Monetary incentives for confessions

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Monetary Incentives For Confessions

Julia Claudia Mezals University of Amsterdam Graduate School of Economics

Master Thesis 15 ECTS

Student number: 11375329

MSc Business Economics - Managerial Economics and Strategy 12July2017

ABSTRACT: This paper experimentally investigates if it is possible to monetarily incentivize dishonest people to confess that they have lied. Furthermore, this study examines if the knowledge of a confession possibility influences participants’ lying behavior. Using an adapted version of Shalvi’s (2011) Die-Under-Cup game, subjects were brought into a situation where lying was easy and profitable for them. After reporting the outcome of their private die roll, participants were asked if they had been honest or if they wanted to confess that they had reported a wrong number. In line with standard economic theory, the highest confession rate was found in the Reward treatment, where subjects were offered an additional euro on top of their earnings for a confession, followed by the No Consequence treatment. No confessions were made in the Punishment treatment, where subjects had to face payoff cuts after confessing to dishonest behavior. Interestingly, the knowledge of a confession possibility had a miscellaneous impact on lying behavior, it increased the number of liars in the No Consequence treatment but decreased the number of liars significantly in the remaining two treatments.

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Statement of Originality

This document is written by student Julia C. Mezals 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

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I. INTRODUCTION

“No man would keep his hands off what was not his own when he could safely take what he liked out of the market, or go into houses and lie with anyone at his pleasure, or kill or release from prison whom he would, and in all respects be like a god among men.” — Plato, Republic, 360b–d.

As early as 360 BC, Plato suggests that it lays in human nature to behave dishonestlyand immoral and that often the only thing preventing people from doing thewrong are social norms and other people's judgment. In standard economics, it is assumed that people think rationally and weigh external costs and benefits of their actions. Croson et al. (2005) find that a significant number of people behave in line with theory and indeed lie when this increases their profit. Life presents us with an abundance of opportunities every day to stretch the truth and gain more respect, more status, or more money. A prevalent view among behavioral econ omists and psychologists is that everybody lies, at least every now and then, starting from a very young age (see Ayal and Gino, 2011; Mazar and Ariely, 2006). In a study by DePaulo and Kashy (1998), people report that they tell on average one or two lies per day.

Nowadays, where hierarchies in modern organizations are becoming flatter and more decentralized, lower level employees hold more responsibility than ever before. An increasing number of individuals is exposed to an internal “conflict between selfishly pursuing their own financial goals and being honest” (Mazar and Ariely, 2006). It is therefore important to investigate if people can be incentivized to admit to their wrongdoing once they have been dishonest. If this is possible, bigger harm may be prevented within organizations where decisions are made based on employee's private information. Mazar and Ariely (2006) claim that the only possibility to prevent dishonest behavior is to increase either the possibility of being caught or the magnitude of punishment. On the contrary, Ayal and Gino (2011) find that another effective way to diminish the likelihood of future dishonest behavior is a confession. After coming clean, people are more aware of the importance of honorable behavior and moral standards, at least temporarily.

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This paper contributes to the existing confession literature with a novel experiment that not only examines if it is possible to get dishonest people to make a confession, but it also tests if the knowledge of a confession possibility influences people's lying behavior.

In many companies, the CEOs suffer from an information overload and are therefore forced to delegate important tasks to their managers, who then further delegate work to lower level employees (Aghion and Tirole, 1997). It is easy to come up with examples where employees might have an incentive to conceal, falsify, or deviate from the truth. In her book “The Truth about Lies in the Workplace”, Goman (2013) lists exaggeration and omission as two of the most common workplace lies. While there is a growing literature t hat studies what circumstances make people more likely to lie (e.g. Gino and Ariely, 2012; Zhong et al., 2010; Serra-Garcia et al., 2013), the motivations for lying (e.g. Ayal and Gino, 2011), or how to prevent people from lying (e.g. Mazar and Ariely, 2006), there are very few studies that look at confessing behavior. Shalvi et al. (2014) as well as Peer et al. (2014) study the magnitude of lies and corresponding confessions. They find that 40% of the confessing subjects confessed only partially and not to the full extent of the lie. The authors also find that those partial confessions made people feel even worse than not confessing at all. Gudjonsson and Petursson (1991) interview convicted criminals in prison to study the reasons that cause offenders to confess during custodial interrogation. They identify three main factors: internal pressure, external pressure and proof. In a follow up study, Gudjonsson (1992) finds evidence that the suspects' perception of proof is the most important predictor for a confessi on.

Not only suspect behavior in police questioning has been broadly studied, there is also ample literature on confessions in Catholic church (e.g. Kettunen, 2002; Todd, 1985). However, there is no study that focusses on how different monetary incentives might affect and stimulate confessions.

In order to answer the question if monetary incentives are a mean to elicit confessions and how the knowledge of a confession possibility impacts lying behavior, a novel experiment was designed for this study, which is based on Shalvi’s (2011) Die-Under-Cup game. In this experiment, participants were asked to roll a die covered by a cup and report the outcome. The cup participants played with had a small hole i n the bottom part where subjects could look through to check the number on the die. It was transparently clear forsubjects that the die roll

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outcome was private information and unknown to the experimenter. Participants knew that the number they reported would determine their payoff in the experiment, which gave them an incentive to report a high number. Treatment variable in this experiment was a confession question that offered participants the opportunity to admit that they had lied about the outcome. What varied in the different treatments was the consequences for a confession. There was either a punishment fee, no consequence, or an additional reward for a confession. Contrary to previous papers that used the Die-Under-Cup game to examine dishonest behavior (Shalvi et al, 2011; Fischbacher and Heusi, 2008), this paper does not only compare the distributions of reported and expected die roll outcomes, but it also gives insight into the proportion of liars in each treatment with the help of an econometric technique developed by Garbarino et al. (2016).

Consistent with previous studies from Shalvi et al. (2014) and Peer et al. (2014), a positive number of participants confessed to dishonest behavior. In line with theory, the average confession rate is highest in the Reward treatment, positive in the No Consequence treatment, and zero in the Punishment treatment of this experiment. Most remarkably, in the Reward treatment, where participants were offered additional payment for a confession and it is rational to confess for both liars and truth-tellers, more than 100% of the estimated number of liars confessed. This is evidence for the existence of participants that act as a homo economicus. The number of liars decreased in the second round of the game in the Punishment treatment and the Reward treatment, but it increased significantly in the No Consequence treatment. At the same time, the proportion of confessions increased in the Reward treatment and the Punishment treatment, when subjects were informed about the confession possibility.

