Univeristeit van Amsterdam
When the cup runs over
An experimental study into the
spillover effect of overconfidence
Maarten Hopman, 10579168
Behavioral economics and Gametheory
15 ects
Supervisor: Jo¨
el van der Weele
Statement of originality
This document is written by Student Maarten Hopman who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are 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 supervi-sion of completion of the work, not for the contents.
Abstract
Overconfidence has been the topic of many previous studies. These studies have shown both negative and positive consequences of this common phe-nomenon. In this paper I experimentally examine a possible spillover effect of overconfidence, which has not yet been studied before. A spillover effect of overconfidence exists if people who become overconfident after a first task, remain more confident about their performance in a second, unrelated task. Since overconfidence can lead to suboptimal managerial decisions, and man-agers engage in many different types of tasks everyday, a spillover effect of confidence could have serious economic consequences. In the experiment, two groups of randomly selected respondents had their relative confidence exogenously manipulated by making an easy or a hard version of an IQ test. This test led to a significant difference in relative confidence between the two groups. However, after a real effort task, this difference in confidence was no longer present. Furthermore, the first test led to underconfidence in the hard group instead of overconfidence in the easy group. The question about the existence of a spillover effect of overconfidence therefore remains unanswered. Finally, due to a selection effect, the respondents that faced the hard quiz performed better in the real effort task.
Contents
1 Introduction 4
2 Literature 6
2.1 Overplacement . . . 6
2.2 Spillover effect . . . 8
2.3 Confidence and performance . . . 9
2.4 The current research . . . 11
3 Method 11 3.1 Respondents and instructions . . . 11
3.2 First task - Quiz . . . 12
3.3 Second task - Cognitive slider task . . . 13
3.4 Belief-elicitation . . . 15 3.5 Questionnaire . . . 16 4 Hypotheses 17 5 Results 18 5.1 Treatment effect . . . 18 5.2 Spillover effect . . . 20 5.3 Effect on performance . . . 22 5.4 Gender differences . . . 24 5.5 Mood differences . . . 25 6 Discussion 26 6.1 Spillover effect . . . 26
6.2 Direct treatment effect . . . 27
6.3 Selection effect . . . 29
6.4 Online experiment . . . 29
1
Introduction
Overconfidence, the tendency of people to overestimate themselves, is a well-documented phenomenon. Combined findings from several disciplines such as economics, finance, and psychology form an overwhelming body of evidence that shows the existence of overconfidence. Economists have extensively studied overconfidence due to the diverse economic consequences this com-mon phenomenon can have. Some of these studies show that overconfidence can have negative repercussions. For instance, overconfidence can lead to suboptimal managerial decisions (Malemedier & Tate, 2005; Malmendier & Tate, 2008), excessive trading on the stock market (Barber & Odean, 2001), and undue entry into competition (Camerer & Lovallo, 1999; Koellinger, Minniti, & Schade, 2006; Niederle & Vesterlund, 2007). However, from an evolutionary perspective, the fact that overconfidence exists indicates that it should also have positive consequences. Bernardo and Welch (2001) show that groups with overconfident individuals have a evolutionary advantage over groups without overconfident agents. Moreover, Johnson and Fowler (2011) present a model in which overconfidence has an evolutionary advan-tage at the individual level. Other papers have indeed shown positive conse-quences of overconfidence. It has been shown that overconfident individuals are better at persuading others (Burks et al., 2013; Schwardmann & Van der Weele, 2016), they work harder (Puri & Robinson, 2007), and enjoy a higher social status (Kennedy, Anderson, & Moore, 2013).
Although there has been much research into overconfidence, no research has been done on how confidence gained in one task influences the belief of an individual about their performance in a subsequent, unrelated task. Such a spillover effect of overconfidence could potentially have serious economic consequences. A lot of the negative consequences listed above are related to managers and CEOs. According to Lehner (1992), managers and CEOs engage in many heterogeneous tasks every day, most of which are important for the growth of the firm. If a spillover effect of overconfidence exists, a manager that gains confidence from one of these tasks might make suboptimal decisions in a subsequent task. On the aggregate level, such suboptimal decisions can have an impact on the economy as a whole.
