Peer Pressure in a Seniority
Environment
Master Thesis
by
Andoni Fornio Barusman
Student number
: 10827757
Specialization
: Managerial Economics & Strategy
Supervisor
: Jeroen van de Ven
Calender year
: 2016-2017
Number of credits : 15 ECTS
Statement of Originality
This document is written by Student Andoni Fornio Barusman who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
This research analyzed the existence of peer pressure due to the presence of a senior in the punishment context of the public good game. Using a controlled experiment on a semi-military high school students, this study found that juniors’ decision to punish was not only influenced by how much someone contributed to the public good, but also by the presence of a senior who could observe their decisions. The feeling of respect towards the senior peer is expected to be the main driver of this type of peer pressure. As a result, the juniors were motivated to impress the senior by being more assertive in giving punishment relative to the situation when only another junior who was observing their decisions.
Table of Contents
1. Introduction………... 5 2. Related Literature………... 8 3. Methodology………...12 3.1. The school………. 12 3.2. Experimental Design………... 12 3.2.1. Public Good Game……… 12 3.2.2. Payoffs………. 15 3.2.3. Treatments……… 15 3.2.4. Description of Main Variables……… 16 3.2.5. Data Collection……….17 3.2.6. Scenario and Experimental Settings……….. 18 3.3. Hypothesis………. 20 4. Results………..21 4.1. Descriptive Statistics: Contribution Level………..21 4.2. Descriptive Statistics: Punishment Level………25 4.3. Hypothesis Test……….……….... 26 4.3.1. Statistical Test……… 26 4.3.2. Regression Analysis………... 30 5. Discussion………... 35 6. Conclusion……….... 40 7. References……….... 41 8. Appendix………... 43
1. Introduction
In a society, social influence has an important role in determining people’s behavior and action. One way this social influence could happen is simply due to the presence of a peer that might influence a person’s attitude. This phenomenon is commonly known as peer pressure. Many studies have been conducted to analyze the existence of this phenomenon. Mas & Moretti (2009) analyzed the peer pressure among the checkers in the grocery chain. They found that an introduction of a new worker into a shift increased the productivity of the incumbent worker. Falk & Ichino (2006) also found that people who worked in pairs tend to have similar productivity relative to when they worked alone. There are several factors that make people conform to peer pressure. Fear of being isolated and inadequate (Lashbrook, 2001) as well as guilty and shame (Kandel & Lazear, 1992) for not working hard might be some reasons why people respond to peer pressure. In addition, the feeling of respect towards peer could be another factor that generates peer pressure. We can think of a situation where the peer pressure might occur as a result of the feeling of respect towards another peer. For example, in a school with a military system, law enforcement is one of the major concerns that need to be emphasized in order to protect the norms that are applied in this society. A senior is often given an authority that allows her to punish those who violate the law. By having this authority, it also makes other students, especially the juniors, to respect her. We can think of a particular condition when this kind of authority is given to a junior. There might be a case when the junior is less willing to use her authority, especially towards her own friends. In some cases, the junior’s attitude towards using her authority might be affected by the presence of a senior near her. It could be the case that due to the feeling of respect towards the senior, the junior is motivated to impress the senior by using her authority properly. One way is by being more assertive in punishing those who violate the law. In another situation, this kind of motivation might be less likely to occur in the case of the presence of another junior. This might happen due to the feeling of respect towards another junior is not as much as the feeling that the punisher has towards the senior. These different types
influenced by the presence of a senior worker who has much more experience. Therefore, it is important to analyze whether the intensity of the peer pressure might be different when a junior is assigned near a senior peer (seniority condition) compared to when a junior is assigned near another junior peer (non-seniority condition). This leads me to the research question of this study:
“How could the peer pressure due to the presence of a senior peer affect the behavior of a junior in making a decision? Is there any difference in the intensity of the peer pressure between the seniority condition and the non-seniority condition in influencing the junior’s decision?”
Many previous studies analyzed how the peer pressure could influence people’s effort. In this study, instead of examining through the effort level, I would like to observe on how different types of peer pressure (i.e., seniority and non-seniority) could differently affect the junior’s behavior towards decision-making. In particular, this study tries to analyze how the presence of a senior peer could influence the junior differently when compared to the presence of another fellow junior peer in terms of giving punishment. It could be the case that if the junior respects the senior more than she respects another fellow junior, it motivates the junior to impress the senior by being more assertive in giving punishment. Therefore, higher punishment under the seniority condition could be expected.
To address the research question, this study used a lab experiment that was conducted on students in a semi-military school in Indonesia. In the experiment, students were asked to play a public good game. There were three roles in the experiment: player, punisher, and inspector. The main focus of this study is on the punishment stage, where the study deeply analyzes how a junior punisher’s decision to punish the player given the player’s contribution might be affected by the presence of a senior inspector who could observe her and how the punishment decision might be different from the case when the junior punisher was being observed by another fellow junior inspector. The reason to use the punishment context via the public good game in this study is due to the channel through which the seniority peer pressure might exist in a more general context. In the real working environment, the motivation of a junior worker to impress her senior peer
should not come through a monetary factor that could benefit the senior. In reality, the more experience someone has, the less sensitive she is towards monetary incentive. Therefore, a senior worker might be less sensitive towards monetary incentives relative to a junior worker. Due to this wealth effect, the motivation of the junior to impress the senior should come from a non-monetary element, such as the feeling of respect that is predicted in this study. This mechanism could be captured in public good game, where the junior punisher can have an incentive to impress the senior inspector by being strict in giving punishment without having any consequence on the monetary payoff of the senior.
There are several main findings in this study. First, it is found that the lower the contribution level given by the player, the higher the punishment given by the punisher both under the seniority condition and under the non-seniority condition. This finding supports the claim by Fehr & Gachter (2000) that people’s decision to punish is emotionally driven, which means that the more someone shows a free-riding behavior, the more people want to punish the free-rider even though punishment is costly. Second, it is also found that in overall, the punishment was higher under the seniority condition compared to the non-seniority condition. Therefore, it supports the hypothesis of this study that the presence of senior influences the junior punisher to be more assertive in giving punishment. Furthermore, the punishment in both the seniority condition and the non-seniority condition was increasing throughout the rounds, with a higher increase in the seniority condition. Also, it is found that the punishment under the seniority condition is less sensitive towards the change in the contribution level relative to the punishment under the non-seniority condition.
