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(donkor@stanford.edu). 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).

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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).

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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<=

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AT

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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

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15.5

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16.5

^ _ ` a^ _ ` b

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xyz

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¨ © ª « ¬ ­ ® ¯ ° ¨ © « ± ² ³ ´ µ ¶ ´ · ¸

¨ © 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

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1 3 5 7 , 11 -. 15 -/ -,

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CDE FGH IJKL MOPCD FGH IJKL MOP

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Taxi Fare ∈ ($7, $9] Taxi Fare ∈ ($9, $11]

0.0

0.1

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0.3

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0.5

1 3 5 7 W 11 XY 15 XZ XW

[\]^_ `a bcdef

ghijk

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Taxi Fare ∈ ($11, $13] Taxi Fare ∈ ($13, $15]

0.0

0.1

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0.4

1 3 5 7 § 11 ¨© 15 ¨ª ¨§

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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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023 456 78:; <=>02 456 78:; <=>

? @ 4ABC44D

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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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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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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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

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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

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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

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1 3 5 7 ú 11 ûü 15 ûý ûú

þÿ �� �� �����

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N � �����

Taxi Fare ∈ ($43, $45] Taxi Fare ∈ ($45, $47]

0.0

0.1

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0.3

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0.5

1 3 5 7 9 11 1� 15 1� 19

�!"#$ %& '()*+

,-./0

234 567 8:;< =>?23 567 8:;< =>?

@ A 5BCBD

0.0

0.1

0.2

0.3

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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{|}~

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��� ��� ���� ����� ��� ���� ���

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0.0

0.2

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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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1 3 5 7 ä 11 åæ 15 åç åä

èéêëì íî ïðñòó

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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����

��� ��! "#$% &'(�� ��! "#$% &'(

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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