The effect of reference-dependent preferences on small monetary
transactions: the case of taxi tipping
University of Groningen
Master Thesis
January 9, 2020
Abstract
I study the occurrence of reference-dependent preferences in taxi tipping by using the outcome of sporting events as a proxy for mood. By combining pre-game betting odds data with game outcomes from a major sports team, I identify games that deviate from pre-game expectations. I focus on taxi rides that depart from the stadium of a major sports team 0-60 minutes after a home game has ended. The main result of this study is that when actual outcomes deviate from a rational reference point, taxi tipping is not affected. I do find that positive surprising game outcomes correlate with a higher tipping percentage. However, this only holds for very large surprises and I fail to establish causality. When the home team is predicted to lose and the team in fact loses, this decreases taxi tipping percentage by about 1.5 percentage points, which corresponds to a 20 cents decrease in the average tip. This finding is not in line with reference-dependent preferences, which would predict that unexpected outcomes should have a larger effect than expected outcomes. The results from my study should not be interpreted as evidence against the occurrence of reference-dependent preferences. Rather, I show that there does not seem to be a link between sports sentiment and taxi tipping.
Author: Joost Stoffel, s2558459
Supervisors: Romensen, G.J. and Schippers, A.L.
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1. Introduction
More than forty years ago, Kahneman and Tversky (1979) developed prospect theory as an alternative model to expected utility theory for decision-making under risk. Standard expected utility theory would predict that an individual makes choices based on the expected final state of wealth and not the change in wealth. A distinct feature of prospect theory, on the other hand, is that it evaluates uncertain future events based on whether it is a gain or a loss compared to a reference point. This reference point can be the current holding of assets, but can also be based on expectations about the future (Kahneman and Tversky, 1979). For example, receiving a bonus of $500 may be a pleasant surprise if you expect nothing, but a disappointment when you expect $1000.
The applications of this theory vary from incorporating expectations into macroeconomic models (see for example Bordalo, Gennaioli and Schleifer, 2018) to showing that marathon runners exhibit loss averse behaviour with respect to their finishing times (Allen, Dechow, Pope and Wu, 2017). To effectively measure the occurrence of reference-dependent preferences, the research setting must satisfy several criteria. A reference point must be observable and relate to an actual outcome that is also measurable. In this way, the magnitude of the deviation from the reference point can be determined. Furthermore, this deviation from expectations should be sufficiently important to the individual such that it generates a positive or negative emotion. Ideally, this emotion results in quantifiable behaviour.
An area that satisfies these criteria is the study of sports games. From betting data, one can derive the pre-game expected probability of winning as implied by the market. This measure can therefore serve as a standard for pre-game predictions1. In addition, Wann, Dolan, Mcgeorge and Allison (1994) show that sports fans often experience positive emotions when their team wins, and negative emotions after a loss. Reference-dependent preferences would predict that wins that are not expected beforehand magnify this positive emotion. In addition, when fans anticipate that their team will win the game but they in fact lose, the disappointment would be greater than after a loss that is already expected. To measure this effect, I rely on findings of Piff, Dietze, Feinberg, Stancato and Keltner (2015) who have established a link between emotions and the level of altruism. I then assume that this effect can be measured by the amount of tips given to taxi drivers for rides immediately following a game.
Using reference-dependent preferences, Edmans, Garcia and Norli (2007) established that losses in the soccer World Cup elimination stage lead to abnormal negative stock returns. To estimate whether reference-dependent preferences also affects small monetary transactions such as taxi tips, I
1 Wolfers and Zitzewitz (2006) find that prediction markets aggregate beliefs about the probability an event
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assume the following scenario. A sports fan forms a belief about the probability that his favourite team will win, and takes a taxi to the stadium. The individual then experiences a negative or positive emotion based on the game outcome, which may be magnified depending on whether it was expected or not. Immediately after the game, the sports fan takes a taxi ride back home and makes a decision about how much to tip the driver. In the occurrence of reference-dependent preferences, one would assume that as the team is expected to lose the game but wins, taxi tips increase. On the contrary, if the team was expected to win the game but in fact loses, tips are expected to decrease. When wins or losses are fully expected, this should not have an influence on tipping behaviour as it does not generate positive or negative surprises.
I will test this by using a high-frequency dataset containing all taxi rides of Chicago. Among other things, this includes information about the tip given and the pick-up and drop-off location. I use this data to identify rides that started at the stadium of the Chicago White Sox2 right after a game has ended. The Chicago White Sox is a Major League Baseball (MLB) team and is the third most popular sports team in Chicago. What makes the White Sox particularly suitable for this research goal is that the stadium lies in a quiet neighbourhood, and I provide convincing evidence that nearly all taxi rides taken in this area are taken by sports fans who visited a game of the White Sox. I use pre-game betting odds data as the reference point and incorporate this in a model based on Kőszegi and Rabin (2006) and Card and Dahl (2011).
The main finding of this study is that I do not find convincing evidence that taxi tipping immediately after a sports game is characterized by reference-dependent preferences. I do find that larger positive surprising game outcomes correlate with a higher tipping percentage. However, this only holds for very large surprises and I fail to establish causality in this respect. Without incorporating a reference point, wins and losses do not affect the tipping percentage differently. Both wins and losses decrease the tip percentage for rides immediately after the game by about 1 percentage point. However, I find that losing games even though this was expected beforehand generates a reduction in tipping percentage of about 1.5 percentage points. This corresponds to a decrease of 20 cents in the average tip. I do not find an effect on tipping when the team is expected to lose the game but wins, when the team is expected to win the game and wins, or when the team is expected to win the game but loses.
2 I also considered the Chicago Bears (National Football League) and Chicago Cubs (Major League Baseball), which
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This finding is not in line with previous research by Ge (2018), who found that unexpected wins generated an increase in the tipping percentage. Ge (2018) is the first to study the relation between reference-dependent preferences and taxi tipping. The fact that I do not find the same results stipulates the importance of replicating novel results in a different research setting. The results from my study should not be interpreted as evidence against the occurrence of reference-dependent preferences. Rather, I show that there is no link between sports sentiment and taxi tipping. My study therefore contributes to a larger body of tipping literature. For example, the fact that I find no link between mood and tipping is not in line with findings from studies on restaurant tipping (see for example Strohmetz, Rind, Fisher and Lynn (2002) and Azar (2007)). The wage of workers who earn a tipped wage in the hospitality industry generally depends for over 50% on tips (Shierholz, Cooper, Wolfe and Zipperer, 2017). Many of these workers earn minimum wages (Shierholz et al., 2017) and may have less influence on tips than previously thought if the mood of the tip giver does not influence the tip percentage. It is important for policymakers to consider this when setting the minimum wage. The remainder of this thesis is structured as follows. Section 2 covers the related literature. In section 3, I discuss the conceptual model I use to capture the effect of deviations from a reference point. Section 4 covers the data used and section 5 outlines the methodological approach. In section 6 and 7, I present my results and relate them to previous studies. Section 8 concludes.
2. Literature review
I first discuss the reference-dependence literature closely related to my research setting. I proceed by outlining other studies that covered other determinants of taxi tipping behaviour.
