu Tip Options
Notes: This is an example of a taxi screen displaying a menu of tip options and the taxi fare atthe end of a taxi ride.
Figure A2: Changes in Menu Tip Options Over Time by Vendor
Notes: This figure illustrates the changes and differences in the menus presented by the two mainNYC Yellow taxi credit card machine providers (CMT and VTS).
2
Online Appendix Donkor
A2 Empirical Support for Assumptions
Assumption A1
A1–People’s beliefs about the social norm tip are jointly independent of the tip menu and
the taxi fare.
Although we cannot formally test assumption A1, I examine whether the observed tip
rate ti is independent of the menu of tip options D. I compare tipping decisions under two
different tip menus D1 and D2, where some of the options in D2 are higher than the options
in D1.
Suppose a passenger’s preferred tip is ti is not in either of the menus. She tips ti if her
decision cost is low enough not to benefit from choosing a menu tip option. Let H(ti|D1)
and H(ti|D2) be the distribution functions of tips when passengers are shown D1 and D2
respectively. If ti depends on the menu, then H(ti|D1) and H(ti|D2) will differ across the
entire support of ti. Thus, H(ti|D2) will be shifted to the right of the distribution of tips
under the menu with lower tip options H(ti|D1) . However, if ti⊥D, then H(ti|D1) and
H(ti|D2) will differ only around the neighborhood of the tip options across the two menus.
I use the CMT’s tip menu change to assess whether ti is independent of D by comparing
the distribution of tips before and after the change. Figure 1 shows the distribution of tips
before and after CMT’s menu change. The figure shows stark differences in the share of
passengers who choose menu options and in the share for tips within the neighborhood of
the menu options. However, the two distributions remain relatively similar for non-menu
tips. I take this as indirect evidence in support of A1.
Assumption A2
A2–Decision costs are independent of the tip menu and constant over time.
It is conceivable that traveler may learn after some time and become skilled at computing
their preferred tip, subsequently alleviate their cognitive cost. If so, we ought to expect the
share of travelers tipping at non-menu choices to increase after some time. To check for such
a pattern, I compare the distribution of tips across years where the tip menu stayed same
in CMT taxis. That is the period between 2011 and 2015. I find no significant changes in
the distribution of tips across the different years depicted in the figure below. I take this as
partial evidence in support of A2.
3
Onlin
eA
ppen
dix
Don
kor
Figure A3: Overlapping Distribution of Tip (%) in Years with No Change in CMT Tip Menu
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20 25 30 35
Tip (% of Fare)
Sh
are
20112013
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 16 20 25 Ä Å Ä Æ
Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò
ÓÔ
ÕÖ×
2012
Ø Ù Ú Û
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 16 20 25 Ü Ý Ü Þ
ß à á â ã ä å æ ç è é ê
ëì
íîï
ð ñ ò ó
2015
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 16 20 25 ô õ ô ö
÷ ø ù ú û ü ý þ ÿ � �
S�
��
�
20122015
Notes: These figures compare the distribution of tips between 2011 and 2011. This period is five years after CMT–a Yellow taxi creditcard machine vendor–changed its tip menu in 2011 from 15%, 20%, and 30%, to showing 20%, 25%, and 30%. The sample restrictionare standard rate taxi trips, with no tolls, paid for via a CMT credit card machine along with a positive tip. The points in the figure areestimates from non-overlapping bins of width 1% for tips between 0.5% and 35.5% of the taxi fare. The tips rates are truncated at 35.5%where the share becomes essentially zero.
4
Online Appendix Donkor
Verifying Assumption A3
A3 - A passenger’s cognitive cost is jointly independent of the taxi fare and her preferred
tip.
Because we do not observe ci, there is no straightforward way to test A3. Therefore, I
check first for evidence that ci is independent of one’s preferred tip t∗i . Then, I check for
evidence that ci is independent of the taxi fare F .
ci ⊥ Fi. The cognitive cost ci associated with computing a tip is independent of the taxi
fare. There is no straightforward way to test this assumption, because we do not observe
ci. However, we find it reasonable to assume that passengers find it easy to compute the
dollar amount of their tip rate if the taxi fare is a multiple of $10. Thus, if percent to dollar
conversions are relatively easier for fares that are multiples of $10, then passengers should
be less likely to choose a menu tip option for these fares.