The remainder of the paper is organized as follows. Section 2 presents the experimental design and procedures, a behavioral analysis, and the main hypotheses. In section 3, an estimation of participants’ lying behavior is given and the confession rates in each treatment are analyzed. Section 4 discusses limitations of the experiment, and section 5 concludes.

II. METHODOLOGY

The following section describes the experimental design, procedures, and behavioral predictions according to standard and behavioral economics.

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2.1 Experimental Design and Treatments

Participants were invited to play two rounds of the Die-Under-Cup game (Shalvi et al., 2011; based on Fischbacher and Heusi, 2013) to bring them into a situation where it was profitable and easy to lie. Once participants reported their die roll outcome they were offered different monetary incentives for a confession.

In this experiment, subjects had to shake a die under a cup and report the number of the die roll outcome. A small hole was cut into the bottom part of the cup that let participants check the die roll outcome in private. Participants were told that the number they reported also determined their pay for participating in the experiment. Thus, reporting a one resulted in a €1 payment, rolling a two resulted in a €2 payment, and so forth. Unless participants were lucky and the number underneath the cup was actually a six, they found themselves in a conflicting situation. Subjects had to choose between maximizing their own payoff and being honest. After having written down a number on an answer sheet, participants were asked about their honesty and were given the possibility to confess to over-reporting the number they had rolled.

There were three different treatments constructed for this experiment, each divided into two steps. Treatment variable was a confession question after the die roll, which differed in the monetary incentive participants were offered for a confession. Table 1 gives an overview of the 2x3 treatment design:

Punishment

(after confession) No(after confession)  Consequence (after confession) Reward No (prior) Information about

confession possibility Treatment P_NoInfo NC_NoInfo Treatment R_NoInfo Treatment Information about

confession possibility Treatment P_Info Treatment NC_Info Treatment R_Info TABLE 1. Treatments - Overview

The Die-Under-Cup game that participants played in this experiment differed from the original game in two ways. Firstly, right after participants rolled the die and reported the outcome on an answer sheet they were given the opportunity to confess that they had lied about the outcome

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(treatments P_NoInfo, NC_NoInfo, and R_NoInfo). Secondly, thereafter, participants were instructed to roll the die and report the outcome a second time, before they were asked to answer the same question about their honesty in this game again (treatments P_Info, NC_Info, and R_Info). Participants played the game in two consecutive rounds so that it was possible to compare their behavior in two different situations. In the first round of the game, subjects were in a position where they did not know that there would be a confession possibility (treatment X_NoInfo, with X∊{P, NC, R}). On the other hand, in round two participants knew from prior experience that there would be a confession possibility (treatment X_Info, with X∊{P, NC, R}). This procedure made it less artificial to test for different effects of the Info condition compared to the NoInfo condition, rather than having an independent treatment where participants were explicitly told before the die roll that they would be asked about their honesty.

2.2 Confession Question

The confession question slightly varied in each treatment.

In the Punishment treatment participants were told that if they decided to confess that the reported die roll outcome differed from their true die roll outcome, they may keep the earnings belonging to the true outcome, not the originally reported one though. The exact question was the following:

“As you can probably imagine, not everybody tells the truth in this game. Can you tell me if you just told me the truth or not? You will receive the payment that belongs to the true, actual die roll outcome, not the one you just reported, if you decide to admit that you didn’t tell the truth.”

In the No Consequence treatment participants were given the possibility to confess without any consequences to their payment. They could keep the earnings from their reported die roll outcome, even if they confessed that they had lied about the true outcome and actually rolled a lower number. The exact question was: 1

1 _{Only one participant confessed under-reporting the die roll outcome and admitted that he had actually} rolled a higher number.

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“As you can probably imagine, not everybody tells the truth in this game. Can you tell me if you just told me the truth or not? You can keep the earnings that belong to your originally reported die roll outcome, even if you decide to tell me that you just didn’t tell the truth.”

In the last treatment, the Reward treatment, participants were offered an additional euro on top of the earnings belonging to their originally reported die roll outcome if they confessed that they had lied about the number they first reported. The exact question was the following:

“As you can probably imagine, not everybody tells the truth in this game. Can you tell me if you just told me the truth or not? You can keep the earnings of the die roll outcome that you just reported, and I will give you an additional euro on top of that if you decide to tell me that you just didn’t tell the truth.”

2.3 Participants and Procedures

This study was conducted in five sessions (i.e. five days) as a lab in the field experiment with a total number of 60 participants (20 in each treatment condition, 42% females), all students of the University of Amsterdam, Netherlands. Table 2 summarizes the total number of sessions and participants in each treatment.

Treatment Number of

sessions participants Number of Total number of die rolls Number of female participants

Punishment 2 20 40 11 (55%)

No Consequence 1 20 40 9 (45%)

Reward 2 20 40 5 (25%)

Total 5 60 120 25 (41.67%)

TABLE 2. Summary of Sessions

Participants were approached on and around the UvA campus and were asked if they were interested in playing a simple game where they could possibly win real money. Participating students were handed a sheet with instructions in English (see Appendix A1) and were given approximately one minute to read those. Before the game started it was made sure

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that participants had understood the instructions and possible questions were clarified. Prior to the first die roll, participants could check if the die they were playing with was fair. The game was usually played right where the participant was approached, i.e. either in the cafeteria, a bench outside the main building, or on the ground in the grass. Before the game started, a cardboard divider was set up between the experimenter and participants to make them more comfortable and not give them the feeling of being directly watched (see Figure 1). In addition, the experimenter also pretended to take notes on a piece of paper while the participant checked the number on the die underneath the cup.

FIGURE 1. Experimental Setup

Once participating students had rolled the die and checked the number through the hole in the cup, they were asked to write down their answer on an answer sheet. Thereafter, the question concerning their honesty was posed. When a participant confessed that she had lied, she was told to cross out the original answer and write down the true outcome. Nevertheless, in this experiment confessions were treated as a binary variable - people either confessed or they did not confess. Contrary to Peer et al. (2014), this study does not look at the extent of participants’ confessions since it was not possible to verify if a confession was a full or only a partial confession. As the outcome of the die roll was truly private and not visible to the experimenter, participants had the possibility to lie about their die roll. Subjects had an incentive to do so since the higher the number they reported, the more money they earned.