2.1 Reference-dependent preferences in field settings
While the foundations of prospect theory originate from thought experiments with students, numerous studies have attempted to proof the occurrence of reference-dependent preferences outside of laboratory settings. Camerer et al. (1997), for example, analyse close to 2000 shifts of New York City taxi drivers and find that drivers base the length of their shift on a daily income target. The authors hypothesize that due to loss aversion the taxi drivers are reluctant to stop working if they have earned less than this reference point. There is, however, no consensus about this finding and using a similar dataset Farber (2005) finds no evidence for reference-dependent preferences in this context. Farber (2005) concludes that instead of a daily income target, the cumulative daily hours worked determine when taxi drivers stop working. This finding emphasizes the importance of replicating studies such as that of Camerer et al. (1997) in order to check the robustness of the results.
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individuals frame the occurrence of events based on a rationally expected reference point3. As explained in more detail in section 1, the topic of sports games lends itself particularly well for this because objective pre-game win probabilities can be derived from betting data. Card and Dahl (2011), for example, use betting odds data from National Football League (NFL) games to investigate the link between game outcomes of the local NFL team and family violence. The authors find that when a team is predicted to win by four or more points but instead loses the game, male-on-female domestic violence increases by 10%. When the home team unexpectedly wins it does not lead to a decrease in domestic violence.
A more recent example is the study of Ge (2018), who investigates the occurrence of reference-dependent preferences in relation to sports games by studying taxi tipping behaviour in New York City. Ge (2018) uses a high-frequency dataset containing all taxi rides of New York City and focuses on taxi rides that depart from a basketball stadium. Ge (2018) finds that game outcomes by itself (in essence a win or a loss) do not affect tipping behaviour. When incorporating a reference point based on betting odds, however, unexpected close wins result in a 1.936 percentage points increase in tips. Contrary to what prospect theory would predict, tips after a taxi ride do not decrease when the home team is expected to win but instead loses the game. Ge (2018) attributes the absence of loss aversion in this context to the strong role of social norms with respect to tipping.
The example of Farber (2005) above, who found no evidence for reference-dependent preferences of taxi drivers while Camerer et al. (1997) did, shows the importance of replication studies. Because Ge (2018) is the first one to study reference-dependent preferences by analysing tipping behaviour, it is essential to verify the results. I will do this by using an almost identical dataset on taxis from Chicago instead of New York City, and use a comparable research design. Below, I will briefly discuss other determinants of taxi tipping and differences in methodology compared to similar studies.
2.2 Factors influencing taxi tips 2.2.1 Ride characteristics and time
Some factors, such as distance travelled, ride duration, date4 and time are used as control variables in most studies and I will do so as well (see for example Haggag and Paci (2014); Deveraj and Patel (2017); Ge (2018)). When studying the effect of sunlight on taxi tipping, Deveraj and Patel (2017) find that as ride distance and duration increase, the tiping percentage decreases. While Ge (2018) finds similar results for ride distance, he finds that ride duration does not have a statistically significant effect on
3 This model will be discussed in more detail in section 3.
4 For Chicago specifically, this in part accounts for the introduction of ride-hailing services such as Uber and the
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the tip percentage. Both studies use the dataset of all taxi rides from New York City, but their sample and methodologies differ.
2.2.2 Payment system and passenger count
Haggag and Paci (2014) study the presence of default tipping5 behaviour, using the same high-frequency taxi dataset of New York City as Deveraj and Patel (2017) and Ge (2018). Making use of the fact that the two payment systems used different default tipping amounts in 2009, they find that higher default tip suggestions6 result in an increase of tip amounts of $0.27 - $0.30.
There is no consensus in the taxi tipping literature about the influence of the amount of passengers on the tip percentage. Deveraj and Patel (2017) find that tip percentage increases with the amount of passengers, and they hypothesize that sharing a ride may induce larger tips due to the amount being spit. Ge (2018), however, finds a negative relation between passenger count and tipping percentage. The effects found in both studies are small. While the New York City taxi dataset contains information on which payment system is used and the amount of passengers, the Chicago dataset I use does not include this information. In section 4 I will discuss in more detail why this does not have to be a problem.
2.2.3 Weather, driver and location
Additional factors that may influence the taxi tip percentage are the weather, the driver or the pick-up and drop-off location. In the taxi tipping literature there is no consensus about the effect of these variables, and they are therefore not included in every study.
The effect of weather on taxi tips is not clear-cut. Deveraj and Patel (2017) study the effect of sunlight on taxi tipping and find a small but statistically significant effect of sunlight. Tipping percentage increases by 0.5 to 0.7 percentage points when comparing full sunshine to a dark sky, even when controlling for hour of the day and other weather conditions. In addition, the authors find that low average daily temperatures have a negative influence on tipping behaviour. High average daily temperatures positively affect taxi tips. Snowfall and rainfall, on the other hand, do not affect the tip behaviour when controlling for driver and day-of-the-year fixed effects. Farber (2015), however, does find that during hours with rain the tip percentage increases by 0.2 percentage points.
Including driver fixed effects is not standard in the taxi tipping literature. Nevertheless, Haggag and Paci (2014) do include driver fixed effects when studying the effect of default tips and Deveraj and Patel (2017) do so too in their study on the effect of sunlight on taxi tips. Ge (2018) explicitly states
5 When paying by credit card, three buttons are shown containing a default tip percentage (for example 15%,
20% and 25%). Alternatively, you can manually select another tip amount.
6 Haggag and Paci (2014) study two different schemes of default options for fares higher than $15. One version
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that he excludes the effect of drivers in his study of reference-dependent preferences and taxi tipping. Ge (2018) argues that service quality does not vary systematically among taxi drivers and that it is unlikely for someone to encounter the same taxi driver within a short period of time. In line with Ge (2018), I do not include driver fixed effects7.
An additional factor that can influence the amount of tips given to taxi drivers is the pick-up or drop-off area. Taxi drop-offs in wealthier areas, for example, may induce higher tipping percentages. Haggag and Paci (2014) account for this by linking the median household income to each pick-up and drop-off census tract8 of New York. Ge (2018) adopts an alternative approach and uses drop-off neighbourhood fixed effects in order to account for differences in tipping behaviour between home and away fans of a basketball team. Deveraj and Patel (2017) do not account for either area fixed effects or income when studying the tip effect of sunlight. I will follow the approach of Ge (2018), but use census tract fixed effects instead of neighbourhoods to allow for a higher level of granularity9.
3. Conceptual model
I use a conceptual model that is similar to Card and Dahl (2011) and Ge (2018). The foundations of this model lie in the gain-loss utility function developed by Kőszegi and Rabin (2006), which I first briefly cover below.
3.1 Utility function with reference-dependent preferences
I will model reference-dependent preferences using the utility function developed by Kőszegi and Rabin (2006), consisting of “consumption utility” and “gain-loss utility”. In this particular context of sports games, consumption utility could refer to the utility of attending a game of the White Sox. The gain-loss utility consists of the (dis)utility when the actual outcome of the game deviates from one’s pre-game expectations of which team was going to win (see for example Card and Dahl (2011); Ge (2018)). Let 𝑊 represent the game outcome, where 𝑊 = 1 is a win and 𝑊 = 0 a loss. The probability of
7 In addition, Aydin and Acun (2019) find that making conversation with the driver has a marginally significant
and small effect on the tip received. Haggag and Paci (2014) and Deveraj and Patel (2017) both use a sample consisting of several million taxi rides when accounting for driver fixed effects. As Ge (2018) and I use a substantially smaller sample size, realistically measuring the limited effect drivers have on tips is not feasible.