Psychological research has revealed that confidence impacts judgement differently depending on thinking conditions. In conditions where individu-als can not think freely, for instance due to a heavy cognitive load, confidence
emotions if they felt confident during the action. However, managers often make important decisions when they can think free from distractions. Under such circumstances, confidence can lead to a bias in judgement by creating overly positive thoughts (Brinol et al., 2010). Additionally, in such conditions confident individuals are less likely to carefully process all available informa-tion (Tiedens & Linton, 2001). Managers that became overconfident in their professional abilities might therefore underestimate the risk or overestimate the profitability of a project and consequently, engage in value destroying activities.
This research is an attempt to fill the gap in the overconfidence literature by experimentally proving the existence of a spillover effect of overconfidence. Due to the experimental design, I am also able to draw inferences about the relationship between confidence and performance in a real effort task. So far, the relationship between confidence and performance has mainly been studied theoretically. For instance, in a theoretical model by Compte and Postlewaite (2004), overconfidence leads to an increase in performance. This is in line with the theory of ’the motivational value of confidence’, which postulates that more confident individuals exert more effort since they believe that they face a high return for their effort (Chen & Schilberg-H¨orisch, 2018).
In total, 136 respondents participated in a four-stage online experiment. In the first stage both groups were faced with a 10 question IQ-quiz that consisted of Raven-matrices. However, the ‘easy group’ was faced with a significantly easier version of the quiz than the ‘hard group’. In the second stage, respondents reported their subjective probability of placing in the top half. The third stage was the same for all respondents and consisted of a ”cognitive slider-task”, a novel adaptation of the slider-task that was originally developed by Gill and Prowse (2018). Finally, in the fourth stage respondents reported their beliefs of placing in the top half of the slider-task. The experiment was concluded after subjects filled out a short questionnaire. The first stage was designed to make use of the hard-easy effect (Healy & Moore, 2008) and created two groups with different levels of relative con-fidence. Hypothesized was that the easy group would, on average, indicate a higher subjective probability of placing in the top half. Indeed, in line with the literature and this hypothesis, the easy group reported a significantly higher subjective probability of placing in the top half. However, the stated beliefs of neither group constituted overconfidence. Rather, the hard group exhibited underconfidence. Analysis of the data showed that the discrep-ancy in beliefs between the two groups that was found in the second stage
was no longer present in the beliefs reported in the fourth stage. The average subjective probability that was reported was the same for the easy and the hard group. In light of this finding, the second hypothesis, that stated that those who faced the easy quiz would report a significantly higher subjective probability of placing in the top half of the slider task, was rejected.
Lastly, regression analysis showed that after controlling for mouse usage, respondents in the hard group positioned more sliders correctly than those in the easy group.
The remainder of this paper will continue as follows. In section two, re-lated literature is discussed and compared to the current research. In section three the experimental design is explained and in section four the hypotheses are presented. The results are presented in section five. In section six these findings are discussed. Finally, section seven concludes.
2
Literature
2.1
Overplacement
In the vast body of literature on overconfidence, a distinction between differ-ent types of overconfidence has been made. Moore and Healy (2008) distin-guish three different “faces” of overconfidence: overestimation, overprecision, and overplacement. Overestimation occurs when an individual overestimates their performance and is also referred to as absolute overconfidence. This type of overconfidence is often found when subjects are asked to indicate how many questions they think they got right on a quiz (e.g see Grossman & Owens, 2012). Overprecision refers to the tendency of people to be overly certain of their beliefs. For instance, Soll and Klayman (2004) find that the subjective confidence intervals that people submit are consistently too nar-row. Lastly, Larrick et al., (2007) introduced the term overplacement to refer to people who overestimate themselves relative to others. It has therefore also been called relative overconfidence. Usually this is examined empirically by having subjects take a test and ask them to indicate how well they think they did compared to others (Gneezy et al., 2016). This last type of over-confidence is most closely related to this research and will therefore be the main focus of this section.