To test the previous statement, I regress a dummy variable that equals one if the tip is a
menu tip option and zero otherwise on a set of dummies that indicate fares that are multiples
of $10. If it is significantly easier to calculate tips when the fare is a multiple of $10, then
ci will be notably lower, and passengers will be less likely to choose menu tips. Hence, we
should observe a negative coefficient on the dummy variable for fares that are multiples of
$10.
Table A.5 shows estimates from this regression. The coefficients on the dummy variables
for fares that are a multiple of $10 are all positive or not statistically significantly distin-
guishable from zero. This suggests that passengers are just as likely if not more likely to
choose a menu tip option when the fare is a multiple of $10 than otherwise. This is in direct
opposition to what we predicted. Although, this observation is not sufficient evidence to
establish assumption A3, it does suggest that the data seems consistent with it.
ci ⊥ t∗i . Since ci is unobservable, I cannot measure ci for all possible tip rates ti. How-
ever, if we assume that tips are smooth across all fares (that is, the distribution of ti does not
have point masses or holes), then we can take advantage of the fact that some percentage
tips (such as 10%) are easy for passengers to compute. Then, we can see whether these cases
create point masses. More formally, suppose that the distribution of tips is smooth across
all fares and a 10% tip rate (and possibly a 15% tip rate) is fairly easy to compute. Then
there should be a point mass at 10% (and possibly at 15%) in the distribution of tip rates.
I use data from 2014 and restrict attention to tips less than 20% of taxi fare. I check for
point masses at 10% and 15% in the distribution of tips. If 10% and 15% are fairly easy to
5
Online Appendix Donkor
compute, then a notably large share of passengers should be concentrated at these two rates
relatively to other tips. Figure A4 shows a bar graph of the shares of passengers whose tips
fall in non-overlapping bins of width 1%. Most tips are concentrated between 8% and 18%.
However, the shares of tips in bins that include 10% and 15% are not any higher than the
majority of the other tip bins. Rather, the highest concentration of tips is at 12%. Whereas
this is not a formal test of assumption A3, the data are consistent with this assumption.
6
Online Appendix Donkor
Table A1: Evidence for Assumption A3
Dependent variable:
1(Tip = Menu Tip)
1(Taxi Fare = $10) 0.104∗∗∗
(0.0004)
1(Taxi Fare = $20) 0.050∗∗∗
(0.001)
1(Taxi Fare = $30) 0.037∗∗∗
(0.002)
1(Taxi Fare = $40) 0.056∗∗∗
(0.004)
1(Taxi Fare = $50) 0.038∗∗∗
(0.007)
1(Taxi Fare = $60) 0.005(0.013)
1(Taxi Fare = $70) −0.003(0.026)
1(Taxi Fare = $80) −0.065(0.076)
Constant 0.601∗∗∗
(0.0001)
Observations 41,620,580R2 0.002
Note: The data are standard rate NYC Yel-low taxi trips in CMT taxi cabs from 2014.The trips are limited to fares paid for usinga credit/debit card, has no tolls, and passen-gers leave a positive tip. ∗p<0.1; ∗∗p<0.05;∗∗∗p<0.01
7
Online Appendix Donkor
Figure A4: Distribution of Tips < 20%
0.00
00.
025
0.05
00.
075
0.10
00.
125
0 2 4 6 8 10 12 14 16 18 20 Tip (% of Fare)
Sha
re
Note: This plot shows the distribution of tips in non-overlapping bins of width 1% between0.5% and 19.5% tip rate using data from CMT taxi rides in 2014.