8 New York City is divided into 2,208 census tracts. Source: NYC OpenData – 2010 Census Tracts, accessed
[December 13, 2019], https://www.census.gov/geographies/reference-files/2010/geo/state-local-geo-guides-2010/new-york.html.
9 Chicago has 866 census tracts and 77 neighbourhoods. Census tracts are small areas that are supposed to be
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winning 𝑝𝑊 is represented by 𝑝𝑊 = 𝐸[𝑊] = 1 ∗ 𝑝𝑊+ 0 ∗ (1 − 𝑝𝑊). The utility function is therefore given by equation (1):
𝑈𝐴+ 𝜇(𝑊 − 𝑝𝑊) (1)
where 𝑈𝐴 is the consumption utility of the outcome of the game10 and 𝜇(𝑊 − 𝑝𝑊) is the gain-loss utility that depends on whether the outcome deviates from pre-game expectations. Individuals perceive gains differently than losses and exhibit loss aversion (Kahneman and Tversky, 1979). The magnitude and sign of the gain-loss utility 𝜇 therefore depends on whether the game outcome is a positive or negative surprise relative to the reference point 𝑝𝑊. For positive and negative surprises respectively, the gain-loss utility is given by:
𝜇(𝑊 − 𝑝𝑊) = 𝛼(𝑊 − 𝑝𝑊) > 0, 𝜇(𝑊 − 𝑝𝑊) = 𝛽(𝑊 − 𝑝𝑊) < 0,
if W = 1 (positive surprise since W − pW> 0)
if W = 0 (negative surprise since W − pW < 0) (2)
with 𝛼, 𝛽 > 0 and 0 < 𝑝𝑊 < 1. In the occurrence of loss aversion, 𝛽 > 𝛼 because the absolute effect of a negative surprise is larger than that of a positive surprise. If, for example, a fan of the White Sox believes there is only a 40% chance that his team will win (𝑝𝑊= 0.4), and the team indeed wins (𝑊 = 1), there is a positive gain-loss utility of 𝛼(1 − 0.4). The gain-loss utility is positive because the win was a large positive surprise. If the individual expected the team had an 80% chance to win, he or she will derive a smaller gain-loss utility of 𝛼(1 − 0.8) because the win was more or less expected. However, if in the latter scenario the Chicago White Sox lost the game (𝑊 = 0), the individual faces a negative gain-loss utility of 𝛽(0 − 0.8) because losing the game was a large and negative surprise relative to the pre-game reference point.
3.2 A model of tipping with reference-dependent preferences
Similar to Ge (2018), I assume that a passenger faces the following choice at the end of a taxi ride:
𝑇 = { 1, if the passenger gives a high tip %
0, if the passenger gives a low tip % (3)
10 It is often assumed that the consumption utility from witnessing your team winning is larger than when losing,
meaning 𝑈𝑊 > 𝑈𝐿 where 𝑈𝑊 refers to the team winning and 𝑈𝐿 to losing (see for example Card and Dahl (2011);
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The probability of tipping a high percentage is given by 𝑔, where 𝑔 = Pr(𝜏 = 1) , ∀τ ∈ 𝑇. I assume that the probability of tipping a high percentage exhibits reference-dependent preferences similar to the utility function from equation (1) as developed by Kőszegi and Rabin (2006).The probability of tipping a high percentage consists of a baseline probability 𝑔𝑊 in case of a win and 𝑔𝐿 in case of a loss (similar to the concept of consumption utility from above). Combined with reference-dependent preferences the probability of tipping a high percentage is given by:
𝑔 = { 𝑔
𝑊+ 𝛼(𝑊 − 𝑝𝑊) 𝑔𝐿+ 𝛽(𝑊 − 𝑝𝑊)
if W = 1 (positive surprise since W − pW> 0)
if W = 0 (negative surprise since W − pW< 0) (4)
Again, the parameters 𝛼, 𝛽 > 0 and 0 < 𝑝𝑊 < 1. Loss aversion would imply 𝛽 > 𝛼. Substituting the game outcome into equation (4) results in the probability of tipping a high percentage 𝑔 as a function of the pre-game expected probability of winning (𝑝𝑊):
𝑔 = { 𝑔 𝑊+ 𝛼(1 − 𝑝𝑊) 𝑔𝐿+ 𝛽(0 − 𝑝𝑊) = 𝑔𝑊+ 𝛼 − 𝛼𝑝𝑊 = 𝑔𝐿− 𝛽𝑝𝑊 if W = 1 if W = 0 (5)
Irrespective of the game outcome, the probability of tipping a high percentage decreases as the pre-game expectation increases. In the absence of reference-dependent preferences, 𝑔 = 𝑔𝑊 after a win and 𝑔 = 𝑔𝐿 after a loss.
3.3 Hypotheses
Coates, Humphreys and Zou (2014) find that the consumption utility of watching your sports team win is higher than that of a loss. If there is a link between the consumption utility of a game outcome and tipping, this would imply 𝑔𝑊> 𝑔𝐿. Ge (2018), on the other hand, finds no evidence that people who attended a sports game tip their taxi driver differently based on whether the game was won or lost (𝑔𝑊= 𝑔𝐿). A link between the consumption utility and tipping percentage is therefore not established11. I therefore formulate the following hypothesis:
Hypothesis 1: The consumption utility derived from a game outcome does not affect tipping behaviour, meaning that (𝑔𝑊= 𝑔𝐿).
11 Note that this does not imply that the consumption utility derived from witnessing your team win or lose (𝑈𝑊
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Even though the game outcome itself may not affect the tipping percentage, it is possible that gain-loss utility will. This is confirmed by the finding of Ge (2018) that people tip more after witnessing a game with an unexpected close win. In line with what the theory of reference-dependent preferences would predict, I test the following hypothesis:
Hypothesis 2: The positive gain-loss utility derived from an unexpected win leads to an increase in tipping percentage (𝛼 > 0). This effect increases as 𝑝𝑊 becomes smaller.
Reference-dependent preferences would predict that the absolute effect of an unexpected loss is larger than that of an unexpected win (𝛽 > 𝛼), and that the effect it is negative. While unexpected losses may in fact generate negative gain-loss utility, it may not necessarily manifest itself in lower tipping percentages. This may be due to strong social norms with respect to tipping (Azar, 2007) or default tip options (Haggag and Paci, 2014), which may both mitigate the effect of loss aversion. In line with the above, Ge (2018) does not find evidence for loss aversion in taxi tipping and I thus hypothesize the following:
Hypothesis 3: The negative gain-loss utility derived from an unexpected loss has no effect on tipping percentage (𝛽 = 0).
Lastly, I expect that unlike unexpected wins, expected wins and expected losses will have no effect on tipping behaviour. It is not a deviation from the reference point and therefore does not generate gain-loss utility in addition to the consumption utility.
Hypothesis 4: Expected wins and expected losses do not generate gain-loss utility and therefore do not affect tipping percentage.
The implication of these hypotheses for equation (5) are summarised in Figure 1 below12. The maximum probability of tipping a high percentage is given by 𝑔𝑊+ 𝛼. This is attained when the team was fully expected to lose (𝑝𝑊 = 0) but the team wins (𝑊 = 1). Given that the team has won, the probability of tipping a high percentage decreases as the win was more expected before the game. The slope of the 𝑊 = 1 line is given by 𝛼. The 𝑊 = 0 line represents the probability of tipping high when the team has lost. Hypothesis 3 implies that this line is flat, and that it is not influenced by the
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game expectations. In addition, Hypothesis 1 implies that the probability of tipping a high percentage is equal at 𝑝𝑊 = 1, such that 𝑔𝑊= 𝑔𝐿.