This study has the following structure. Some related literature about the peer pressure would be discussed in section 2. Then, the methodology of this study would be explained in section 3. In this section, the experimental design and the hypotheses of the study would be elaborated. Furthermore, the results of the experiment would be discussed in section 4. Next, some discussion regarding the potential statistical problems that might exist in the results, the external validity, and the limitation of the study would be addressed in section 5. Finally, the
2. Related Literature
There have been many studies that examine peer pressure, with a variety of channels through which it occurs. However, to my knowledge, there is no study that specifically analyzes the peer pressure in the case of the presence of a senior peer. Mas & Moretti (2009) studied how the productivity of a worker varied as a function of the productivity of co-workers in a group production process. In particular, they analyzed the evidence of peer pressure among the checkers in a grocery chain. Since the checkers worked in a shift, it allowed the authors to examine whether introducing a new worker into a shift would increase the productivity of the incumbent worker. They found that the productivity of the incumbent worker increased as a result of the presence of co-workers that could see her, but there was no significant change in productivity of the incumbent worker by the presence of co-workers that could not see her. Mas & Moretti (2009) concluded that the motivation behind this was due to social pressure, where the workers could have a disutility for working less hard than the others when the other workers noticed.
Veldhuizen, Oosterbeek, and Sonnemans (2014) tried to clarify the evidence that was found by Mas & Moretti (2009) into the lab. They tried to capture similar work settings using a computerized experiment. Studying this research in a lab experiment allowed them to control some elements, such as communication, the position of the workers, and the possibility to measure worker’s ability independently. In contrast to Mas & Moretti’s finding, they did not find any significant evidence of peer pressure. This indicates that Mas & Moretti (2009)’s findings are less generalizable.
Falk & Ichino (2006) did a controlled field experiment, where they tested the evidence of peer pressure using a real task. The study was conducted on high school students, where they were given a short-term four-hour job to stuff letters into envelopes. In the main treatment, i.e. pair treatment, two participants did the task at the same time and in the same room, where the environment was designed in such a way that subject was aware of the output of her pair. In the control treatment, i.e. single treatment, participant worked in isolation. They found that peer pressure could lead to similar working behavior among workers. Also, they found that the
average output was higher in the pair treatment than in the single treatment. This implies that peer pressure increased the productivity of the workers.
Sacerdote (2001) also found that the presence of peers could lead to an increase and similarity in performance and decision. He measured the peer pressure among freshman college roommates. Using an observational data, he found that roommates’ average freshman GPA increased one’s own freshman GPA. He also found that roommates had influence on the decision to join social groups such as fraternities.
Bandiera et al. (2009) also studied how the peer pressure can lead to a convergence in productivity according to whether social ties exist between the subjects. They found support for conformism theory. In particular, they found that compared to the situation under no social ties, a worker’s productivity increased when she worked alongside friends who were more able than her. However, a worker experienced a decrease in productivity when she worked alongside friends who were less able than her. They argued that the support for conformism theory was driven by the workers’ desire to socialize with their friends.
Mittone & Ploner (2011) studied whether the peer pressure could influence people to show more reciprocity behavior. Using an investment game in a laboratory experiment, they found that subjects were influenced by others’ decisions to reciprocate more, but only when the others’ involvement actually influence the outcome.
Studies by Mas & Moretti (2009) and Falk & Ichino (2006) only focused on the presence of peer pressure under the fixed wage incentive scheme. Bellemare et al. (2010) studied whether the intensity of peer-pressure on productivity varies among genders and different incentive schemes. They used an experiment with a task of inputting data on a computer. The peer pressure in the experiment came from the private information about the productivity of another worker in the past experimental session. They found that women were less responsive to peer-pressure than men. Furthermore, they also found a non-linear relationship between the productivity of men and the level of peer pressure they face. Men significantly reduced their productivity after knowing that another participant performance in
was very high. This result suggests that peer pressure in some cases could lead to decrease in productivity.
Mas & Moretti (2009) observed the peer pressure that came from the channel through which people change their working behavior as a consequence of being observed by the other. On the other hand, Bellemare et al. (2010) analyzed the peer pressure that came from the act of observing the performance of others. Georganas et al. (2015) tried to disentangle these two different channels in which peer pressure could influence productivity. Using experimental analysis, they found that peer pressure increased the productivity of the observed subjects. Furthermore, they also witnessed a non-linear effect of peer pressure on the observer’s productivity. However, in contrast to Bellemare et al. (2010), they found that the observer increased their effort when observing both high and low productivity.
Some of the studies that have been mentioned above mostly focused on the evidence of peer pressure that happened when people did a regular task. In this paper, I would like to study whether there is a difference in the intensity of peer pressure when a junior is assigned near a senior peer compared to when a junior is assigned near a same-level peer when making decision. Considering the motivation of the junior to impress her senior peer should not come from monetary factor, using a regular task with some compensation scheme in this study might not be relevant. As an alternative, this study will use a public good game.
Falk et al. (2003) also used a public good setting in order to study whether social interactions between peers could influence their behavior. The focus of their study was on the contribution stage, where they found that participants’ contributions were subject to their respective group-mates’ decisions. In particular, participants tended to give higher contribution in a group with higher average contribution and tend to give a lower contribution in a group with lower average contribution.
Unlike Falk et al. (2003), which analyzed the peer pressure from the contribution stage, the core analysis of my study came from the punishment stage. To my knowledge, there has been no study that analyzes how the peer pressure could influence people’s decision to punish. In the public good game in my experiment, the junior punisher should decide the amount of punishment that she
would give based on the contribution level of the other participants. Then, a custom element was added, where an inspector, who could be either a senior (main treatment) or a junior (control treatment), could observe the junior punisher’s decision. From this setup, any difference in the punishment intensity between the two different treatments could be explained as an indication of a different level of peer pressure between the seniority condition and the non-seniority condition.