A3 Appendix Figures for Nonparametric Approach
A3.1 Tips Before and After CMT Tip Menu Change by Fare
Figure A5 shows the distribution of positive tips (truncated at the tip rate of 19.5%) before
and after CMT—a New York City taxi credit card machine vendor—changed the menu of
tips that is presented to taxi passengers in 2011. The figures correspond to the subset of
taxi trips whose fare falls within different ranges of the taxi fares. CMT presented customers
with three tip options in percentages (15%, 20%, and 25%) before the menu change. After
CMT removed the lowest tip option (15%) and added a higher percentage option (30%), so
that it offered 20%, 25%, and 30%. The shaded bars present the distribution of tips one
year before the menu change, and the un-shaded bars show the distribution of tips about a
year after the change. Data from 2010 and 2011 standard rate taxi trips, with no tolls, paid
for via a CMT credit card machine are used in these figures.
8
Online Appendix Donkor
Figure A5: Distribution of Tip (%) less than 20% Before and After CMT Tip Menu Change
Taxi Fare ∈ ($3, $5] Taxi Fare ∈ ($5, $7]0
.00
.10
.20
.30
.40
.5
1 3 5 7 9 11 1� 15 1� 19
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1 3 5 7 , 11 -. 15 -/ -,
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Taxi Fare ∈ ($7, $9] Taxi Fare ∈ ($9, $11]
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 W 11 XY 15 XZ XW
[\]^_ `a bcdef
ghijk
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0.0
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Taxi Fare ∈ ($11, $13] Taxi Fare ∈ ($13, $15]
0.0
0.1
0.2
0.3
0.4
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0.3
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0.5
1 3 5 7 Ñ 11 ÒÓ 15 ÒÔ ÒÑ
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áâãäå
æçè éêë ìíîï ðñòæç éêë ìíîï ðñò
ó ô õêéö÷øø
9
Online Appendix Donkor
Figure A5 continued
Taxi Fare ∈ ($15, $17] Taxi Fare ∈ ($17, $19]0
.00
.10
.20
.30
.4
1 3 5 7 ù 11 úû 15 úü úù
ýþÿ � �� �����
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0.0
0.1
0.2
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1 3 5 7 9 11 1� 15 1� 19
��!"# $% &'()*
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023 456 78:; <=>02 456 78:; <=>
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Taxi Fare ∈ ($19, $21] Taxi Fare ∈ ($21, $23]
0.0
0.1
0.2
0.3
0.4
1 3 5 7 E 11 FG 15 FH FE
IJKLM OP QRTUV
WXYZ[
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i j k`lmk`
0.0
0.1
0.2
0.3
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1 3 5 7 n 11 op 15 oq on
rstuv wx yz{|}
~����
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Taxi Fare ∈ ($23, $25] Taxi Fare ∈ ($25, $27]
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 � 11 �� 15 �� ��
����� �� ¡¢£¤
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0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 ½ 11 ¾¿ 15 ¾À ¾½
ÁÂÃÄÅ ÆÇ ÈÉÊËÌ
ÍÎÏÐÑ
ÒÓÔ ÕÖ× ØÙÚÛ ÜÝÞÒÓ ÕÖ× ØÙÚÛ ÜÝÞ
ß à ááâãäå
10
Online Appendix Donkor
Figure A5 continued
Taxi Fare ∈ ($27, $29] Taxi Fare ∈ ($29, $31]0
.00
.10
.20
.30
.40
.5
1 3 5 7 æ 11 çè 15 çé çæ
êëìíî ïð ñòóôõ
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� ��� �� �����
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Taxi Fare ∈ ($31, $33] Taxi Fare ∈ ($33, $35]
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 0 11 23 15 24 20
5678: ;< =>?@A
BCDEF
GHI JKL MOPQ RTUGH JKL MOPQ RTU
V W XYZ[\
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 ] 11 ^_ 15 ^` ^]
abcde fg hijkl
mnopq
rst uvw xyz{ |}~rs uvw xyz{ |}~
� � vu���
Taxi Fare ∈ ($35, $37] Taxi Fare ∈ ($37, $39]
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 � 11 �� 15 �� ��
����� �� �����
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��� ��� �� ¡ ¢£¤�� ��� �� ¡ ¢£¤
¥ ¦ §¨©§�
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 ª 11 «¬ 15 « «ª
®¯°±² ³´ µ¶·¸¹
º»¼½¾
¿ÀÁ ÂÃÄ ÅÆÇÈ ÉÊË¿À ÂÃÄ ÅÆÇÈ ÉÊË
Ì Í ÎÏÃÐÑ
11
Online Appendix Donkor
Figure A5 continued
Taxi Fare ∈ ($39, $41] Taxi Fare ∈ ($41, $43]0
.00
.10
.20
.30
.40
.5
1 3 5 7 Ò 11 ÓÔ 15 ÓÕ ÓÒ
Ö×ØÙÚ ÛÜ ÝÞßàá
âãäåæ
çèé êëì íîïð ñòóçè êëì íîïð ñòó
ô õ êö÷øù
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 ú 11 ûü 15 ûý ûú
þÿ �� �� �����
S��
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Taxi Fare ∈ ($43, $45] Taxi Fare ∈ ($45, $47]
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 9 11 1� 15 1� 19
�!"#$ %& '()*+
,-./0
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@ A 5BCBD
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 E 11 FG 15 FH FE
IJKLM OP QRTUV
WXYZ[
\]^ _`a bcde fgh\] _`a bcde fgh
i j klmln
Taxi Fare ∈ ($47, $49] Taxi Fare ∈ ($49, $51]
0.0
0.1
0.2
0.3
0.4
0.5
1 3 5 7 o 11 pq 15 pr po
stuvw xy z{|}~
�����
��� ��� ���� ����� ��� ���� ���
� � ����
0.0
0.2
0.4
1 3 5 7 � 11 �� 15 �� ��
����� �� ¡¢£¤
¥¦§¨©
ª«¬ ®¯ °±²³ ´µ¶ª« ®¯ °±²³ ´µ¶
· ¸ ¹º»
12
Online Appendix Donkor
Figure A5 continued
Taxi Fare ∈ ($51, $53] Taxi Fare ∈ ($53, $55]0
.00
.20
.4
1 3 5 7 ¼ 11 ½¾ 15 ½¿ ½¼
ÀÁÂÃÄ ÅÆ ÇÈÉÊË
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0.0
0.2
0.4
1 3 5 7 ä 11 åæ 15 åç åä
èéêëì íî ïðñòó
ôõö÷ø
ùúû üýþ ÿ �� ���ùú üýþ ÿ �� ���
N � ü���
Taxi Fare ∈ ($55, $57] Taxi Fare ∈ ($57, $59]
0.0
0.2
0.4
1 3 5 7 9 11 1 15 1 19
�� �� �� �����
S����
��� ��! "#$% &'(�� ��! "#$% &'(
) * �++,
0.0
0.2
0.4
1 3 5 7 - 11 ./ 15 .0 .-
23456 78 :;<=>
?@ABC
DEF GHI JKLM OPQDE GHI JKLM OPQ
R T GUVW
Taxi Fare ∈ ($59, $61]
0.0
0.2
0.4
1 3 5 7 X 11 YZ 15 Y[ YX
\]^_` ab cdefg
hijkl
mno pqr stuv wxymn pqr stuv wxy
z { |}p
13
Online Appendix Donkor
A3.2 Bounds On the Conditional CDFs of Decision Costs
Figure A6 shows the lower and upper bounds for the CDF of decision costs computed for
passengers who tip at rates less than 18%. The computation of these bounds relies on CMT’s
change in the menu of tips that is presented to taxi passengers in 2011. These bounds are
computed using the increase in the share of passengers who tip at a particular rate at different
levels of the taxi fare. Generally, for a given fare F and tip rate t < 20%, the lower and
upper bounds for the decision cost of switching from 15% to some non-menu tip t is given
by [|0.15− t|F, |0.20− t|F ]. Data from 2010 and 2011 standard rate taxi trips, with no tolls,
paid for via a CMT credit card machine along with positive non-menu tips (that are not
round-number dollar amounts) are used in this figure.