Figure 1: Probability of tipping a high percentage, depending on the game outcome and expectations.
4. Data
I first introduce the main dataset used that contains all taxi rides in Chicago. I then use this dataset to motivate why the Chicago White Sox are suitable for my research purpose. I then give a brief overview of the game data, betting odds data and weather information used for the main analysis. By combining these datasets, I conclude this section with visual evidence for the tipping percentage around the end of a game.
4.1 Taxi data
I obtain detailed information of each taxi ride taken in Chicago from 2013 onwards from a dataset made publicly available by The Department of Business Affairs and Consumer Protection (BACP) from the City of Chicago. The period included in my analysis is up until July 31, 2019, which amounts to 184,273,427 rides in total. The dataset contains trip-level data for each ride, including an anonymised trip and driver identifier, start and end time rounded to the nearest 15 minutes, the pick-up and drop-off census tracts, duration in seconds, distance in miles, fare, tip amount, tolls, extra costs and the payment type.
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used different default tip suggestions prior to 2012. However, since 2012 both payment systems use the same default tip options (Donkor, 2019), and not including this variable in my analysis is therefore not likely to bias the results13. The fact that the Chicago dataset does not allow me to include the amount of passengers is a slight limitation14.
The BACP has undertaken several steps to get rid of infeasible data before publication of the dataset15. My main sample consists of all rides that started or ended at the White Sox stadium and I follow similar steps as Haggag and Paci (2014) and Ge (2018) to further tailor the data to my needs. Appendix A shows a detailed description of which data is removed. The largest sample reductions are from the removal of zero trip distance (11.39%) and the removal of rides paid in cash16 (52.94%). This leads to a total of 17,801 rides that started or ended at the White Sox stadium in the period January 2013 up until July 2019. The summary statistics shown below in Table 1 differ slightly from those presented by Haggag and Paci (2014) and Ge (2018), which are based on data from New York City17. They are, however, similar to those presented by Chen et al. (2018) who use the same Chicago dataset for their study on the operational efficiency of individual taxis18.
Table 1: Summary statistics of all taxi rides near the White Sox stadium, January 2013 – July 2019
Variable Mean S.D. Min Max
Fare 16.529 6.561 3.25 132.75 Toll amount 0.000 0.013 0 1.5 Extra costs 1.03 1.834 0 54 Tip amount 3.444 1.926 0 40 Total fare 21.138 8.827 5.25 204.99 Tip percentage 19.873 8.407 0 214.477
Ride duration (minutes) 16.245 7.849 0.383 106.517
Ride distance (miles) 5.078 3.291 0.040 57
Observations 17,801
13 The payment systems used in Chicago taxis are the same as in New York City (Source: personal communication
with the BACP department of Chicago, November 21, 2019). Not surprisingly, Ge (2018) shows that passengers do not tip differently based on the payment system used after 2012.
14 Deveraj and Patel (2017) find that each additional passenger increases tip percentage by 0.04 percentage
points. Ge (2018) finds a negative effect of each additional passenger of -0.1 percentage points. Even though statistically significant, both effects are small.
15 Rides with a negative fare, duration or distance were removed. In addition the BACP removed fares above
$10,000, durations longer than 24 hours and distances of more than 3,500 miles.
16 Cash tips are not included in the data because they are not administered by the payment systems and are not
manually entered by drivers.
17 Notable differences are that the average distance travelled is more than two times as high in my sample. In
addition, ride duration is about 30% longer. The tip percentage, however, is almost identical.
18 Chen et al. (2018), however, do not drop trips paid in cash and only show summary statistics for ride duration
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4.2 Motivation for the Chicago White Sox
Using the taxi dataset described above, I now describe in more detail why the White Sox are suitable for this research purpose. Despite the richness of the taxi dataset of Chicago, it does not contain information about the passenger itself. It does, however, include the pick-up and drop-off location aggregated by census tract for each ride. Figure 2 below shows the census tracts around Guaranteed Rate Field, the stadium of the White Sox. The blue census tracts show the area surrounding the White Sox stadium. Of the 17,801 taxi rides that started or ended in this area, more than 97% took place on a day with a home game of the White Sox and 3% was on a day without a home game19. The fact that rides solely seem to take place on days with a home game provides some evidence that the passengers are passengers with sports sentiment20.
Figure 2: Identifying passengers with sports sentiment.
Figure 3 below provides further visual evidence that the rides that ended or started in this area are taken by people who attended a White Sox game. The blue line in Figure 3shows the distribution of taxi rides throughout the day for the stadium area. I compare this to a control group consisting of rides that started or ended in the city centre21. The pattern of this control group is the same as the city in general and therefore form a good comparison to the stadium rides. The blue line in the left panel
19 For Chicago as a whole, just 22% of taxi rides took place on a day with a home game.
20 Including each of the nine census tracts surrounding the blue area shown in Figure 2 only increases the amount
of rides by 8%. In addition, there is no clear increase of rides in this surrounding area on days with a home game.
21 The control group (red line) in Figure 3 is based on a 1,735,773 sample of all the rides. In section 5 I further
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of Figure 3 shows the taxi drop-offs near the stadium around the start of a game of the White Sox22. As one would expect, the peak of taxi drop-offs is 15 minutes before the start of a game. The blue line in the right panel of figure 3 shows a similar trend around the end of a game. Pick-ups and drop-offs barely occur outside of a two-hour interval around the start and end of a game23.
The increase around the start of a game coincides with a general peak of rides in Chicago around afternoon rush hour, as can be seen from the red line in the left panel of figure 3. The fact that all taxi drop-offs in the stadium area occur in a range of 2 hours around the game start, while this is not the case in the rest of Chicago, provides further evidence that I have identified passengers with sports sentiment. The same holds for pick-ups around the end of a game, with the addition that the peak around the end of a game does not coincide with a general trend in Chicago. I focus mainly on the rides that departed from the White Sox stadium 0-60 minutes after a game. This captures the peak of rides after a game, and in this small time window right after a game the feelings of sports sentiment are expected to be most prevalent.
Figure 3: Trip frequency per 15 minutes around the start (left panel) and end of a game (right panel).
4.3 Game data
I have obtained detailed data for each home game of the Chicago White Sox from baseball-reference.com matching the period covered by the taxi dataset. This includes 540 games in the period from the 2013 season up until half way the 2019 season24. The dataset includes the date, start and end time25, opponent, score and attendance for each game. I drop two games that contain incomplete data
22 Note that games do not always start or end at the same time.
23 Figure 3 only shows rides that occurred up to six hours before or six hours after the start or end of a game. The
trend of no rides occurring is the same when this 12-hour range is extended.
24 The first game played in the sample is on April 1, 2013 and the last game is played on July 31, 2019.
25 I manually obtained game start times from the official MLB game schedule and combined this with the game
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and sixteen games that are a matchup of the Chicago White Sox and the Chicago Cubs26. The descriptive statistics for the 522 home games in the period April 2013 up until July 2019 are shown in Table 2. The White Sox approximately won the same amount of games as they lost. In addition, the average score difference after each game is small (-0.611) but has a large standard deviation (4.225). This implies that the games are not easy to predict and deviations from pre-game expectations seem likely. Table 2 shows that games start and end at different times throughout the sample period. As tipping percentage tends to fluctuate during the day, it is important to control for the pick-up and drop-off hour (see appendix B for a graphical representation of tipping percentage per hour of the day).