The peer pressure in my experiment came from the situation where the junior punisher was being observed by his or her paired-inspector. This kind of channel is similar to what was found in the study by Mas & Moretti (2009). Also, this experiment allows me to test the claim by Mittone & Ploner (2011) of whether the presence of a peer who has no similar involvement in decision-making problem does not influence one’s decision. In particular, this study will clarify whether the presence of a senior inspector who did not face any decision-making problem would influence the junior’s punishment decision. Moreover, while Bellemare et al. (2010) studied the difference in peer pressure under fixed wage and piece rate scheme, this study could also analyze whether peer pressure could influence a costly decision. In my experiment, for every unit of punishment that the punisher imposes will decrease her monetary payoff. So, there might be a trade-off between keeping the maximum amount of payoff by punishing less and trying to impress the senior by punishing more.
3. Methodology
This study analyzes how the peer pressure can influence someone’s decision differently through the presence of a senior peer. There are many factors that can affect people’s behavior in making a decision, such as the social environment where people live, friendships, educational background, personal characteristics, and age. In order to control for those variables, this study used a lab experiment. 3.1 The School The study was conducted on high school students in Cikarang, Indonesia. It is called President Senior High School. One thing that is unique about this school is that it is a semi-military boarding school where a seniority system exists. It means that besides a regular study, the school provides an environment where the students live together in a dormitory and they are tough disciplinary values. There are some laws that the students must obey both in the school and in the dormitory where they live. Furthermore, students should respect those who are at a higher level. Senior students are given an authority to punish the juniors who violate the law. By capturing the seniority element from this school, it can suit the study of whether a junior will make a decision differently when there is a senior near her.
3.2. Experimental Design
3.2.1. Public Good Game
This experiment used a public good game with a similar basic setting that was conducted by Fehr & Gachter (2000). The participants played the game for five rounds. There were two stages in every game.
At the first stage, there were three groups; each consisted of four players that were randomly assigned at the beginning of the experiment. Participants were anonymous, which means that they would never know in which group they belonged to as well as the group members that they were playing with. Also, the composition of the group remained the same in every round. Each player was given initial endowments of 20 points and each player had to decide how many points from the initial endowment that she wants to contribute to the public good. Then, the sum of the contributed points from all players in a group would be multiplied by 0.4. This would be the benefit that every player in a group gets from the public good.
On top of the groups for the game, there was also a customized element in this experiment, where six pairs of outsiders were formed. Each pair of outsiders consisted of two participants. One participant was assigned as the punisher and another participant was assigned as the inspector. At the second stage, each pair of outsiders analyzed the contribution outcome of all the players from a particular group of the public good game. It means that for every group of the game, there were two pairs of outsiders that analyzed the outcome. Then, the punisher had to decide how much punishment that she would give to each player in the group. The punisher could impose between 0 and 10 punishment points to each player. For each punishment point that was given to the player would reduce the player’s payoff by ten percentage points. Also, each punisher was given initial endowments of 30 points and for every punishment point that the punisher gave to the player would reduce the punisher’s payoff by 0.25 point. It means that there was a cost for every unit of punishment that the punisher gave. After the punisher had made the punishment decision, her paired-inspector who was sitting next to her could analyze the decision. After that, the experimenters collected the punishment decisions and the round ended.
In the following rounds after the first round, the players were given a private information about the punishment that they got from the previous round before making contribution decision in the present round. Important to note that due to every group of the game was assigned to two pairs of outsiders, only the punishment decision from one pair of outsiders that would be applicable to the players. This was determined by the experimenters privately without the knowledge of the participants at the beginning of the experiment and would remain the same throughout the five rounds.
Recalling from the public good game setup that was done by Fehr & Gachter (2000), the main difference with this study is at the punishment stage. In Fehr & Gachter (2000), the players both made the contribution and punishment decision. On the other hand, the experiment in this study separated those two roles. Also, this experiment introduced the inspector role as the main element to study the peer pressure.
The timing of the game per round: • Stage 1:
o Players decide between 0 and 20 points from their initial endowment as a contribution to the public good and write it on contribution form (see Appendix 1) that is provided.
After stage 1, the experimenters collected the decision from the players and summarized the outcomes based on the groups on the summary of contribution form (see Appendix 2). Also, the average contribution of a group was indicated in the form. Then, the punishment forms were distributed to each pair of outsiders that corresponds to the group.
• Stage 2:
o Punishers analyze the contributions of all players from a particular group that are given in the summary of contribution form and decide how much to punish each player based on the given contribution. o After writing the punishment decisions, the punishers distribute the
form to their paired inspectors
o Experimenters collect the form from the inspectors
Each inspector was not asked explicitly to analyze the punishment decision of the paired punisher. But, by distributing the punishment form from the punisher to the inspector, it allowed the inspector to see the contribution outcomes and the punishment decisions. As a result, there was a high possibility that each punisher was aware that her punishment decisions were being observed by the inspector. Therefore, the peer pressure might occur in this setting. Figure 1. Sequence of the game per round Players decides how much to contribute to public good Punishers analyze the contribution outcomes and decide how much to punish each player Punishers distribute the decisions form to paired inspectors Experimenters collect the decisions form from the inspectors
3.2.2. Payoffs • Player’s payoff (per round) o 𝑈! = 20 − 𝑦! + !!!,…,!0.4∗ 𝑦! (stage 1) o 1 − % 𝑜𝑓 𝑝𝑢𝑛𝑖𝑠ℎ𝑚𝑒𝑛𝑡 ∗ 𝑈! (after stage 2) , where 𝑈! is the payoff of player i 𝑦! is the number of contribution point given by player i • Punisher’s payoff (per round) o 𝜋! = 30 − 0.25 ∗ 𝑛𝑜. 𝑜𝑓 𝑝𝑢𝑛𝑖𝑠ℎ𝑚𝑒𝑛𝑡 𝑝𝑜𝑖𝑛𝑡𝑠 , where 𝜋! is the payoff of punisher i • Inspector’s payoff from the experiment o A fixed participation fee of IDR 50,000.- (approximately €3.50) For every punishment point that is imposed by the punisher corresponds to 10 percentage points of payoff reduction to the player. Also, for the players and the punishers, only the payoff from one of the five rounds which would be selected for payment. A conversion rate of 1 point = IDR 2,000.- (approximately € 0.14) was used.