To make the amount participants could possibly win as attractive as possible (€1 per dot on the die instead of 10 cents), but with insufficient funds to pay all of the 60 participants, only one out of every five subjects was paid. Participants were informed about this procedure in the instructions and knew they would find out if they were chosen for payment at the end of the experiment. A list with a random selection of participant IDs that were chosen for payment was

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used to eliminate any possible subconscious manipulating behavior from the experimenter. Knowing if a certain participant was going to be paid or not could have endangered the validity of this study. On this list, there was a field next to the participant ID that was covered by a small piece of sticky note which said either “Yes, lucky you!”, when a participant was chosen for payment, or “No, sorry!” otherwise. Participants were asked to reveal the field themselves at the end of the experiment.

A total of ten participants were paid and mean earnings were €3.70 (SD = 1.42). 2 Remaining participants were offered candy and chocolate as a thank you instead.

2.4 Theoretical Analysis and Hypotheses

The following section will present the main hypotheses, which are based on standard and behavioral economics assumptions as well as recent findings in psychology.

Standard economics considers individuals to be selfish utility maximizers. It is assumed that people do not refrain from lying to get what they desire, especially if it is to their own advantage. In the context of this experiment, people can earn money according to their self-reported private die roll outcome, and according to economists, the more money the better. A rational utility maximizer should therefore always report a six, no matter the true outcome. However, behavioral economists and psychologists have found ample evidence for lying aversion (e.g. Gneezy, 2005; Lundquist et al., 2009). People seem to experience a disutility from being dishonest, which might keep them from lying in the first place. Mazar and Ariely (2006) criticize the standard economic claim that “people trade off only external costs and benefits of an outcome” and suggest that “decisions about honesty also include considerations of internal reward mechanisms”. Nevertheless, DePaulo et al. (1996) and Mazar and Ariely (2006) find that many people do lie on an everyday basis.

The Catholic Church introduced mandatory individual confessions in the 11th century , 3 and even though confessions are no longer mandatory, millions of Catholics all over the world still voluntarily confess their sins regularly to relieve their conscience. Halevy et al. (2014) found that 24% of participants took the opportunity to voluntarily confess that they had been dishonest

2_{Two participants did not want to accept the money they were offered and chose candy instead.} 3_{https://en.wikipedia.org/wiki/Sacrament_of_Penance#History}

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during an experiment. Therefore, a positive number of people is expected to confess in this experiment in at least one of the three treatments.

The first hypothesis is based on a rather classic economics assumption. While some subjects are expected to confess that they have lied about the outcome in this experiment, it is assumed they will not be willing to pay a price for their confession. Harris et al. (1975) find that significantly fewer people are willing to donate to charity after confessing in a church. The authors introduce the notion of moral licensing: “[...] after confession, people feel they have already restored their shattered moral self and thus have no need for reparation ”. When confessing to a priest, people do not have to face any consequences, which might be one of the reasons why confessions are so popular. You can come to terms with yourself without having to pay for it. Also from an economics point of view, it is more rational to confess without facing consequences than admitting to wrongdoing and paying for it. The first hypothesis therefore is: More dishonest subjects will confess in the No Consequence treatment than in the Punishment treatment.

Following the standard economic idea of a homo oeconomicus, a fully rational individual would always report a six in the Reward treatment, and then confess lying in any case, even if they had truly rolled a six, to maximize their earnings and get a payoff of €7. Even though the idea of the homo economicus has long been dismissed, it is expected that the confession rate in the Reward treatment, where participants are offered additional money for a confession, will be the highest among all three treatments. Consequently, the second hypothesis is the following: More dishonest participants will confess in the Reward treatment than in the No Consequence treatment.

Punishment No Consequence Reward No (prior) Information about

confession possibility Treatment P_NoInfo NC_NoInfo Treatment Treatment R_NoInfo

Information about confession

possibility Treatment P_Info Treatment NC_Info Treatment R_Info

Total Confession Rate X < Y < Z Hypothesis One Hypothesis Two TABLE 3. Hypothesis One and Hypothesis Two - Illustrated

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To sum up, going from the Punishment treatment over to the No Consequence treatment and finally the Reward treatment, the confession rates are expected to increase (see Table 3).

The final hypothesis is regarding the treatment difference between X_NoInfo with X∊{P, NC, R}. It looks at participants’ lying and confession behavior when they know that they will be given the possibility to confess before rolling the die. Ayal when informing participants about a confession possibility at the beginning of an experiment, the rate of dishonest behavior decreases. In a different Die-Under-Cup experiment, Shalvi (2012) find that honesty requires time and that people’s selfish behavior is an automatic “reflex” that can only be overcome when given enough time and when there is a lack of justification for self-serving behavior. Serra-Garcia et al. (2013) come to the conclusion that people to lie about private information than about actions. Messages about actions are psychologically more costly to violate than messages about a certain state of the world, as the former is perceived more like a promise and not simply false information. In the Die-Under-Cup game subjects initially lie about private information when reporting a wrong die roll outcome, but when being asked about their honesty and if they had just lied they would need to lie a second time, and this time about their action. Hence, more subjects are expected to lie and confess in the first round of the game, where it is unknown to participants that they will be asked about their honesty. The confession question will come as a surprise and this moment of surprise will cause participants to confess. Or, looking at it the other way round, when subjects know beforehand that they will be given an opportunity to confess, they might only lie if they truly plan on sticking to that lie. Hence, the third and last hypothesis is the following: of a confession possibility will decrease (a) the number of liars, as well as (b) the confession rate (see Table 4). and X_Info, et al. (2010) find that et al. it is easier for The knowledge

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Punishment No Consequence Reward No (prior) Information

about confession possibility

(X) ⇩ Treatment P_NoInfo ⇩ Treatment NC_NoInfo ⇩ Treatment R_NoInfo ⇩ Hypothesis Three: Number of Liars and

Confession Rate X ＞ Y (Y) Information about confession possibility Treatment

P_Info Treatment NC_Info Treatment R_Info

TABLE 4. Hypothesis Three - Illustrated

III. RESULTS

The following section is divided into five parts. First, there will be a detailed analysis of the No Information condition where the die roll outcomes of all participants in the first round of the game are combined. This round will serve as a baseline lying indicator, as subjects are not aware that there will be a confession possibility at this point in the experiment. Subsequently, there will be a separate behavioral analysis of lying behavior in the second round of the game and confession rates in both information conditions, for each of the three treatments individually. Lying behavior in the Information condition will be assessed and compared to the No Information condition. For every treatment, the distribution of reported die roll outcomes will be compared to the expected distribution from rolling a fair die. Furthermore, the number of liars will be estimated with the econometric technique developed by Garbarino et al. (2016). Since the number of liars may differ between treatments due to chance, the number of confessions will be presented as a fraction of the estimated number of liars in that treatment. Finally, there will be a brief summary of the overall results.