Table 2: Descriptive statistics of home games of the Chicago White Sox, January 2013 – July 2019 Number of games Fraction of subcategory Game outcome Win 250 0.479 Loss 272 0.521
Game start time
1.10 p.m. 163 0.312
3.10 p.m. 14 0.027
6.10 p.m. 49 0.094
7.10 p.m. 277 0.531
Other 19 0.036
Mean S.D. Min Max
Game length (minutes) 185.856 27.717 91 317
Game end time 8.04 p.m. 167 minutes 2.41 p.m. 12.27 a.m.
Score difference (White Sox minus visitor score)
-0.611 4.225 -16 12
Attendance 20860 6122 10069 39142
Observations 522
4.4 Betting odds data
Pawlowksi et al. (2017) show that betting odds can serve as a proxy for the subjective beliefs of fans about the closeness of a game. As a pre-game reference point for the game outcome, I use betting
26 Not being able to distinguish between home and away fans is a limitation of the data. An unexpected win for
15
data derived from sports betting information site sportsinsights.com27 and convert this into a win probability for the Chicago White Sox. I focus on “money line” betting, which is a simple wager on which team will win the game. An example is the game on April 23, 2015 of the Chicago White Sox versus the Kansas City Royals, where the Chicago White Sox had a money line of -150 and the Kansas City Royals had a money line of +138. This means that one has to bet $150 on the Chicago White Sox in order to win $100. Alternatively, one can bet $100 on the Kansas City Royals and receive a payout of $138. The team with the minus sign is therefore the favourite, and the other team is the underdog. The size of the money line essentially depicts how likely the market thinks that a team is going to win. I obtain the money lines of both teams at the start of the game, and in appendix C I show in more detail how I convert this into pre-game probabilities of winning.
From the above example, I derive that the White Sox had a pre-game win probability of 58.8%. This implies that the White Sox are more likely to win than to lose, but it is questionable whether it is sufficiently high to state that the White Sox are expected to win. For example, when the White Sox have an expected chance of winning of 50.1% this could be classified as an expected win but also as a game that is expected to be close, because it is more like a fifty-fifty chance of winning. It is important to distinguish between the two, because losing a game when the pre-game expected chance of winning was 80% may feel much more like a loss than if it was 50.1%.
Both Card and Dahl (2011) and Ge (2018) account for this by using data on the point spread28 instead of money line betting data. The point spread contains information about whether a game is expected to be close or not. In baseball betting, however, the point spread is always set to the same value (1.5) and therefore does not contain information about whether a game will be close or not. Instead of using the point spread, I will resort to findings of Card and Dahl (2011) and Ge (2018) about how the point spread relates to a win percentage.
Card and Dahl (2011) use NFL point spread data to divide game types in different categories, based on pre-game expectations. By combining the win probability implied by money lines with the point spread, they classify matches with a pre-game win chance of 37% or less as an expected loss, and 63% or more as an expected win. While Ge (2018) does not explicitly state this relation, I approximate that for his sample a win chance of 43% or less is an expected loss, and 61% or more an expected win (see Appendix D for more details). In line with the above, but admittedly somewhat arbitrary, I define
27 For my analysis, I use the average odds of six major sportsbooks: BetUS, GTBets, 5Dimes, Bookmaker, SIA and
SpBK.
28 The point spread is a bet on the expected point difference between the two teams at the end of a game. A
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an expected loss as having a win chance of 40% or less, an expected close game between 40% and 60%, and an expected win as more than 60% pre-game win probability29.
I distinguish between three pre-game expectations: predicted loss, predicted close, predicted win. By interacting each pre-game expectation with a game outcome (win or loss), I end up with six categories: expect a loss and win, expect a loss and lose, expect a close game and win, expect a close game and lose, expect a win and lose, expect a win and win. Table 3 below shows summary statistics for the game categories of the Chicago White Sox for 522 home games in the period April 2013 up until July 2019. A limitation of the data is that relatively few games30 are classified as an unexpected win (expected loss and win) and as an unexpected loss (expected win and lose). For Hypotheses 2 and 3 as discussed in section 3.3, these two game types are of main interest because they deviate the most from a reference point. When Comparing Table 2 to Table 3, it can be seen that the mean expected probability of winning is 0.484 which is very close to the 0.479 share of games that was actually won (see table 2). This provides some evidence that on average, betting odds data are an efficient predictor of actual game outcomes. Figure 4 below, however, shows that many game outcomes deviate from pre-game expectations and are therefore likely to generate gain-loss utility (see section 3).
In the analysis that follows, I focus on the following four game types: predicted wins that were won (expected win), predicted wins that were lost (unexpected loss), predicted losses that were lost (expected loss) and predicted losses that were won (unexpected wins). I therefore exclude the category of predicted close games. The reason for this is that the category of predicted close games is broadly defined and contains 74% of all games31. The other categories are therefore more likely to be defined too strict, which should only magnify the result.
4.5 Weather data
From the National Oceanic and Atmospheric Administration (NOAA), I obtain historical weather data measured at the Chicago O’Hare International airport. Unlike Deveraj and Patel (2017) who make use of daily weather data, I use hourly precipitation and temperature data for more precision. Table 4 shows the summary statistics for the period January 2013 up until July 2019.
29 In section 6.4 I conduct robustness checks for this threshold and show that the results remain similar. 30 Not that the number of games is not the same as the number of taxi rides per game type.
31 As a comparison, in the analysis of Card and Dahl (2011) 44% of games are classified as close games and for Ge
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Table 3: Amount of games per game type for White Sox home games, April 2013 – July 2019 Pre-game probability of winning Number of
games
Percentage of subcategory 𝑝𝑊 ≤ 40% (predicted loss) 87
Expected loss and win 34 0.391
Expected loss and lose 53 0.609
40% < 𝑝𝑊 < 60% (predicted close) 387
Expected close and win 185 0.478
Expected close and lose 202 0.522
𝑝𝑊≥ 60% (predicted win) 48
Expected win and win 31 0.646
Expected win and lose 17 0.354
Mean S.D. Min Max
Pre-game win probability Sox 0.484 0.086 0.240 0.723
Observations 522
Figure 4: Graphical representation of the six game categories as defined in section 4.4.
Table 4: Summary statistics of weather data from Chicago, January 2013 – July 2019
Variable Mean S.D. Min Max
Hourly temperature (Fahrenheit) 50.417 21.216 -23 97
Hourly precipitation (inches) 0.003 0.024 0 1.34
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4.6 Combining the data: visual evidence
In Figure 5 below, I plot the tipping percentage for the four game types of interest: an unexpected win, an unexpected loss, an expected win and an expected loss. To the left of the red vertical line I show the tipping percentage 0-60 minutes before the start of the game. The right side shows the tipping percentage 0-60 minutes after the end of the game. An important assumption of using a control group as a comparison is that in the absence of treatment, the treatment group and control group are very similar32. The control group has a tipping percentage that is roughly 3% higher than the treatment group. However, before the game and thus before the treatment of a game took place, the lines seem to be parallel.
The top left panel of Figure 5 shows that after an unexpected win, the tipping percentage seems to be increasing for rides that start at the stadium. While the control group displays a flat trend, the tipping percentage did increase slightly after the game compared to before the game. When assuming that the rides departing from the stadium would have a similar trend in the absence of treatment, the effect of an unexpected win is not clear a priori. The top right panel shows that the effect of an unexpected loss seems to be slightly negative when taking the increase of the control group into account. Similarly, the effect of an expected win and an expected loss seem to be slightly negative. In the next section, I outline how I will test this empirically.