3.2.3. Treatments
Since the focus of this study is at the second stage of the game, two treatments were introduced for the pairs of outsiders. They are the senior treatment and the junior treatment. In the senior treatment (main treatment), the pair of outsiders consists of a junior punisher and a senior inspector. In this senior treatment, the peer pressure due to the presence of senior peer might occur. In the junior treatment (control treatment), a junior punisher will be assigned with a junior inspector.
Figure 2. Treatments on pair of outsiders
All participants share some common characteristics. All of them live in the dormitory with the same environment and they share common friendships. The participants’ age is also range between 15 to 17 years old. The senior participants are from the 11th grade, while the junior participants are from 10th grade. They also have the same educational background. Also, each participant was randomly assigned to a certain role. The only intervention the experimenter did was on the assignment of inspector’s role, where the experimenter assigned an equal number of juniors and seniors in this particular role. By having this similarity in characteristics and randomization of roles, it allowed the study to have more control of other variables that might affect the participant’s decision. This would minimize any possible statistical bias and help to give a more precise result. Therefore, the only difference between the main treatment and the control treatment should only come from the subject who played the role of the inspector, which could be either a senior or a junior. Also, the pairs of outsiders remained the same throughout the experiment. It means that a between subject study was used.
3.2.4. Description of Main Variables
There is one dependent variable in this study, which is punishment. It is defined as how many percentage reductions of payoff that the punisher would like to impose on a player as a form of punishment. This variable has a range between 0 and 100 percent and can only be a multiple of 10 percentage points.
There are also two main independent variables that were obtained from the experiment. The first independent variable is contribution, which indicates how many points that each player contributes in every round. This variable can be any integer in a range between 0 and 20. The second independent variable is senior,
Senior Treatment Junior
Punisher Inspector Senior
Junior Treatment Junior
which is a dummy variable that explains whether the sample is assigned to the senior treatment (if 1) or to a junior treatment (if 0). This variable explains whether the peer effects due to the presence of senior inspector exists. 3.2.5. Data Collection In total, there were 96 participants in this study; which were divided into 48 players (who played the first stage of the public good game) and 24 pairs of outsiders (which consisted of 24 junior-punishers, 12 senior-inspectors, and 12 junior-inspectors). The pairs of outsiders were divided equally into the senior treatments and the junior treatments. Also, all of the participants were distributed equally into four experiments, which were held sequentially in the span of three days.
Each participant played the game for five rounds. In every round, there were 48 contribution decisions that were made by all players. Furthermore, each punisher gave punishment decisions to 4 players of the same group in every round. Thus, given a total number of 24 punishers, there were 96 punishment decisions given by all punishers in every round. The figure 3 below shows the data collection per round of a single experiment more clearly.
Note: There were 12 contribution decisions made by the players per round in a single experiment. Also, there were 24 punishment decisions made by the punishers from the pair of outsiders per round in a single experiment. Therefore, in a total of four experiments, there were 48 contribution decisions and 96 punishment decisions in each round.
Figure 3. Data collection process per round in a single experiment
3.2.6. Scenario and Experimental Settings
Scenario
The public good game might be relatively complicated, especially for the people who do not have an economics or game theory background. Since this study was conducted on high school students, in which none of the students had ever played a public good game before, it is very important for the participants to fully understand the game in order to avoid bias results. Therefore, a scenario is included in the instructions of the experiment.
The participants were told that they are part of a society. The players of the game were illustrated as a citizen who lived in a district, in which every district consists of four citizens. The central government has promised to provide a public Stage 2 Stage 1 3 groups 4 players contribution 4 decisions
Outsiders 1 4 punishment decisions Outsiders 2 4 punishment decisions
4 players contribution 4 decisions
Outsiders 3 4 punishment decisions Outsiders 4 4 punishment decisions
4 players contribution 4 decisions
Outsiders 5 4 punishment decisions Outsiders 6 4 punishment decisions
transportation in every district, but the benefit of the facility depends on the contribution of each citizen in a district in the forms of cleanliness and maintenance costs. Also, the role of punisher was illustrated as a police and the role of inspector was expressed as it is. Moreover, the participants were given information about the payoff scheme of each role (for the complete instruction form, see Appendix 3).
There are some advantages and disadvantages of having a less abstract scenario in the experiment. One of the advantages might be to provide the participants a better exposure and understanding about the experiment. The scenario that was given is also related to the real life provision of a public good. This scenario would help the participants to give more reasonable decisions according to their roles. On the other hand, having a less abstract scenario might also affect the participants’ actions and generalizability of the results. For instance, participants might have different perceptions after reading the scenario. This might affect their behavior and the decisions that they made. Also, a less generalizable result might occur. However, the nature of the public good game is also not fully abstract and still allows for the people to have a different perception of the game. Therefore, by considering the trade-offs between the benefits and the costs, it is more important to avoid having bias results by providing the scenario in the experiment.
Experimental Settings
The experiments were conducted in a classroom setting, in which each participant was provided with a personal table and chair. There were six rows, in which the first three rows were filled with the players of the game and the last three rows were filled with the punishers and inspectors. The table of the punisher and the inspector were combined, so that they sat next to and close to each other (for the maps of the class setup, see Appendix 4). Each experiment lasted for approximately 1.5 hour. At the beginning of the experiment, instructions were read aloud and subjects were given the opportunity to ask questions. The game started only when all participants fully understood what they should do. After the last experiment was conducted, all participants were gathered and were called one by one in isolation to receive the payment based on
3.3. Hypothesis Previous studies have used the public good game to analyze the existence of free riding behavior and how likely people punish those free riders in the context of the provision of public good. Focusing on the contribution of this study, I would like to analyze more on how the punishment decision is influenced by the presence of different type of peers. Based on the previous literature and to answer the research question of this study, the following hypotheses are formulated:
Contribution-Punishment Hypothesis: “The lower the contribution, the higher the punishment under the senior treatment”
Fehr and Gachter (2000) found the evidence that free riders were heavily punished even though punishment is costly and provides no benefit to the punisher. In particular, they found that the more negative deviations from the mean contribution were associated with higher punishment. This is expected to happen since the people’s motivation to punish is emotionally driven. Therefore, a negative relationship between the contribution and the punishment might also be found, especially under the senior treatment. Seniority Hypothesis: “The punishment under the senior treatment is higher than the punishment under the junior treatment” It is expected that due to the peer pressure from the presence of a senior, a junior punisher under the senior treatment will punish more than a junior punisher under the junior treatment. The reason behind this is related to the feeling of respect, which might motivate the junior to impress the senior by being more assertive in giving punishment to the free riders. By doing this, the junior might wish that the senior would perceive her as fair.