3.1 First Round of Die Rolls - No Information Condition

As the die roll outcome was truly private and only known to the participant, actual lying behavior cannot be analyzed on an individual level in this experiment. Nevertheless, it is possible to give an estimate for the number of liars on an aggregated level.

A total of 60 participants rolled a die and reported the outcome before they knew they would be given a chance to confess. The reported outcomes of the first round of die rolls serve as

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a baseline lying indicator. It is possible to combine the reported die roll outcomes in all three treatments and assess general lying behavior among participants in this experiment as subjects were not aware of the confession possibility in this first stage of the game. The distribution of outcomes in all three treatments should be similar and close to the uniform distribution of rolling a fair die if all participants reported their outcome honestly. Figure 2 shows the distribution of reported die roll outcomes.

FIGURE 2. Distribution of Reported Die Roll Outcomes in No Information Condition, N=60. The red line indicates the expected fraction for each outcome when rolling a fair die, i.e. ⅙. Stars show the significance of a two-sided binomial test that the reported fraction differs from the expected 0.167 (*=10%-level, **=5%-level, ***=1%-level).

A Kolmogorov–Smirnov test for uniform distribution suggests that the reported die roll outcome distribution does not significantly differ from an expected uniform distribution, neither on an aggregated level of all three treatments combined in the NoInfo condition (Kolmogorov–Smirnov Z=0.90, p=0.784), nor in any of the three treatments individually (P_NoInfo: Z=0.671, p=0.965 (see Figure 3a), NC_NoInfo: Z=0.819, p=0.771 (see Figure 4a), and R_NoInfo: Z=0.969, p=0.771(see Figure 5a)). However, a two-sided binomial test reveals that there was significant 4 under-reporting of 4’s, and significant over-reporting of 3’s, 5’s and 6’s. This implies that some subjects reported a higher number than what they have actually observed. The fact that the

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fraction of reported 5’s is significantly higher than 16.7% suggests that there were a number of participants that neither reported the truth, nor lied to the maximum extent possible. Fischbacher and Heusi (2008) call this behavior incomplete cheating. Furthermore, the fraction of participants reporting a six is also significantly higher than expected. This is evidence for the existence of subjects acting as a homo economicus - those subjects incur no cost from lying and always report the highest possible number (Fischbacher and Heusi, 2008). The number of homo economicus can be estimated to be (22%-16.7%)*6/5 = 6.36% in the 5 NoInfo condition. On the other hand, 13% of subjects report the lowest possible outcome, which indicates that there are at least some participants that are truly honest, since there is no reason to believe that anyone reporting a one is lying.

As mentioned before, it is possible to give an estimate for the total number of liars on an aggregated level. Therefore, it is necessary to make certain assumptions about participant’s lying behavior. Assuming that people lie either to the maximum extent possible (reporting a “6”), or they lie incompletely (reporting a “5”), it is possible to compare the reported share of high die roll outcomes (5’s and 6’s) to the expected share of 33%. According to the econometric technique developed by Garbarino et al. (2016) , a total of 17.67% of participants 6 (95%-Confidence Interval (CI): [3.85%; 30.85%], i.e. the minimum and the maximum estimated percent of liars) lied in the first round of the game, which is about eleven participants. Mean earnings after the first round of die rolls were €3.77 (SD = 1.76).

While a Mann-Whitney U test suggests that there is no significant difference between the distributions of reported outcomes in the NC_NoInfo treatment and the R_NoInfo treatment (see

5 _{Fischbacher and Heusi (2008) make use of this formula, which also considers those participants that} actually rolled a “6” but would have lied if they had rolled a lower number.

6_{“This technique estimates the full distribution of the percentage of individuals who lie when they have} an incentive to report dishonestly [here: reporting a high outcome when rolling a number lower than 5 ]. By determining the PDF and CDF of dishonesty, it gives a precise estimate of the mean and the lower and upper bounds on the percent of subjects reporting dishonestly that can be inferred from the full distribution” (Banerjee et al., 2016). The authors note that for a small sample sizes the number of liars may be overestimated with this method though. A link to the free software that implements this technique can be found here: ftp://ftp.gate.cnrs.fr/LyingCalculator/LyingCalculator.zip.

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Figure 4aand Figure 5a, respectively, Z=0.0, p=1), the distribution of die roll outcomes in the P_NoInfo treatment (see Figure 3a) does differ significantly from the aforementioned two treatment distributions (Z=2.179, p=0.029, and Z=-2.051, p=0.040, respectively). This difference might be due to chance and the relatively small sample size. For a sound analysis of confession behavior in the following sections it is therefore necessary to differentiate between the three treatments in the NoInfo condition.

3.2 Punishment Treatment

This section, as well as the next two sections, will analyze the different treatments in details and will be structured as follows. First, mean earnings and the die roll outcome distributions in both information conditions will be presented. Thereafter, the number of liars in the X_Info condition (with X∊{P, NC, R}) will be estimated and compared to the number of liars in the NoInfo condition (all three treatments combined). Finally, the number of confessions in both information conditions will be compared and analyzed.

A. Lying Behavior in P_Info Condition

In the Punishment treatment, mean earnings were €3.00 (SD = 1.69) in the P_NoInfo condition, and €3.65 (SD = 1.69) in the P_Info condition.

FIGURE 3a and FIGURE 3b (top of next page).

Distribution of Die Roll Outcomes in the Punishment Treatment. The red line indicates the expected fraction of ⅙ for each number on the die. Stars show the significance of a two-sided binomial test that the reported fraction differs from the expected 0.167 (*=10%-level, **=5%-level, ***=1%-level).

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FIGURE 3c.

Total Number of Five and Six Die Rolls in Punishment Treatment. Combined frequency of the high die roll outcomes “5” and “6”, which are assumed to be the numbers reported when lying, in both information conditions. The red line indicates the expected fraction of ⅓.

As Figure 3b and a Kolmogorov–Smirnov test for uniform distribution show, the reported die roll outcome distribution in the P_Info condition does not significantly differ from the expected uniform distribution (Z=0.447, p=1). Furthermore, a two-sided binomial test reveals no significant under-reporting or over-reporting of any die roll outcome. This is a strong indicator that there were very few dishonest people. The number of truly honest people is at least 25%. Figure 3c shows that in both information conditions the reported number of high outcomes was indeed very close to the expected number. The total estimated fraction of liars after rolling the die a second time in the Punishment treatment is 9.93% (95%-CI: [0.0%; 28.29%]), i.e. approximately two people lied. This is a 44% decrease compared to the proportion of liars after the first round of die rolls in the NoInfo condition (two-sided two sample test of proportions Z=0.823, p=0.410).