Figure 5:Tipping percentage per game type before and after the game, comparing the treatment of having a game (blue) to the control group (red).
32 In appendix E I show descriptive statistics of taxi ride data for both the treatment and control group, and show
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5. Methodology
I first outline the difference-in-difference framework used to measure the causal effect of a game outcome when excluding a reference point. I then discuss the OLS estimation I will use to identify whether positive surprises have more influence on tipping as the magnitude of the surprise increases. I conclude the section with a difference-in-difference method to estimate the effect of unexpected game outcomes on the tipping percentage.
5.1 The effect of a game outcome without using a reference point
I resort to a difference-in-difference framework to test the first hypothesis that the consumption utility derived from a game outcome does not affect the tipping percentage. As a control group, I use rides that took place in the city centre of Chicago, because about 80% of rides in the White Sox stadium area start or end there. Taxi trips that leave the White Sox stadium 0-60 minutes after the game are compared to all other trips that end at the city centre at the same time33. I therefore have two groups that have to make a decision about how much to tip the driver at the same time and at the same location34. The treatment group consists of White Sox fans who just witnessed a game outcome in the stadium while the control group did not. I compare this to rides that arrived at the stadium 0-60 minutes before the game start, and all other trips that departed from the city centre at the same time. The interested reader can find a map further clarifying the treatment and control groups35 in Appendix F. As stated in section 4.6, Appendix E shows that the descriptive statistics of both groups are very similar.
I estimate the causal effect of a game outcome on the tipping percentage with the following difference-in-difference equation using OLS:
𝑌𝑖𝑠𝑡 = 𝛽0+ 𝛽1· 𝑆𝑜𝑥𝑠+ 𝛽2· 𝐴𝑓𝑡𝑒𝑟𝑡+ 𝛽3· 𝑆𝑜𝑥𝑠· 𝐴𝑓𝑡𝑒𝑟𝑡+ 𝑿𝑖𝑠𝑡· 𝜅 + 𝜀𝑖𝑠𝑡 (6)
Where 𝑌𝑖𝑠𝑡 is the tip percentage for taxi ride 𝑖 in group 𝑠 at time 𝑡. The dummy variable 𝑆𝑜𝑥𝑠 equals 1 if the ride ends or originates at the White Sox stadium, and 0 for rides in the city centre. 𝐴𝑓𝑡𝑒𝑟𝑡 is equal to 1 for rides 0-60 minutes after the end of a White Sox game, and 0 for rides 0-60 minutes before the start of a game. 𝑿𝑖𝑠𝑡 is a set of control variables including ride distance and duration, dummies for
33 The average duration of a ride from the White Sox stadium to the city centre is about 15 minutes. A taxi that
leaves the stadium at 20.00 is expected to arrive at 20.15 and is therefore compared to all other rides that arrive at the city centre at 20.15. Pick-ups at the stadium 0-60 minutes after the game are therefore compared to drop-offs in the city centre 15-75 minutes after a game.
34 I also use this control group for the few rides that start at the stadium but do not end at the city centre. 35 An assumption I make here is that the taxi rides before the game are taken by the same individuals as those
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year, month, day of the week, pick-up hour and drop-off hour, dummies for the pick-up and drop-off census tract and hourly temperature and precipitation36. I estimate the model using robust standard errors and cluster by game day to account for serial correlation between rides on the same day (Bertrand, Duflo and Mullainathan, 2004).
I estimate equation (6) four times to determine the causal effect on tipping percentage of the White Sox having a game, winning a game, losing a game, and comparing the effect of winning a game to losing a game. In each estimation, I restrict the sample to the relevant game outcomes. To determine the effect of a win compared to a loss, I limit my sample to all rides at the stadium and define the treatment variable 𝑆𝑜𝑥𝑠 as equal to 1 for a win and equal to 0 for a loss. In each scenario, the coefficient of interest is 𝛽̂3 which determines the causal effect of the game outcome on tipping behvaiour. When comparing the effect of a win to a loss, 𝛽̂3 estimates the difference between the two which allows for the testing of the hypothesis that 𝑔𝑊= 𝑔𝐿.
5.2 The effect of game outcomes when incorporating a reference point 5.2.1 The effect of surprising game outcomes: preliminary evidence using OLS
As discussed in section 3.1, the gain-loss utility is given by 𝜇(𝑊 − 𝑝𝑊) where 𝑊 − 𝑝𝑊 is the deviation from the reference point. Hypotheses 2 and 3 would predict that for positive deviations from the reference point tips will increase (𝜇 = α > 0) and for negative deviations from the reference point tips are not affected (𝜇 = 𝛽 = 0). I first use a simple OLS regression to estimate whether the magnitude of the positive or negative deviation from the reference point correlates with the tipping percentage right after a game.
Similar to Ge (2018), I denote the deviation from the reference point as 𝛳 = 𝑊 − 𝑝𝑊 where ϴ > 0 for positive surprises and ϴ < 0 for negative surprises. I estimate the effect of surprises on tipping percentage using the following equation:
𝑌𝑖𝑡 = 𝛽0+ 𝑓(𝑊𝑡, 𝛳𝑡, 𝛾 ) + 𝑿𝑖𝑡· 𝜅 + 𝜀𝑖𝑡 (7)
where 𝑌𝑖𝑡 is the tipping percentage of taxi ride 𝑖 at time 𝑡 and 𝑿𝑖𝑡 is the same set of control variables as in equation (6). The surprise factor is denoted by 𝑓(𝑊𝑡, 𝛳𝑡, 𝛾), which I specify as follows:
𝑓(𝑊𝑡, 𝛳𝑡, 𝛾) = 𝛾1· 𝛳𝑡· 𝑊𝑡+ 𝛾2· 𝛳𝑡· (1 − 𝑊𝑡) + 𝛾3· 𝑊𝑡 (8)
21
The effect of positive surprises is captured by 𝛾1, and 𝛾̂1> 0 would mean that as the size of the positive surprise increases, tipping percentage increases as well. This would provide some evidence for hypothesis 2 stating that positive gain-loss utility increases tipping (α > 0). Conversely, 𝛾2 is the effect of negative deviations from the reference point. Hypothesis 3 would predict that 𝛾̂2 = 0, due to the absence of loss aversion in this context (meaning that β = 0 in the gain-loss utility framework)37. While I will formally test Hypothesis 1 using the difference-in-difference estimation from equation (6), 𝛾̂3 also provides information about the difference in tipping percentage between a win and a loss. While 𝛾1 and 𝛾2 capture the correlation of gain-loss utility with tipping percentage, 𝛾3 measures the consumption utility effect on tipping38. Hypothesis 1 implies that 𝑔𝑊= 𝑔𝐿 , predicting 𝛾̂
3 = 0. 5.2.2 Proving causality: a difference-in-difference approach
In order to establish a causal effect of game outcomes when incorporating a reference point, I use a similar difference-in-difference framework as equation (6) discussed in section 5.1. The treatment group again consists of drop-offs at the stadium 0-60 minutes before the game start and pick-ups 0-60 minutes after the game has ended. The control group contains all pick-ups in the city centre 15-75 minutes before the start of the game and drop-offs 15-75 minutes after the end of the game. I interact the two pre-game reference points (expect a win or a loss) with a game outcome (win or loss), leading to four game categories as outlined in section 4.4. I then estimate equation (6) using OLS for expected wins, unexpected wins, expected losses and unexpected losses (see section 4.4). The coefficient of interest is 𝛽̂3, which determines the causal effect of the expected or unexpected game outcome on tipping percentage. Hypothesis 2 would predict that 𝛽̂3> 0 for an unexpected win and Hypothesis 3 and 4 predict 𝛽̂3 = 0 for an unexpected loss, an expected loss and an expected win.