4. Results
In this section, the results of the experiment will be explained. First, the summary statistics of the main variables will be shown. Then, the statistical tests to test the hypotheses will be provided. Finally, regression analysis will be explained to test the robustness of the results and to provide additional findings. 4.1. Descriptive Statistics: Contribution Level Table 1 Summary Statistics of Contribution Level by Round Number of
observations Mean Median Deviation Standard Min Max Round 1 48 9.4 9.5 4.17 3 18 Round 2 48 9.65 10 4.35 1 18 Round 3 48 10.75 11 5.22 2 20 Round 4 48 12.33 14.5 5.46 0 20 Round 5 48 12.27 13 5.77 1 20 Overall 240 10.88 10.5 5.15 0 20 Note: In total, there were 48 participants who played as the player, in which consisted of 40 junior students and 8 senior students. The players were distributed evenly into four experiments. Each player made a single contribution decision in every round.
In table 1, the summary statistics of the contribution level made by the players is presented. It is shown that at the beginning, the average contribution level was 9.4 points. This is an indication that the players might be less selfish and that they were willing to contribute almost half of their endowments to the public good. Also, it can be seen from figure 4 below that the average contribution given by the players was increasing throughout the rounds. To test for the trend in contribution, linear regression can be used (see Appendix 5). By regressing the round variable (t) on contribution, the result shows a positive coefficient; meaning that there was an increasing trend of contribution throughout the rounds (p-value<0.001). This is in line with the findings by Fehr & Gachter (2000). Furthermore, it is also found that some players contributed their entire endowment since round 3. However, given the average contribution in the last round was only 12.27 point, full contribution level could not be reached in this study. Also, some extremely low contributions still existed until the round 5, indicating that extreme free riders were still found until
Figure 4 The average contribution per round. The vertical axis measures the average contribution points given by the players. The number in the horizontal axis indicates the round.
The histograms of the contribution decisions in each round are shown in figure 5 below. At the first round, the distribution was centered at low to moderate level, i.e., from 3 to 11 points. Also, none of the players contributed an extremely high amount. At the following rounds, the distribution slowly shifted towards a higher level. At round 4 and round 5, roughly 50 percent of the players contributed between 15 to 20 points. This implies that there was a tendency towards higher contribution as the players played more rounds. This implication is similar to what we found previously in terms of increase in average contribution over time.
Figure 5. The Histogram of the Contribution Level by Round Recalling that due to the random nature of the experiment, the distribution of the contribution decisions might be different between the treatments. From figure 6 below, the differences in average punishment between the treatments per round are shown.
Figure 6 The average contribution per treatment per round. The vertical axis measures the average contribution received by a particular treatment. The horizontal axis indicates the round.
It can be seen from the bar chart that small differences in average contribution existed between the senior treatment and the junior treatment in each round. In order to test whether there is a significant difference in contribution between treatments in each round, the two-sample Wilcoxon rank-sum test can be used. The reason to use this statistical test instead of the t-test is due to the sample distribution for the contribution level in each treatment might not fully satisfy the normality assumption (see Appendix 6 for the histogram of contribution based on treatment per round). The results of the test are shown in table 2. Table 2 Two-sample Wilcoxon rank-sum test of contributions between treatments Round p-value (Ha: Senior ≠ Junior) 1 0.4166 2 0.9296 3 0.8311 4 0.6536 5 0.8197
None of the tests show a significant difference in contribution between the treatments. Therefore, it can be said that the participants in both the senior treatment and the junior treatment received similar contribution decisions in all rounds. This similarity is important in order to test the seniority hypothesis using the statistical test that will be explained later.
4.2. Descriptive Statistics: Punishment Level
In table 3, the summary statistics of the punishment level is presented. Also, the average punishments based on treatment per round are shown in figure 6 below. Overall, the average punishment was relatively low and it never reached 50 percent average punishment level. It can be seen from figure 6 that the average punishment was increasing throughout the rounds under the senior treatment, while it seems more stable under the junior treatment. The test for significance of the punishment trends in both treatments will be provided later in the regression analysis part of the result section. Table 3 Summary Statistics of Punishment Level Obs Mean
(%) Median (%) Deviation Standard Min (%) Max (%)
Overall 24 32.44 33.5 13.11 11.5 68.5 Senior 12 38.46 35.75 11.36 27 68.5 Junior 12 26.42 23 12.30 11.5 44 Note: The data of each independent observation is calculated based on the average of the punishments that the punisher gave to the same player in 5 rounds as well as the average of the 4 punishment decisions that each punisher made simultaneously in every round. This was done to satisfy the assumption of independent observation, which is a necessary condition in conducting the statistical test. The numbers of the mean, median, min, and max are presented in percentage. It explains how much reduction (in percentage point) of the players’ payoff that the punishers impose as a form of punishment. The indicator senior and
junior in the table are associated with the senior treatment and the junior treatment,
respectively. There are 24 punishers in the experiment, in which they were equally distributed into the senior treatment and junior treatment.
Figure 6. The average punishment based on treatment per round. The vertical axis measures the average punishment (in percentage points). The number in the horizontal axis indicates the round.
4.3. Hypotheses Test
4.3.1. Statistical Test
Some hypotheses tests will be explained in order to answer the research question of this study. First, the contribution-punishment hypothesis will be tested to know whether a negative causal effect exists between the contribution level and the punishment, especially under the senior treatment. Then, it will be followed by testing the seniority hypothesis of whether the punishment under senior treatment is higher than the punishment under the junior treatment as a result of different peer pressure.