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B. Confession Behavior

To assess the impact of the knowledge of a confession possibility on confession behavior in the Punishment treatment, the number of liars in P_NoInfo needs to be estimated separately in order to make sound conclusions. In P_NoInfo, the fraction of liars is estimated to be 6.93% (95%-CI: [0.0%; 23.99%]). Neither after the first round of die rolls, nor after the second round did any of the participants confess to having dishonestly reported a higher number when being confronted with a decrease in payment for a confession (see Table 5).

Number of

Liars Confessions Number of Confessions as % of Liars Change - Confession Rate (NoInfo → Info)

P_NoInfo (1) 0 0% ⎯

P_Info 2 0 0% 0%

TABLE 5. Number of Liars and Confession Rates in the Punishment Treatment - Overview

The information about a confession possibility seemed to have had a positive impact on the number of liars in this treatment (as compared to the fraction of liars across all three NoInfo treatments combined), but it did not impact participant’s willingness to confess.

3.3 No Consequence Treatment

Mean earnings were €4.15 (SD = 1.63) in the NC_NoInfo condition and €4.45 (SD = 1.39) in the NC_Info condition.

A. Lying Behavior in NC_Info

Figure 4b and a Kolmogorov–Smirnov test suggest that the reported die roll outcome distribution in the NC_Info condition significantly differs from an expected uniform distribution (Z=1.639, p=0.059). The two-sided binomial test reveals highly significant over-reporting of die roll outcome five, and under-reporting of all other numbers. This result, as well as Figure 4c, strongly suggests that there was a great number of dishonest people. The share of people reporting a high outcome is significantly greater than ⅓ in both information conditions. In fact, 70% of participants reported a high outcome in NC_Info, which is more than twice as many as

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expected. The minimum number of truly honest people that report the lowest possible outcome after the second die roll is as low as 5%.

FIGURE 4a (top) and FIGURE 4b (middle).

Distribution of Die Roll Outcomes in the No Consequence Treatment. The red line indicates the expected fraction of ⅙ for each number on the die. Stars show the significance of a two-sided binomial test that the reported fraction differs from the expected 0.167 (*=10%-level, **=5%-level, ***=1%-level).

FIGURE 4c.

Total Number of Five and Six Die Rolls in No Consequence Treatment. Combined frequency of the high die roll outcomes “5” and “6”, which are assumed to be the numbers reported when lying, in both information conditions. The red line indicates the expected fraction of ⅓.

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The total estimated fraction of liars in NC_Info is 54.0% (95%-CI: [37.15%; 66.4%]), which makes a total of eleven liars. Compared to the 17.67% of liars in the NoInfo condition, this is a significant increase of 206% in the number of liars (two-sided two sample test of proportions Z=- 3.179, p=0.002).

The fraction of liars in the NC_NoInfo treatment is estimated to be 24.83% (95%-CI: [0.0%; 44.06%]). Only one participant confessed lying in NC_NoInfo, which is 20% of the estimated number of liars. With the number of liars increasing significantly in the second round of the game, also the number of confessions increased. As Table 6 shows, a total of 55% of all liars confessed to having dishonestly reported a wrong number in NC_Info, when being offered a relief of conscience without payoff consequences. This is a 175% increase as compared to the share of confessions after the first round of die rolls.

Number of

Liars Confessions Number of Confessions as % of Liars Change - Confession Rate (NoInfo → Info)

NC_NoInfo (5) 1 20% ⎯

NC_Info 11 6 55% 175%↗

TABLE 6. Number of Liars and Confession Rates in the No Consequence Treatment - Overview

It seems that the knowledge of a confession possibility without any (payoff) consequences stimulates lying behavior, but also significantly increases the rate of confessions (two-sided two sample test of proportions Z=- 2.286, p=0.022).

3.4 Reward Treatment

In the Reward treatment, mean earnings were €4.15 (SD = 1.79) in R_NoInfo, and €3.20 (SD = 1.54) in R_Info.

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FIGURE 5a (top) and FIGURE 5b (middle).

Distribution of Die Roll Outcomes in the Reward Treatment.

The red line indicates the expected fraction of ⅙ for each number on the die. Stars show the significance of a two-sided binomial test that the reported fraction differs from the expected 0.167 (*=10%-level, **=5%-level, ***=1%-level).

FIGURE 5c.

Total Number of Five and Six Die Rolls in Reward Treatment.

Combined frequency of the high die roll outcomes “5” and “6”, which are assumed to be the numbers reported when lying, in both information conditions. The red line indicates the expected fraction of ⅓.

A Kolmogorov–Smirnov test shows that the reported die roll outcome distribution in the R_Info condition does not significantly differ from an expected uniform distribution (Z=0.521, p=1). A

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two-sided binomial test reveals that the reported die roll outcome distribution in the R_Info condition (see Figure 5b) is actually very close to the expected distribution, there was only significant under-reporting of die roll outcome six, but no significant deviation for the remaining numbers. The fraction of people reporting a high outcome is significantly greater than ⅓ in the R_NoInfo condition, but slightly lower than ⅓ in R_Info. The share of truly honest people in R_Info is at least 15%. The total estimated fraction of liars after the second round of die rolls in the Reward treatment is 4.72% (95%-CI: [0.0%; 19.87%]), i.e. one liar. This is a 73% decrease compared to the proportion of liars in the combined NoInfo condition (two-sided two sample test of proportions Z=1.427, p=0.154). The knowledge of a confession possibility greatly reduces lying behavior in the Reward treatment.

The total number of liars in R_NoInfo can be estimated to be 31.59% (95%-CI: [10.25%; 49.62%]), i.e. six participants lied. With three confessions in total, this is a confession rate of 50% after the first round of die rolls. The confession rate increased significantly by 300% after the second round of die rolls, when participants had prior knowledge of the confession possibility that included a reward - a total of two participants confessed lying even though only one subject has been estimated to be dishonest in R_Info (see Table 7). 7

Number of

Liars Confessions Number of Confessions as % of Liars Change - Confession Rates (NoInfo → Info)

R_NoInfo (6) 3 50% ⎯

R_Info 1 2 200% 300%↗

TABLE 7. Number of Liars and Confession Rates in the Reward Treatment - Overview

This result suggests that the knowledge of a confession possibility that comes with an additional reward for honesty has a great influence on lying behavior as well as confession behavior, as it decreases the number of liars and significantly increases the share of confessions.