6. Results
I first use a difference-in-difference framework to show that there is no difference in tipping behaviour between a win and a loss. I then show using OLS that positive surprises correlate with a higher tipping percentage while negative surprises seem to have no effect. I end this section with the result that an expected loss is the only game type that has a significant effect on tipping percentage.
37 Note that in the occurrence of loss aversion it is expected that 𝛾
2 > 0. The surprise factor 𝛳𝑡 is negative and if
𝛾2 > 0 this decreases tipping percentage.
38 The difference in tipping percentage between a win and a loss is equal to 𝐸[𝑌|𝑊 = 1] − 𝐸[𝑌|𝑊 = 0]. As Ge
(2018) shows, equation (8) can be rewritten as 𝑓(𝑊𝑡, 𝑝𝑡𝑊, 𝛾) = 𝛾1· (𝑊𝑡− 𝑝𝑡𝑊) · 𝑊𝑡+ 𝛾2· (𝑊𝑡− 𝑝𝑡𝑊)𝑡· (1 −
𝑊𝑡) + 𝛾3· 𝑊𝑡. The difference in tipping percentage between a win and a loss is 𝐸[𝑌|𝑊 = 1] − 𝐸[𝑌|𝑊 = 0] =
[𝛾1· (1 − 𝑝𝑡𝑊) + 𝛾3] − [𝛾2· (−𝑝𝑡𝑊) ]. This is only influenced by gain-loss utility (𝛾1 and 𝛾2) if 𝛾3 = 0, meaning that
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6.1 The effect of a game outcome
In Table 5 below, I estimate the causal effect on tipping percentage of having a game, a win and a loss. These results are shown together in column (1) – (3). The treatment group consists of drop-offs near the stadium 0-60 minutes before the start of the game and pick-ups 0-60 minutes after the game has ended. The control group consists of pick-ups in the city centre 15-75 minutes before the start of the game and drop-offs 15-75 minutes after the end of the game. For the results of column (4) I use only observations from the stadium area and define the treatment group as wins and the control group as losses. In each estimation, I include control variables for ride distance and duration, date, time, pick-up area, drop-off area, hourly temperature and hourly precipitation39.
Column (1) shows that attending a game of the White Sox decreases tipping percentage by 0.932 percentage points (p = 0.001) when controlling for date, time, pick-up and drop-off census tract and weather. This corresponds to a decrease of 5% in the tip amount, leading to a reduction in the average tip of 16 cents. Using these same control variables, the White Sox winning a game decreases tipping percentage by 0.736 percentage points (p = 0.053) and losing causes a decrease of 1.041 percentage points (p = 0.017). Column (4) shows that the effect on tipping percentage of a win and a loss do not differ from each other. I can therefore not reject the first hypothesis that 𝑔𝑊= 𝑔𝐿. These findings provide evidence that the consumption utility of witnessing a win or a loss does not affect the tipping percentage.
Throughout all estimates of Table 5, the sign and magnitude of the treatment variable is as expected. For columns (1) – (3) this essentially is the baseline difference in mean tipping percentage between the treatment and control group before the treatment occurred, and is expected to be about -3.0 percentage points40. The variable After is positive in all estimations, though not always statistically significant. This shows the effect of the passage of time in the absence of treatment41. The sign and magnitude of ride distance and duration is negative as is expected. This is in line with previous findings (see for example Deveraj and Patel (2017); Ge (2018)).
6.2 The relation between surprises and tipping
Next, I incorporate a reference point to explore whether gain-loss utility derived from unexpected game outcomes correlates with tipping behaviour. I derive the pre-game probability of winning 𝑝𝑊
39 The sign, magnitude and level of significance of the difference-in-difference estimator does not change
substantially when gradually adding the control variables. To preserve space I therefore only show the result when all control variables are included.
40 This is also visible in Figure 5 and can also be deduced from the descriptive statistics for the treatment and
control group as shown in appendix E.
23
Notes: The dependent variable is tipping percentage. The sample contains rides for the treatment and control
group before the game start and after the game has ended. The treatment group consists of drop-offs near the stadium 0-60 minutes before the game and pick-ups 0-60 minutes after the game. The control group consists of pick-ups from the city centre 15-75 minutes before the game and drop-offs at the city centre 15-75 minutes after the game. After is a dummy that is equal to 1 after the game and 0 before. The treatment variable (Game, Win,
Loss or Win versus loss) is equal to 1 for the treatment group and 0 for the control group. The main variable of
interest is Treatment*After (for example, Game*After), which shows the causal effect of a game outcome. Date and time dummies include dummies for year, month, day of the week, pick-up hour and drop-off hour. Area dummies are included for the pick-up and drop-off census tract. Weather controls include hourly temperature and precipitation. Robust standard errors clustered at game-day level are shown in parentheses. P-values for P<0.1, P<0.05 and P<0.01 are denoted by *, ** and *** respectively.
a The win versus loss estimate includes only rides from the stadium area.
from betting data and use this as a reference point. The variable 𝑊 is 1 for a win and 0 for a loss, and the surprise factor 𝛳 = 𝑊 − 𝑝𝑊 captures the gain-loss utility associated with the game outcome. The
surprise factor can therefore be either positive (after wins) or negative (after losses) such that Table 5: Difference-in-difference estimates of the effect of game outcomes on tipping percentage
Dependent variable: Tipping percentage
(1) (2) (3) (4)a After 0.592** (0.272) 0.871* (0.463) 0.507 (0.357) 0.660 (0.661) Game -2.960*** (0.183) After*Game -0.932*** (0.290) Win -3.094*** (0.260) After*Win -0.736* (0.378) Loss -2.854*** (0.254) After*Loss -1.041** (0.434)
Win versus loss 0.103
(0.251)
(Win versus loss)*After 0.305
(0.340)
Ride distance (miles) -0.208***
(0.018) -0.188*** (0.026) -0.227*** (0.024) -0.152*** (0.043)
Ride duration (minutes) -0.275***
(0.009) -0.286*** (0.014) -0.267*** (0.012) 0.005 (0.016) Constant 29.887*** (1.077) 31.918*** (1.655) 28.721*** (1.127) 24.290*** (1.868) Observations 47,655 22,625 25,030 8,273 R2 0.104 0.104 0.111 0.044
Date and time dummies Yes Yes Yes Yes
Area dummies Yes Yes Yes Yes
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𝛳 ∈ [-1, 1]. Hypothesis 2 would predict that as the size of the positive surprise increases, the tipping percentage increases as well (𝛳 · 𝑊 > 0). Hypothesis 3, on the other hand, states that increases in the magnitude of negative surprises will have no effect42 (𝛳 · (1 − 𝑊) = 0). Below, I use an OLS estimation to establish how positive and negative surprises correlate with tipping percentage, while controlling for the game outcome. I limit my sample to taxi pick-ups from the White Sox stadium 0-60 minutes after the game has ended. I use the same control variables as in the difference-in-difference estimation in section 6.1 above, which I gradually add in columns (1) – (5) of Table 6 below.