The Contribution-Punishment Hypothesis Test
We would start the analysis by testing whether there is a negative causal effect of the contribution level given by the player on the punishment imposed on them by the punisher in each treatment.
Figure 7. Scatter plots of punishment by contribution level based on treatment From the scatter plots that are shown in figure 7 above, it can be seen from a bird’s eye view that a negative relationship between the contribution level and the punishment existed in both treatments. Furthermore, the correlation tests in table 4 show that negative correlation between the contribution and punishment existed in both treatments and in overall. It means that the higher the contribution given by the player, the lower the punishment that the punisher would give, and vice versa. However, the conclusion of whether the contribution-punishment hypothesis is supported in this study cannot be drawn yet. A regression analysis is necessary to find out whether the relationship is significant. This test will be provided in the next
Table 4 Correlation Test between Punishment and Contribution Senior Treatment -0.4782 Junior Treatment -0.3026 Overall -0.3697 The Seniority Hypothesis Test A deeper analysis of whether the intensities of the punishment between the two treatments were different will be discussed. This is the main part of the study, where the existence of the peer pressure due to the presence of a senior peer will be answered through testing the seniority hypothesis. Figure 8 Average punishment based on treatment in overall rounds
Figure 8 shows the average punishment in both treatments, in which each treatment consisted of 12 independent observations. Due to each punisher made 4 decisions to the players in every round and a single decision to each player for five rounds, the average of those punishment decisions was taken in order to form a single independent observation. This was done to satisfy the independence of the samples, which is a necessary assumption to conduct a statistical test.
The t-test for group mean comparison shows that the average punishment is 12.04 percentage points higher under the senior treatment than under the junior
treatment and highly significant (one sided p-value=0.0104). However, as shown from figure 9, the distribution of the sample in both treatments is far from a bell-shaped curve. Also, the Shapiro-Wilk normality test was rejected for the senior treatment (p-value<0.05). It means that the samples might not normality distributed. Therefore, a t-test might not be valid due to the violation of the normality assumption. Figure 9 Histogram of punishment under the senior treatment & junior treatment
The Wilcoxon rank-sum test could be used to relax the normality assumption. It is found that the non-parametric test also rejects the null hypothesis that the punishments in both treatments are the same (p-value=0.0463, z-statistic= -1.993). Therefore, it can be said that the seniority hypothesis is supported in this study. One might argue that the punishment might be possibly higher under the
However, given the statistical tests that were presented in table 2 have shown the similarity in contribution decisions between the treatments, the reason why the punishment under the senior treatment was higher than under the junior treatment should not happen due to the differences in the distribution of contributions, but should solely happen due to the differences in the treatment itself. Therefore, testing the seniority hypothesis using the statistical test of differences between the two samples should be considered reliable.
4.3.2. Regression Analysis
In this part, the regression analysis will be presented. There are several reasons to conduct the regression analysis in addition to simple statistical test. The first reason is to avoid the problem of omitted variable. In the experiment, one external factor that might influence the punishment decision in addition to the contribution level of the player and the treatment effect was the time effect. In particular, the intensity of the punishment decision might change as the punisher played more rounds. As shown in figure 6, the average punishment varies throughout the round, especially under the senior treatment. The simple statistical test that was shown in the previous section did not explicitly control for the time effect. Therefore, regression analysis could be used to control for the trend in the punishment.
The second reason is to test the significance of the negative relationship in the contribution-punishment hypothesis. Also, regression analysis is necessary to have more robust results in testing the main hypotheses of this study by including the time effect that was mentioned previously.
The third reason to conduct the regression analysis is to have some additional findings regarding the seniority peer pressure. Specifically, two interaction terms will be added to see whether the differences in peer pressure between the senior treatment and junior treatment could also be explained by the changes in contribution level by the player as well as the number of rounds that the punishers have played. The two interaction terms are senior x contribution and senior x t.
Given that the experiment consisted of 5 rounds with 24 cross sectional units, it is better to have a regression that can control both the longitudinal aspect
and the cross sectional aspects of the data. One way is by using the panel data regression. However, this type of regression cannot be used in this study. The reason is due to the fixed-effect panel data regression was unable to estimate the coefficient of the treatment variable senior, which is a time-invariant dummy variable indicating the treatment (senior=1 if senior treatment, senior=0 if junior treatment). The random effect model also could not be used due to the Hausman test was rejected (p-value<0.01, see Appendix 7). Therefore, since the treatment variable is the core attention of this study, instead of using panel data regression, this study uses a cross sectional regression analysis with time variable to control for the time effects. It is important to note that some adjustments in the data sets were made in order to satisfy the condition of independent observation in the regression. From the experiment, there were 480 punishment decisions made by 24 punishers in 5 rounds. Each punisher made 4 different decisions in every round. Therefore, the average of the 4 simultaneous punishment decisions was taken in order to satisfy the assumption of an independent sample. By doing this, it shrank the samples into 120 observations, where all the samples became independent within the same round. However, the samples might still be considered serially correlated. Given that the panel data regression could not be used in this study, the inclusion of time variable that indicates the number of rounds would help increase the reliability of the cross-sectional model.