3.5 Summary of Results

7 _{Indeed, one participant independently confessed in a conversation after the experiment that she falsely} admitted to lying in the R_Info just to get the additional euro.

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In line with previous studies (see Halevy et al., 2014; Peer et al., 2014), a significant proportion of participants confessed to their dishonest behavior in this experiment. Across all three treatments, twelve out of 26 liars confessed that they had been dishonest, i.e. 46%. By far the biggest proportion of confessions among all three treatments was found in R_Info with a confession rate of 200%, followed by NC_Info with 55% (see Figure 6b). Taking both information conditions together, the total combined confession rate is 0% in the Punishment treatment, 37.5% in the No Consequence treatment, and 125% in the Reward treatment. A one-sided two-sample test of proportions to test whether there are significantly more people confessing in the No Consequence treatment than in the Punishment treatment shows that the difference between the treatments is highly significant ( Z= -4.297, p=0.0). Furthermore, this study also finds support for the hypothesis that more people will confess in the Reward treatment than in the No Consequence treatment.

FIGURE 6a. Estimated Number of Liars in NoInfo Condition (combined) Compared to X_Info Condition, with X∊{P, NC, R}.

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FIGURE 6b. Confession Rates by Treatment - Overview

Taking all the NoInfo treatments together (P_NoInfo, NC_NoInfo and R_NoInfo), a total of 23.3% of dishonest participants confessed to lying when they were surprised by the confession question. Across all three Info treatments (P_Info, NC_Info and R_Info), the combined confession rate is 85%. This is a highly significant increase of 265% in the confession rate when participants have prior information about the confession opportunity (one-sided two sample test of proportions Z= -6.782, p=0.0). Hence, the hypothesis that no prior information about the confession possibility would increase the number of confessions is not supported by the data. The number of liars in the Info condition decreased in the Punishment as well as the Reward treatment, but the number significantly increased in the No Consequence treatment (see Figure 6a). This refutes the hypothesis, at least for one treatment, that the number of liars would decrease when participants were informed about the confession possibility.

IV. DISCUSSION

There are a number of important limitations to this study that will be discussed in the following section.

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Even though it was obvious that some participants in this experiment had lied given their behavior , as mentioned before, it was not possible to actually control if an individual was lying8 or not. While this might be criticizable, participants needed to be put into a situation where it was transparent to them that their dishonest behavior could not be detected. Furthermore, this limitation does not influence the general conclusions, as the focus of this study lays on the different treatment effects. Nevertheless, regarding the experimental design, there are several difficulties that need to be addressed.

Firstly, this experiment was conducted in English, to allow for a participant pool as large as possible, on the campus of the University of Amsterdam, in the Netherlands. Caldwell-Harris and Ayçiçeği-Dinn (2009) find that lying in a foreign language is harder and “requires additional cognitive resources to monitor lie production” than lying in your native language - the authors refer to this as the “double stressor”. People are more aware and afraid of finding the right words and matching gestures in a second language than in their first language which causes a majority of people (55%) to avoid lying in the first place. While conducting the experiment I also asked participants if English was their first or second language and only two out of 60 participants were English native speakers. Although the task was simple, and all participants were highly educated it is possible that this language barrier distorts the general conclusions that follow from the results. Assuming that fewer people lied due to the language being English this consequently lead to fewer confessions. If the experiment had been conducted in a native English speaking country, the results may possibly differ.

Secondly, when casually talking to participants after the experiment, several subjects reported that they did not think about lying in the Die-Under-Cup game until after the first round, when they were asked about their honesty. While this might have been only a strategic comment to appear honest in front of the experimenter it might as well be true and explain why there are significantly more people lying after rolling the die a second time in the No Consequence treatment.

8 _{E.g. several participants conspicuously made sure that I didn’t see their die roll outcome, or they} nervously looked through the hole in the cup several times and corrected the number on their answer sheet.

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More generally, but probably most importantly, confessing a lie to the experimenter, someone with whom the subject did not have any kind of long-term relationship, did not have any future consequence for the participant. On the other hand, lying and admitting a lie to your partner, your best friend, or your employer is a completely different situation. In real life, confessing to your boss that you have “stretched the truth” in your sales report, even if it was only a minor change just to get the end of the year bonus, might seriously endanger your job and is far more severe than confessing to a student experimenter. Also, it might be easier to confess to someone that is not the person you lied to. In this experiment though, participants that lied had to directly confess to the experimenter only a few minutes after the lie. Gneezy (2005) suggests that the consequences of a lie matter to the person lying and that the more serious those consequences are for the person affected by a lie, the less likely people are to lie. Fischbacher and Heusi (2013), on the other hand, find empirical evidence for the opposite. In their experiment, the authors vary the person that is affected by dishonest behavior (instead of the experimenter they let dishonest behavior hurt another subject’s payoff). It appears that this change does not affect subjects’ lying behavior. The same was found by Van de Ven and Villeval (2015), who let participants play Gneezy’s (2005) deception game. In their paper Dishonesty under Scrutiny, the authors claim that “[...] senders whose identity is revealed to their observer do not lie less when their interests are misaligned with those of the observer” . In another Die-Under-Cup experiment by Halevy et al. (2014) participants were also asked about their honesty at the end of the experiment session. The difference between their procedure and the approach used in this study is that participants in Halevy et al .’s experiment were not directly asked about their honesty by a real person but on a piece of paper, and participants had already received their payment when answering the question. This procedure eliminated possible doubts of participants that might have been sceptical if they really received the full payment when confessing that they had been dishonest. Nevertheless, the confession rate in their study amounted to 23.5%, which is only about half of the overall confession rate that was found in this experiment. Those findings support the experimental procedure of this experiment as they suggest that the presence of the experimenter did not affect participants’ lying behavior to a great extent.

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As the number of participants in this experiment was limited due to time and budget constraints, another experiment with a greater number of participants should be conducted for more insight. Also, a different setting where participants do not lie and confess to the same person would be interesting to study.