Notes: The dependent variable is tipping percentage. The sample consists of all rides that departed from the
White Sox stadium 0-60 minutes after a home game has ended. 𝛳 · 𝑊 represents all positive devations from the reference point, and 𝛳 · (1 − 𝑊) captures negative surprises. The dummy variable 𝑊represents the game outcome, where 𝑊 = 1 is a win and 𝑊 = 0 is a loss. Date and time dummies include dummies for year, month, day of the week, pick-up hour and drop-off hour. Destination dummies include dummies for each drop-off census tract. Weather controls include hourly measures for temperature and precipitation. Robust standard errors clustered at game-day level are shown in parentheses. P-values for P<0.1, P<0.05 and P<0.01 are denoted by *, ** and *** respectively.
The results from Table 6 provide some evidence that increases in the magnitude of positive surprises correlate with a higher tipping percentage while negative surprises do not43. From adding date and time dummies onward in columns (3) – (5), the coefficient for positive surprises 𝛳 · 𝑊 is positive and marginally significant (p = 0.089). Negative surprises 𝛳 · (1 − 𝑊) do not correlate with tipping (p =
42 Note that loss aversion would imply 𝛳 · (1 − 𝑊) > 0, since 𝛳 < 0 and 𝑊 = 0 after negative surprises.
43 Similar to the difference-in-difference results from section 6.1, the controls for ride distance and duration have
the expected sign and magnitude.
Table 6: OLS estimates of the effect of positive and negative surprises on tipping percentage Dependent variable: Tipping percentage
(1) (2) (3) (4) (5) ϴ · W (positive surprise) 2.744 (2.086) 2.619 (1.994) 3.904* (2.022) 3.494* (2.098) 3.615* (2.118) ϴ · (1 − W) (negative surprise) -0.053 (1.753) 0.131 (1.756) 1.868 (1.943) 1.835 (2.018) 2.043 (2.003) W -1.125 (1.340) -1.120 (1.301) -2.612* (1.488) -2.273 (1.528) -2.413 (1.532)
Ride distance in miles -0.114**
(0.045) -1.333*** (0.047) -0.097* (0.053) -0.096* (0.053)
Ride duration in minutes -0.063***
(0.020) -0.039* (0.023) 0.003 (0.027) 0.001 (0.027) Constant 19.358*** (0.804) 21.052*** (0.886) 33.351*** (2.517) 29.825*** (3.151) 29.940*** (3.172) Observations 4,307 4,307 4,307 4,307 4,307 R2 0.001 0.011 0.029 0.074 0.074
Date and time dummies No No Yes Yes Yes
Destination dummies No No No Yes Yes
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0.308) in any of the estimation results above. This is expected in the absence of loss averse behaviour as predicted by Hypothesis 3. However, the actual effect of a positive surprise should be interpreted together with the coefficient of 𝑊, since a positive surprise always occurs after a win. The coefficient of 𝑊 (-2.413) is close to being significantly different from zero (p = 0.116). If I would interpret it as if it were marginally significant, given that there is a win tips are 2.413 percentage points lower. This
increases by 0.362 percentage points for each 0.1 increase in the positive surprise, 𝛳 · 𝑊. Positive surprises larger than about 0.666 would therefore positively correlate with tipping
percentage44.
These results provide some minor evidence for Hypotheses 2 and 3, which state that positive gain-loss utility affects tipping while negative gain-loss utility does not. However, it seems that positive surprises that are small, only make the effect on tipping less negative. Since these OLS estimates do not allow me to establish a causal inference I resort to a difference-in-difference estimation below.
6.3 The causal effect of expected and unexpected game outcomes
I will now estimate the causal effect of gain-loss utility from game outcomes on tipping behaviour. The surprise factor used in the estimates of Table 6 is positive for all wins and negative for all lost games, essentially dividing the game outcomes in only two categories. In order to bring more nuance into this, I divide all game outcomes into one of four categories as motivated in section 4.4: an expected win, an unexpected win, an expected loss, and an unexpected loss. Consequently, instead of having one category for positive surprises, I now divide this into a large positive surprise (unexpected win) and a small positive surprise (expected win). The same holds for negative surprises. The treatment group and control group are identical to the difference-in-difference framework of section 6.1 and I use the same controls as the analyses of section 6.1 and 6.2 above. The variable of interest is the interaction between the After and Treatment variable of each game type, which shows the causal effect on the tipping percentage.
The main finding of Table 7 below is that the taxi tipping percentage is not influenced by game outcomes that deviate from expectations. In addition, the effect of an expected win is not significantly different from zero. This does not change when less control variables are added. The effect of an expected loss is not statistically different from zero when all control variables are added. When not controlling for weather, however, expected losses lead to a 1.549 percentage points decrease in tipping percentage (p = 0.083)45. This corresponds to a decrease of 20 cents in the average tip, which
44 This is the equivalence of expecting that the White Sox have less than 34% chance of winning, but they in fact
win.
45 The results for expected losses specifically are shown in Appendix G, where I show the effect of adding extra
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is a decrease of 6%. I therefore reject Hypothesis 4 stating that expected losses have no effect on tipping behaviour.
The effect of an unexpected win is not significantly different from zero (p = 0.834). I therefore reject Hypothesis 2 stating that α > 0, since I do not find evidence that positive gain-loss utility increases the tipping percentage. Similarly, unexpected losses do not affect the tipping percentage either as the coefficient of (Unexpected loss)*After is not significantly different from zero (p = 0.796). This is in line with Hypothesis 3 that predicts that negative gain-loss utility does not affect tipping behaviour (β = 0) due to strong social norms. Moreover, in line with Hypothesis 4 I find that expected wins do not affect tipping behaviour. Even though these results seem to confirm Hypothesis 3 for unexpected losses and Hypothesis 4 for expected wins, they only provide evidence for reference-dependent preferences if Hypothesis 2 (α > 0) holds. Since this is not the case, Hypothesis 3 and 4 are meaningless since the results ofTable 7 simply imply that taxi tipping is not affected at all by game outcomes relative to a reference point.
The OLS estimate in section 6.2 provided minor evidence that unexpected wins could increase tipping behaviour, because larger positive surprises correlate with a larger tipping percentage. The difference-in-difference results are not in line with this finding. A reason for this could be that the surprises of the unexpected wins are not large enough to exert a positive influence on the tipping percentage46.
6.4 Robustness checks
I conduct several robustness checks for the main results from section 6.3 that can be found in Appendix H. First, I change the pre-game win chance threshold for a game that is predicted to be lost from less than 40% to less than 45%. I do the same for predicted wins and change the threshold from 60% to 55%. This leads to the same results as discussed in section 6.3. The only game type that is significantly different from zero is again an expected loss, with a similar magnitude as before. An expected loss leads to a decrease of 1.532 percentage points in the tip percentage following a White Sox game.
I present another robustness check in Appendix H with respect to the timing of the win probability used for determining the game categories. I use betting data from one hour after the game has started to test whether updated beliefs form a better reference point than pre-game beliefs. Card and Dahl (2011), for example, find that fans react to emotional cues based on their expectations at the start of the game and do not update their beliefs at half time. I also find no evidence that fans update
46 Indeed, the majority of unexpected wins do not meet the requirement of having a pre-game win probability