Table 5 Correlation Matrix of Included Variables
Pun. Cont. Senior t Senior x Cont. Senior x t Punishment 1.0000 Contribution -0.3697 1.0000 Senior 0.3659 0.0385 1.0000 t 0.1638 0.4798 0.0000 1.0000 Senior x Contribution 0.2246 0.3133 0.9392 0.0933 1.0000
From table 5, it is shown that the correlation between the two interaction terms (i.e., between senior x contribution and senior x t) as well as between the interaction term and the dummy variable senior are very high. If I add all of those variables in one model, there will be much noise in the estimation. Therefore, several variations of the model will be presented in order to avoid the problem of perfect multicollinearity. Also, the robust standard error was used to address the heteroskedasticity problem that existed in some of the models. The results of the regression analysis are shown in table 6, which consist of five models with different variations. Table 6 Determinants of the Percentage Punishment Imposed Dependent Variable: Percentage Punishment Model 1 2 3 4 5 Senior=1 Senior=0 Contribution -3.982*** -4.794*** -3.911*** -4.050*** -3.694*** (0.517) (0.580) (0.519) (0.609) (0.990) Senior 12.805*** (2.313) t 5.266*** 5.509*** 3.281** 6.309*** 4.011** (0.948) (0.955) (0.949) (1.289) (1.430) Senior x Contribution 1.147*** (0.195) Senior x t 3.851*** (0.624) Constant 53.560*** 61.766*** 59.365*** 63.980*** 54.217*** (5.427) (5.728) (5.671) (7.275) (9.469) N 120 120 120 60 60 R-square 0.439 0.437 0.438 0.467 0.198 Note: robust standard error in parentheses; *p<0.05, **p<0.01, ***p<0.001
Regression Analysis of Main Hypothesis: Contribution-Punishment Hypothesis
It is shown that the coefficient of the contribution in model 1 is negative and highly significant. It implies that on average, for every unit increase in contribution point, the punisher would decrease the punishment by 3.982 percentage points, ceteris paribus. Interpreting the result in another way, the lower the contribution level given by the player, the higher the punishment that the punisher would give. Similar results are also found when interaction terms are included in model 2 and model 3. Furthermore, when the samples are separated based on treatment, it is shown that similar results are also found both under the senior treatment (model 4) and under the junior treatment (model 5). Therefore, the regression analysis has completed the discussion of the contribution-punishment hypothesis and it can be concluded that the negative causal effect between the contribution level and the punishment is supported in this study (this causal interpretation would be discussed in the discussion part). As it is claimed by Fehr & Gachter (2000), this result implies that even though punishment is costly, people are willing to punish others as a form of emotional expression and they tend to give a higher punishment to those who show free riding behavior.
Regression Analysis of Main Hypothesis: Seniority Hypothesis
Model 1 tries to estimate the effect of the treatment on the level of punishment by also controlling for the contribution level and time effect. It is shown that the coefficient of the dummy variable senior, which indicates the sample’s treatment (senior=1 if senior treatment, senior=0 if junior treatment), is positive and highly significant. It implies that on average, the punishment under the senior treatment is 12.805 percentage points higher than the punishment under the junior treatment, ceteris paribus. Therefore, the seniority hypothesis is also supported by the regression analysis. It can be said that junior tends to give higher punishment as a result of the presence of senior near her.
Additional findings
additional round that the punisher played, the punishment increased by 5.266 percentage points, ceteris paribus. A similar result is found when the regression is run based on treatment. As given in model 4 and model 5, the positive coefficient of the time variable suggests that the level of punishment increased throughout the rounds, both under the senior treatment and under the junior treatment. As previously presented in figure 4 that the average contribution in the experiment showed an increasing trend throughout the rounds, the reason why punishers increased their punishment as they played more rounds is not due to an increasing number of free-rider, but might be due to the changes in the punisher’s expectation. The experiment was designed in a way that the players and the punishers interacted repeatedly throughout the rounds. It could be the case that the punishers were less strict at the beginning. Then, after they were playing several rounds, the punishers might expect that the players understood about how much the punishers expect the players to contribute by signaling through the punishment. The more rounds the participants have played, the higher the punishers’ expectation. Therefore, the punishers increased their punishment intensity in the following rounds.
The regression analysis also provides some additional results of the seniority peer pressure. Given that on average, the punishment increased as the punisher played more rounds, a deeper analysis of whether the increase is different between the treatments could be analyzed by looking at the variable senior x t, which indicates the interaction term between the treatment dummy variable and the time variable. It is shown in model 3 that the interaction term senior x t has a coefficient of 3.851 (p-value<0.001). It can be said that the increase in the punishment level as a result of playing additional round is 3.851 percentage points higher under the senior treatment than under the junior treatment.
Second, given that negative relationship exists between the contribution level and the punishment in both treatments, further analysis can be done of whether the intensity of this relationship is different between the senior treatment and the junior treatment. As shown in model 2, the coefficient of the interaction term senior x contribution is 1.147 and highly significant (p-value<0.001). This result implies that on average, for every unit increase in contribution level, there will be 1.147 percentage points less decrease in the punishment under the senior treatment relative to the decrease under the junior treatment. This means that the
presence of a senior might make the junior less willing to decrease her punishment in the case when the player gives a higher contribution.
In addition to the models that are presented in table 6, some other regressions using models that include both the dummy variable senior as well as the interaction terms of the dummy are also conducted (see Appendix 8). However, a serious multicollinearity problem between the dummy and the interaction terms are found in these models. This problem leads to a very high standard error of the dummy variable and makes the estimation to be less accurate. As a result, the coefficient of the main treatment dummy variable is not significant in these models, while the statistical test and the main regression analysis have actually supported the seniority hypothesis. As a response to this issue, I decided not to include the models in the main regression analysis.
5. Discussion
In this section, discussions of the results will be presented. In particular, some potential problems in the statistical analysis such as the test of OLS assumptions, reverse causality, measurement error, causal interpretation of main results, and external validity of the result will be discussed. Then, some limitations in this study will be analyzed. The OLS Assumptions There are four assumptions that need to be satisfied in order to use the OLS in multiple regression analysis according to Stock and Watson (2015, pp. 245-246). First, the conditional distribution of the error term given all the independent variables has a mean of zero. In other words, there should be no omitted variable. As shown in table 6, one control variable is included in the regression analysis, which is the time variable. Also, two interaction terms are included in the regression in order to provide more findings regarding the seniority peer pressure. On top of those variables that were mentioned, three possible omitted variables are the gender of the punisher, the gender of the inspector, and the group’s average contribution. I already tried to include additional dummy variable male_punisher and
independent variables that were actually included in the regression analysis. Also, as we can see from table 7 below, the correlation between these gender variables and the included independent variables are very low. Moreover, analyzing the effect based on gender differences might not be appropriate in this study, since the number of samples is too small. Therefore, excluding these two variables will not produce any problem of omitted variable bias. Another possible omitted variable is the group’s average contribution. This information was provided to the punisher on top of the information about the contribution of each player. However, due to the averaging of the data sets to satisfy the independent condition of the samples, including this variable would produce a perfect multicollinearity problem with the contribution variable. Therefore, this variable should not be included. Table 7 Correlation between the possible omitted variables and the included variables Included Variables Correlation Coefficient Male Punisher Male Inspector Punishment 0.3513 -0.0999 Contribution -0.1749 0.1052 Senior 0.2750 -0.2750 t -0.0000 -0.0000 Senior x Contribution 0.2183 -0.2069 Senior x t 0.2288 -0.2288
The second assumption is that the samples should be independently and identically distributed. As mentioned before, some adjustments of the data sets were made in order to satisfy the condition of independent sample. In particular, due to each punisher made 4 decisions at the same time in every round, the average of each 4 decisions was taken in order to form an independent sample. However, the samples might still be serially correlated. I decided not to take the average of the samples based on the round since one of my purposes in conducting the regression analysis in addition to the statistical test is to capture the time aspect of the data. Due to the panel data regression could not be used, I still assume that the samples that were used in the regression to be independent. Also, time variable was introduced in the regression in order to explain the time effects as well as to increase the reliability of the cross-sectional model. Moreover, each observation was drawn through an identical process. Therefore, the second assumption is satisfied.