average” effect is considered to be one of the most robust cognitive biases (Alicke and Govorun, 2005). A well known empirical example of this effect is that the majority of drivers think that they are better than others (Svenson 1981), a belief that is present even in drivers that have been in a recent car accident (Preston & Harris, 1965). Furthermore, other studies have shown that most people think they are more knowledgeable1 , more virtuous, luck-ier, and more likeable than others (Dunning, 2005; Dunning, Heath, & Sulls, 2004; Moore & Small, 2007; Benoit et al., 2015). The propensity of most individuals to think of themselves as above average has often been used as a sign of irrationality. However, recent theoretical work has shown that it can be rational for a majority of people to believe that they are. In a theo-retical paper, Benoit and Dubra (2011) show that if people are uncertain of their type, and form beliefs based on a common prior, Bayesian updating can result in a majority of people believing they are better than average. The authors refer to findings such as by Svenson (1981) as “apparent overconfi-dence”. Furthermore, in a later paper, Benoit and colleagues (2015) formalize a framework to distinguish real and apparent overconfidence. However, even within the more stringent boundaries of this framework, the authors find evidence of overplacement in an experimental setting. They conclude that there are few experiments that properly test for overplacement and that it is therefore unclear how widespread overplacement truly is.
In their review, Moore and Healy (2008) note that overplacement is more likely to occur on easy tasks, whilst hard tasks seem to generate underplace-ment. This is also known as the hard-easy effect. Barron and Gravert (2018) use this effect to experimentally influence the confidence of their subjects. In their experiment, subjects had to make a quiz and subsequently indicate their subjective probability of placing in the top half of quiz-takers. How-ever, half of the subjects faced a harder version of the quiz. In line with the hard-easy effect, subjects that faced the harder quiz were significantly less confident in placing in the top half. In the second part of the experiment subjects were asked to choose between different payment schemes in a labor market experiment. The authors conclude that an exogenous upward shift in relative confidence can lead low skilled workers to self-select into the wrong payment scheme which has a detrimental effect on their earnings.
This research also uses the hard-easy effect to exogenously modulate
rela-1This is also true for professionals such as doctors (Tracy et al., 1997) and lawyers
tive confidence. However, it differs from the aforementioned paper by Barron and Gravert (2018) in that the main interest is not a decision in a labor mar-ket setting. Rather, the hard-easy effect will be used to examine possible spillover effects of overconfidence by testing if a change in relative confidence persists into the beliefs about performance in an unrelated task.
2.2
Spillover effect
A review by Brinol and colleagues (2010) outlines a psychological foundation for a spillover effect of confidence. They state that as confidence in a belief about the self increases, the impact of that belief on thoughts and behaviour increases too. Furthermore, the authors note that “confidence can influence judgement by validating self-relevant thoughts” (Brinol et al., 2010, p 21). Therefore, confidence gained in one task affects confidence in subsequent tasks through enhancing, or increasing the validity of, a positive self-image. This relates directly to the notion that overconfidence stems in part from a desire to see oneself positively (Blanton et al., 2001). People who have been made to think of themselves positively compared to others because they made an easy test, might therefore want to perpetuate this positive self-image in a following task.
Moreover, this might happen even if the two tasks are completely unre-lated. Multiple papers have argued that affirming an unrelated but important aspect of an individual can increase confidence (Binol et al., 2007; Mcgregor et al., 2001). In situations where people can think free from distractions, con-fidence can lead to a more positive self-image, compared to a situation where said confidence is absent (Binol et al., 2010). In such situations, even though the individual engages in critical and detailed thinking, the presence of over-confidence can cause an individual to create an overly optimistic self-image which can lead to an underestimation of their mistakes.
In addition to these theoretical arguments, there exists empirical evidence that an increase in confidence affects economic decision-making. Puetz and Ruenzi (2011) look at the trading behaviour of professional fund managers. They find that managers trade significantly more after a good past perfor-mance. After ruling out some plausible alternative explanations, the authors conclude that this change in behaviour is driven primarily by an increase in confidence. Moreover, top performing managers that increased their trading volume did significantly worse than similar performing managers that kept
of Odean (1999). In his influential paper, Odean showed that overconfidence caused investors to trade excessively to their own financial detriment.
Similarly to fund managers, CEOs and managers have also been found to become overconfident after a successful period (Billet & Qian, 2008; Doukas & Petmezas, 2007). Subsequently, this upward shift in overconfidence leads to an increase in acquisitions which ultimately lowers the stock price of the firm. However, overconfidence in CEOs or managers does not have to be a detriment to the firm. Multiple theoretical models have shown that moderate overconfidence in CEOs benefits the shareholders (Gervais et al., 2011; Goel & Thakor, 2008). However, they also note that there exists a tipping point beyond which CEO overconfidence becomes a detriment to the firm.