14
Online Appendix Donkor
Figure A6: Conditional CDFs of Decision Costs
Tip Rate = 1% Tip Rate = 2%0
.00
0.2
50
.50
0.7
51
.00
1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.2
50
.50
0.7
51
.00
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 3% Tip Rate = 4%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 5% Tip Rate = 6%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
15
Online Appendix Donkor
Figure A6 continued
Tip Rate = 7% Tip Rate = 8%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 9% Tip Rate = 10%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 11% Tip Rate = 12%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
16
Online Appendix Donkor
Figure A6 continued
Tip Rate = 13% Tip Rate = 14%0
.00
0.2
50
.50
0.7
51
.00
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 15% Tip Rate = 16%
0.2
50
.50
0.7
51
.00
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.2
50
.50
0.7
51
.00
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 17%
0.2
50
.50
0.7
51
.00
0 1 2 3 4 5 6 7 8 9 10 11Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
17
Online Appendix Donkor
A4 Appendix Figures for Semiparametric Approach
Figure A6 shows the lower and upper bounds for the CDF of decision costs computed for
passengers who tip at rates less than 20%. The computation of these bounds relies on CMT’s
change in the menu of tips that is presented to taxi passengers in 2011. These bounds are
computed using the increase in the share of passengers who tip at a particular rate at different
levels of the taxi fare. Generally, for a given fare F and tip rate t < 20%, the lower and
upper bounds for the decision cost of switching from 15% to some non-menu tip t is given
by [|0.15− t|F, |0.20− t|F ]. Data from 2010 and 2011 standard rate taxi trips, with no tolls,
paid for via a CMT credit card machine along with positive non-menu tips (that are not
round-number dollar amounts) are used in this figure.
18
Onlin
eA
ppen
dix
Don
korFigure A7: Predicted Probabilities by Level of Taxi Fare of Choosing Tips < 20%
16% 17% 18% 19%
11% 12% 13% 14% 15%
6% 7% 8% 9% 10%
1% 2% 3% 4% 5%
5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30
5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30
5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30
5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30
0.00
0.02
0.04
0.06
0.00
0.02
0.04
0.06
0.00
0.02
0.04
0.06
0.00
0.02
0.04
0.06
Fare ($)
Pre
dict
ed P
roba
bilit
y
Note: This figure shows the estimated predicted probabilities for non-menu tip rates below 20% as functions of the fare. The probabilitiesare computed from an ordered logistic regression using data limited to trips with tip rates 20% or less and selected from CMT taxi ridesin 2014. The range of fares used in this analysis is between $3 and $30. The sample restriction are standard rate taxi trips, with no tolls,paid for via a CMT credit card machine along with a positive tip.
19
Online Appendix Donkor
Figure A8: Conditional CDFs of Decision Costs
Tip Rate = 1% Tip Rate = 2%0
.00
0.2
50
.50
0.7
51
.00
1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 3% Tip Rate = 4%
0.0
00
.25
0.5
00
.75
1.0
0
1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 5% Tip Rate = 6%
0.0
00
.25
0.5
00
.75
1.0
0
1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
20
Online Appendix Donkor
Figure A8 continued
Tip Rate = 7% Tip Rate = 8%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 9% Tip Rate = 10%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 11% Tip Rate = 12%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
21
Online Appendix Donkor
Figure A8 continued
Tip Rate = 13% Tip Rate = 14%0
.00
0.2
50
.50
0.7
51
.00
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 15% Tip Rate = 16%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
Tip Rate = 17% Tip Rate = 18%
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
0.0
00
.25
0.5
00
.75
1.0
0
0 1 2 3 4 5 6 7Decision Cost ($)
Sh
are
Lower BoundMidpointUpper Bound
22
Online Appendix Donkor
A5 Parametric Approach
Figure A9
a. Share of Menu Tips by Taxi Fare b. Average Tip by Taxi Fare
.56
.58
.6.6
2.6
4.6
6.6
8S
ha
re o
f M
en
u D
efa
ult
Tip
s
3 6 9 12 15 18 21 24 27 30Taxi Fare ($)
17
18
19
20
21
22
23
Tip
(%
of
Ta
xi F
are
)
3 6 9 12 15 18 21 24 27 30Taxi Fare ($)
Notes: Figures A9a is a binned scatter plot that illustrates the relationship between the share ofpassengers who choose any one of the suggested menu tips presented at the end of a taxi ride atdifferent levels of the taxi fare. Figures A9b is a binned scatter plot that illustrates the averagetip rate at different levels of the taxi fare.The data used in both figures are from 2014 standardrate taxi trips, with no tolls, paid for for via a CMT credit card machine along with a positive tipamount.