V. CONCLUSION

This paper presented a novel experimental investigation of confession behavior. After letting participants play the Die-Under-Cup game, which put them into a morally conflicting situation where they had to choose between maximizing their own payoff and being honest, they were asked to confess if they had lied about the die roll outcome. Not only was the effect of monetary incentives on individuals’ confession behavior studied, but also the effect of information about a confession possibility on lying behavior. In line with previous expectation, the knowledge of a confession opportunity decreased the number of liars in the Punishmenttreatment, as well as the Reward treatment. The opposite effect was found for the No Consequence treatment though. Furthermore, the results indicate that it is indeed possible to incentivize subjects to make a confession. The data suggests that the most successful way to elicit a confession from a dishonest individual is to offer a reward. This may be difficult to enforce in real life, but ensuring subjects that they will not have to face negative consequences after a confession is definitely feasible in a professional environment.

From the results of this experiment it follows that informing people about a confession possibility only pays off when they can be offered a reward for a confession. It decreases the number of liars and increases the confession rate. Letting people know that they can confess and they will not have to face any consequences after their confession, paradoxically does more harm than good, as it increases the number of liars disproportionately to the increase of the confession rate. If lying is so deeply anchored inside us, this study about confession incentives is only a drop in the ocean though and there is still a lot of work to be done by future research.

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VI. REFERENCES

Aghion, P., & Tirole, J. (1997). Formal and real authority in organizations. Journal of political economy, 105(1), 1-29.

Ayal, S., Gino, F., Mazar, N., & Ariely, D. (2010). Finding balance on the moral scale: Dishonest behavior and the promise of confession. Working paper.

Ayal, S., & Gino, F. (2011). Honest rationales for dishonest behavior. The social psychology of morality: Exploring the causes of good and evil. Washington, DC: American Psychological Association, 149-66.

Banerjee, R., Datta Gupta, N., & Villeval, M. C. (2016). The Spillover Effects of Affirmative Action on Competitiveness and Unethical Behavior.

Caldwell-Harris, C. L., & Ayçiçeği-Dinn, A. (2009). Emotion and lying in a non-native language. International Journal of Psychophysiology, 71(3), 193-204.

Croson, R., Fatas, E., & Neugebauer, T. (2005). Reciprocity, matching and conditional cooperation in two public goods games. Economics Letters, 87(1), 95-101.

DePaulo, B. M., Kashy, D. A., Kirkendol, S. E., Wyer, M. M., & Epstein, J. A. (1996). Lying in everyday life. Journal of personality and social psychology, 70(5), 979.

Fischbacher, U., & Föllmi-Heusi, F. (2013). Lies in disguise—an experimental study on cheating. Journal of the European Economic Association, 11(3), 525-547.

Garbarino, E., Slonim, R., & Villeval, M. C. (2016). Loss Aversion and lying behavior: Theory, estimation and empirical evidence.

Gino, F., & Ariely, D. (2012). The dark side of creativity: original thinkers can be more dishonest. Journal of personality and social psychology, 102(3), 445.

Gneezy, U. (2005). Deception: The role of consequences. The American Economic Review, 95(1), 384-394.

Gneezy, U., & Rustichini, A. (2000). A fine is a price. The Journal of Legal Studies, 29(1), 1-17. Goman, C. K. (2013). The Truth about Lies in the Workplace: How to Spot Liars and what to Do about Them. Berrett-Koehler Publishers.

Gudjonsson, G. H. (1992). The psychology of interrogations, confessions and testimony. John Wiley & Sons.

Gudjonsson, G. H., & Petursson, H. (1991). Custodial interrogation: Why do suspects confess and how does it relate to their crime, attitude and personality?. Personality and Individual Differences, 12(3), 295-306.

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Halevy, R., Shalvi, S., & Verschuere, B. (2014). Being honest about dishonesty: Correlating self-reports and actual lying. Human Communication Research, 40(1), 54-72.

Harris, M. B., Benson, S. M., & Hall, C. L. (1975). The effects of confession on altruism. The Journal of social psychology, 96(2), 187-192.

Kassin, S. M., & Gudjonsson, G. H. (2004). The psychology of confessions: A review of the literature and issues. Psychological Science in the Public Interest, 5(2), 33-67.

Kettunen, P. (2002). The function of confession: A study based on experiences. Pastoral Psychology, 51(1), 13-25.

Lundquist, T., Ellingsen, T., Gribbe, E., & Johannesson, M. (2009). The aversion to lying. Journal of Economic Behavior & Organization, 70(1), 81-92.

Mazar, N., & Ariely, D. (2006). Dishonesty in everyday life and its policy implications. Journal of public policy & Marketing, 25(1), 117-126.

Peer, E., Acquisti, A., & Shalvi, S. (2014). “I cheated, but only a little”: Partial confessions to unethical behavior. Journal of Personality and Social Psychology, 106(2), 202.

Plato (360 BC). The Republic. Trans. by Benjamin Jowlett, Book II, 358d—361d.

Serra-Garcia, M., Van Damme, E., & Potters, J. (2013). Lying about what you know or about what you do?. Journal of the European Economic Association, 11(5), 1204-1229.

Shalvi, S., Dana, J., Handgraaf, M. J., & De Dreu, C. K. (2011). Justified ethicality: Observing desired counterfactuals modifies ethical perceptions and behavior. Organizational Behavior and Human Decision Processes, 115(2), 181-190.

Shalvi, S., Eldar, O., & Bereby-Meyer, Y. (2012). Honesty requires time (and lack of justifications). Psychological science, 23(10), 1264-1270.

Todd, E. (1985). The value of confession and forgiveness according to Jung. Journal of Religion and Health, 24(1), 39-48.

Van de Ven, J., & Villeval, M. C. (2015). Dishonesty under scrutiny. Journal of the Economic Science Association, 1(1), 86-99.

Zhong, C. B., Bohns, V. K., & Gino, F. (2010). Good lamps are the best police: Darkness increases dishonesty and self-interested behavior. Psychological science, 21(3), 311-314.

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APPENDIX A1 - Instructions

Instructions

Hello and thank you for taking five minutes to help me with my master thesis!

Today I am going to ask you to play two rounds of a short game called “die-under-the-cup”.

For this experiment, you will be given the opportunity to roll a single die to determine the amount of money you can win.

The procedure is as follows:

1) Leaving the die under the cup, shake the cup back and forth vigorously to roll the die.

2) Without removing the cup, look through the hole in the cup to see what number you rolled.

3) Write the number you got on the answer sheet. Important: Do not remove the cup afterwards. At no point_{during or after the experiment} will I, the experimenter, look under the cup to check if the number you reported is correct. Before the first roll of the die, I am going to give you the chance to look at the die under the cup so that you can verify for yourself that the die is fair.