Third, large outliers should be unlikely. From the data that I gathered, outliers are rarely found. Also, due to the value of contribution and the punishment were restricted to certain ranges, this problem could be minimized.
Fourth, there should be no perfect multicollinearity. From table 5, the correlation matrix of all included variables is presented. It is shown that the problem of perfect multicollinearity between the independent variables is not found. Therefore, the fourth assumption should be satisfied.
Another important assumption is the homoscedasticity. The problem of heteroscedasticity is found in most of the regression models, where the Breusch-Pagan test was rejected (e.g., Breusch-Breusch-Pagan test of model 1 shows prob > chi2 = 0.001). As a solution, all of the models in the regression analysis used the robust standard error to minimize the likelihood of false estimation of standard error.
Other Potential Problems in the Statistical Analysis
Some potential problems that might arise in the statistical analysis will be addressed. First, there might be a potential problem of reverse causality, especially between the contribution and the punishment. By referring to the design of the experiment, it already provided a control for the possible reverse causality problem. Specifically, the timing of the experiment was designed in a way that the punishment was given as a response to how much contribution that the player gave in each game and not the other way around. The punishment might affect the contribution decision for the following round since each player was given information about the punishment that was given to her in the previous round, but this is neither the main interest of the study nor a reverse causality problem that happen in the same round. Therefore, the reverse causality problem should not be found.
Next, a problem of measurement error cannot be totally eliminated in the experiment. Even though most of the participants (especially the punishers) gave decisions in a reasonable way, one punisher still gave punishment in an absurd way. For example, some punishers always gave the same punishment in all rounds, irrespective of the player’s contribution. However, this small number of error
Another potential problem is the unobserved heterogeneity in the samples. There is always a possibility of unobserved heterogeneity. However, as mentioned in the treatment part of section 3, I already tried to minimize this problem by having samples with some similarity among participants, such as educational background, living environment, friendship, and age. Also, there might be a problem of whether causal interpretation of seniority peer pressure on higher punishment decision is appropriate. This study used a randomized controlled experiment, where the treatment was assigned randomly to eliminate any possible systematic differences that might affect the dependent variable other than the treatment itself (Stock and Watson, 2015, pp. 52-53). As mentioned in the treatment part of section 3, each participant in the experiment was assigned to certain role randomly except for the inspector, in which we assigned an equal number of senior and junior to satisfy the treatment condition. By using the randomized controlled experiment, it facilitates the estimation of causal effects in this study.
Finally, the external validity of the results will be discussed. It is known that this study was conducted in a school with a semi-military system. The experiment also used a public good game, which specifically dealt with punishment context. The result, which shows that the presence of a senior peer leads to a higher punishment decision by a junior, might not always hold in general. There are three possible cases where the result could be applied in reality. First, it might depend on the culture and norm where the situation happens. In particular, this result might be more commonly found in a culture that highly values respect to someone older or in a situation that promotes seniority environment. Second, it might be more commonly happened to the people with relatively young age, since the interaction between older people with different ages might not influence the way people behave as much as the interaction between relatively young people with different ages. Third, the definition of a senior in samples can also be defined as someone with a higher position among students. The argument that the peer pressure due to the presence of senior exists due to the feeling of respect might be more relevant to happen in reality if the senior is defined as someone with a higher position in an organization, instead of someone who is simply older in age or has been working for a longer time.
Limitations of Study
There are several limitations of this study. First, the individual sample size of the experiment is relatively small. There were 96 participants, in which only 24 of them played the role of a punisher. Knowing that there were two treatments, it means that there were only 12 punishers in each treatment. Even though each punisher gave 20 punishment decisions from all rounds, there might be less diverse outcome due to lack of individuals who played the role. By having more punishers could have given more robust results. The reason for the lack of individual sample is because the school has relatively small number of students as well as a limited budget to conduct the experiment on a larger scale.
There are some possible heterogeneity in results regarding the seniority peer pressure that cannot be estimated in this study. First, it might be that the intensity of the seniority peer pressure varies according to the contribution level. It could be that the pressure is at the highest level when the contribution level is extremely low, and it might decline as the contribution increases. This kind of result could have been estimated in the regression by including both the treatment dummy variable and the interaction term between the dummy and contribution level. This model is actually presented in Appendix 8. However, due to the high multicollinearity problem, a large noise in the regression makes the results less reliable. Second, it might be that the intensity of the seniority peer pressure changes as the punishers played more rounds. This kind of result could have also been estimated by the model in Appendix 8. Another potential heterogeneity in the results is whether the intensity of the peer pressure differs based on gender. However, as previously mentioned, the lack of samples made the estimation unachievable in this study. Third, this study only has two treatments to test the existence of seniority peer pressure by comparing the difference between two kinds of peer pressure. In particular, this study only focuses on the comparison between the peer pressure that happened due to the presence of same-level peer and the peer pressure that happened due to the presence of a senior peer. It does not explicitly examine whether the presence of a senior could change one’s decision relative to when one makes the decision in isolation. A previous study by Falk & Ichino (2006) is one