Table A2: Heckman Selection Correction Estimates: First-Step Probit Estimates
2014 2010− 2011Dependent Variable: 1(Tip=Non-Menu Tip)
Taxi Fare −0.02917∗∗∗(0.00004) −0.04046∗∗∗(0.00004)
Number of Passengers -0.44228∗∗∗(0.00041) -0.40071∗∗∗(0.00035)
1(Post Menu Change) 0.11246∗∗∗(0.00043)1(Round Number Tip) Yes YesObservations 41,620,591 59,861,675Log Likelihood -14,436,606 -20,633,368Akaike Inf. Crit. 28,873,217 41,266,745
Notes: This table reports the first stage probit estimates of the Heckman selection correction modelpresented in Table II, Panel A. In column (1), I use CMT taxi rides from 2014, and in column (2),I use CMT taxi rides from 2010-201. The sample restriction are standard rate taxi trips, with notolls, paid for via a CMT credit card machine along with a positive tip. Both columns are estimatedwithout a constant term. I report robust white standard errors in parenthesis. *p<0.1, **p<0.05,***p<0.001.
23
Online Appendix Donkor
Table A3: OLS Estimates of αT and θ
2014 2010− 2011(1) (2)Dependent Variable: Tip rate
Taxi Fare −0.00326∗∗∗(0.00001) −0.00420∗∗∗(0.00001)
1(Post Menu Change) -0.00649∗∗∗(0.00005)
Constant 0.20458∗∗∗(0.00013) 0.20640∗∗∗(0.00007)
norm-deviation Cost Parameter θ(= − 1
2β
)151.9757 119.0844
1(Round Number Tip) Yes YesObservations with Non-Menu Tips 16,394,917 25,206,358R2 0.01639 0.04196
Notes: This table reports estimates of the social norm tip Ti and the norm-deviation cost parameterθ from an OLS regression that does not account for sample selection bias. In column (1), I use CMTtaxi rides from 2014, and in column (2), I use CMT taxi rides from 2010-201. The sample restrictionare standard rate taxi trips, with no tolls, paid for via a CMT credit card machine along with apositive non-menu tip. I report robust white standard errors in parenthesis. *p<0.1, **p<0.05,***p<0.001.
A6 Welfare
24
Onlin
eA
ppen
dix
Don
korFigure A10: Distribution of Tip (%) by Type of Tip Menu Versus No Menu Tips
a) Previous Tip Menu b) Current Tip Menu
Average (No Menu) = 15.83 %Average (with Menu)= 17.2 %
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Average (No Menu) = 15.83 %
Average (with Menu)= 18.14 %
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c) Tip-Maximizing Menu d) Utility-Maximizing Menu
Average (No Menu) = 15.83 %
Average (with Menu)= 18.15 %
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Average (No Menu) = 15.83 %
Average (with Menu)= 15.78 %
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Note: This figure shows the model predicted distribution of tips for four different tip menus namely used for the welfare analysis presentedin Table IV. The predictions are made using the estimated parameters of the model. The data shown are tips between 0.5% and 35.5%of the taxi fare. The tips rates are truncated at 35.5% where the share becomes essentially zero.
25