Payoff: In this experiment, one out of five participants is going to be actually paid in real euros. You will find out if you are selected for payment after you have played both rounds of the game.

The number on the die (i.e., 1, 2, 3, 4, 5, or 6) is the number of euros that you can earn for this experiment. Rolling a 1 → _1€ Rolling a 2 → _2€ Rolling a 3 → 3€ Rolling a 4 → 4€ Rolling a 5 → _5€ Rolling a 6 → _6€

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APPENDIX A2 - Two-Sided Binomial Test for Die Roll Outcomes

Die Roll Outcome

n 1 2 3 4 5 6 NoInfo (P, NC and R combined) 60 _0.13 _0.15 _{0.2 (+)} _{0.07 (***) 0.23 (++) 0.22 (+)} P_NoInfo 20 0.25 0.2 0.2 0.05 (*) 0.25 0.05 (*) NC_NoInfo 20 0.05 (*) 0.1 0.3 (+) 0.05 (*) 0.2 0.3 (+) R_NoInfo 20 _0.1 _0.15 _0.1 _0.1 _0.25 _{0.3 (+)} P_Info 20 _0.15 _0.15 _0.1 _0.25 _0.2 _0.15 NC_Info 20 0.05 (*) 0.1 0.05 (*) 0.1 0.55 (+++) 0.15 R_Info 20 0.15 0.25 0.15 0.2 0.2 0.05 (*)

TABLE A2. Percentage of Reported Die Roll Outcome by Treatment. *( + ) stars (crosses) display the significance of two-sided binomial test that the observed frequency is smaller (larger) than 0.167 (*( + ) =10%-level, ** ( ++ ) =5%-level, *** ( +++ ) =1%-level).

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Monetary Incentives for Confessions Tuesday July 11 13:40:41 2017 Page 1 ___ ____ ____ ____ ____(R) /__ / ____/ / ____/ ___/ / /___/ / /___/ Statistics/Data Analysis User: Julia C Mezals Project: Master Thesis ___ ____ ____ ____ ____ (R)

/__ / ____/ / ____/

Statistics/Data Analysis StataCorp

4905 Lakeway Drive

Special Edition College Station, Texas 77845 USA

800-STATA-PC http://www.stata.com 979-696-4600 stata@stata.com 979-696-4601 (fax)

26-user Stata network perpetual license: Serial number: 40120558831 Licensed to: DITNBP

NARODOWY BANK POLSKI Notes:

1. (/v# option or -set maxvar-) 5000 maximum variables

1 . import excel "C:\Users\Julia\Desktop\Mann Whitney U.xlsx", sheet("Sheet11") ce > llrange(A1:B61) firstrow

2 . ranksum Outcome in 1/40, by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test Treatment obs rank sum expected

NC 20 410 410

R 20 410 410

combined 40 820 820

unadjusted variance 1366.67

adjustment for ties -66.41

adjusted variance 1300.26

Ho: Outcome(Treatm~t==NC) = Outcome(Treatm~t==R)

z = 0.000

Prob > |z| = 1.0000

3 . ranksum Outcome in 21/60, by(Treatment)

P 20 335.5 410

R 20 484.5 410

combined 40 820 820

Ho: Outcome(Treatm~t==P) = Outcome(Treatm~t==R)

z = -2.051

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Monetary Incentives for Confessions Tuesday July 11 13:40:41 2017 Page 4 44 . ranksum Outcome, by(Treatment)

NC 20 489 410

P 20 331 410

combined 40 820 820

Ho: Outcome(Treatm~t==NC) = Outcome(Treatm~t==P)

z = 2.179

Prob > |z| = 0.0293

45 . prtesti 60 0.1767 20 0.54

Two-sample test of proportions x: Number of obs = 60

y: Number of obs = 20 Variable Mean Std. Err. z P>|z| [95% Conf. Interval]

x .1767 .0492404 .0801906 .2732094

y .54 .1114451 .3215717 .7584283

diff -.3633 .1218385 -.6020991 -.1245009

under Ho: .1142965 -3.18 0.001

diff = prop(x) - prop(y) z = -3.1786

Ho: diff = 0

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0

Pr(Z < z) = 0.0007 Pr(|Z| < |z|) = 0.0015 Pr(Z > z) = 0.9993

46 . prtesti 60 0.1767 20 0.0993

x .1767 .0492404 .0801906 .2732094

y .0993 .0668728 -.0317683 .2303683

diff .0774 .0830457 -.0853666 .2401666

under Ho: .0940181 0.82 0.410

diff = prop(x) - prop(y) z = 0.8232

Ho: diff = 0

Pr(Z < z) = 0.7948 Pr(|Z| < |z|) = 0.4104 Pr(Z > z) = 0.2052

47 . prtesti 60 0.1767 20 0.0472

x .1767 .0492404 .0801906 .2732094

y .0472 .0474195 -.0457405 .1401405

diff .1295 .068361 -.0044851 .2634851

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Monetary Incentives for Confessions Tuesday July 11 13:40:41 2017 Page 5 Ho: diff = 0

Pr(Z < z) = 0.9232 Pr(|Z| < |z|) = 0.1535 Pr(Z > z) = 0.0768

48 . prtesti 20 0.2 20 0.55

x .2 .0894427 .0246955 .3753045

y .55 .111243 .3319678 .7680322

diff -.35 .142741 -.6297673 -.0702327

under Ho: .1530931 -2.29 0.022

Ho: diff = 0

Pr(Z < z) = 0.0111 Pr(|Z| < |z|) = 0.0222 Pr(Z > z) = 0.9889

49 . prtesti 20 0.5 20 2 2 not in [0,1]

r(198);

50 . prtesti 40 0.0 40 0.375

x 0 0 0 0

y .375 .0765466 .2249715 .5250285

diff -.375 .0765466 -.5250285 -.2249715

under Ho: .0872765 -4.30 0.000

Ho: diff = 0

Pr(Z < z) = 0.0000 Pr(|Z| < |z|) = 0.0000 Pr(Z > z) = 1.0000

51 . prtesti 40 0.375 40 1.25 1.25 not in [0,1]

r(198);

52 . prtesti 60 0.233 60 0.85

x .233 .0545758 .1260334 .3399666

y .85 .0460977 .7596501 .9403499

diff -.617 .0714389 -.7570177 -.4769823

under Ho: .0909721 -6.78 0.000

Ho: diff = 0

Pr(Z < z) = 0.0000 Pr(|Z| < |z|) = 0.0000 Pr(Z > z) = 1.0000

Monetary incentives for confessions