2.3
Confidence and performance
Overall, evidence of the impact of confidence on performance is ambiguous. Although it seems that overconfidence is an unfavourable trait for investors and, to a certain extend, managers, some have argued that confidence has a positive effect on performance. Theoretical models have shown that a certain level of overconfidence can increase the welfare of an individual in the long run (B´enabou & Tirole, 2002). Compte and Postlewait (2004) reach a similar conclusion. In their model, the likelihood of successfully completing a task and the amount of tasks that an individual undertakes depend positively on the confidence of the individual. Therefore, overconfident individuals under-take more tasks. Although some of these tasks have a negative net value for the individual, due to ‘confidence-enhanced performance’, an overconfi-dent agent offsets the suboptimal decision of undertaking too many tasks by exerting more effort in these tasks. The authors therefore conclude that a reasonable level of overconfidence is welfare enhancing in the long run. Moreover, Kr¨ahmer (2007) shows that in repeated contests where agents are uncertain of their relative abilities, relative overconfidence increases an agent’s probability of winning due to an increase in effort. In turn, this indi-vidual might never learn her true relative ability and an overconfident agent can prevail in the long run.
Experimental literature on the relationship between confidence and per-formance is scarce. In a discussion paper, Chen and Schilberg-H¨orisch (2018), first present a model wherein the output of an agent depends on chosen ef-fort and an unknown productivity parameter. Due to the assumptions of the productivity function, the effort provision and productivity beliefs of utility
maximizing agents are positively related. The productivity function is there-fore in line with the motivational value of confidence theory. The authors hypothesize that individuals that hold high beliefs about their productivity exert more effort in a real effort task. Chen and Schilberg-H¨orisch test this hypothesis using an adaptation of the slider-taks by Gil and Prowse (2018). In this task, subjects are asked to position a total of 220 sliders within a small interval. Subjects could not see if they had positioned the sliders correctly which left scope for under- or overconfidence. After the first slider task sub-jects could indicate how well they think they did on an absolute level. This allowed the researchers to identify overconfident subjects. In a subsequent part of the experiment subjects were again faced with the slider task. How-ever this time they could choose their own effort level by stopping whenHow-ever they wanted. The results indeed showed a positive relationship between pro-ductivity belief and effort. Moreover, this relationship was even stronger for overconfident subjects. The authors conclude on that this finding is proof of the motivational value of confidence.
The finding by Chen and Schilberg-H¨orisch (2018) is contrasted by that of Barron and Gravert (2018). In their paper, Barron and Gravert find no ev-idence of a relationship confev-idence and exerted effort. However, there are two important differences between the two experiments. First, the papers look at different types of overconfidence. Chen and Schilberg-H¨orisch examine the relationship between absolute overconfidence on effort whereas Barron and Gravert look at relative overconfidence. Second, Barron and Gravert mea-sured overconfidence in a task that was different than the task where effort was exerted. The beliefs elicited by Chen and Schilberg-H¨orisch related to the same task where effort was measured.
This research differs from the Chen and Schilberg-H¨orisch paper in two ways. First, although this research will also look at the influence of over-confidence on the performance and effort in an adaptation of the slider task, the focus of the current research is on relative confidence as opposed to absolute confidence. Second, in the current research an exogenous shift in overconfidence is used to examine the relationship between performance and confidence. The differences between the current research and the paper by Barron and Gravert were mentioned earlier in this section.
2.4
The current research
This research will add to the existing economic literature in two ways. First, a spillover effect of overconfidence between unrelated tasks has not yet been studied. There is a psychological foundation for the effect and studies have shown that overconfidence gained by past success influences behaviour and judgement in similar tasks, even for professionals such as CEOs and man-agers. Second, this research adds to the small body of experimental literature that currently exists about the relationship between confidence and perfor-mance in a real effort task.
3
Method
3.1
Respondents and instructions
To answer the research question an online experiment was created in qualtrics. Through email, messages on multiple social media outlets, and in person, 136 respondents were recruited. Although some of the respondents have social ties with the researcher, none of them knew what the experiment was about. All they knew before starting the experiment was that it would take 15 to 20 minutes to complete. Every message that was send to the respondents included a link to the experiment.
After clicking on the link respondents were faced with the first set of instructions. These included general information about the two tasks that they were going to encounter during the experiment as well as an explanation of the possible payment. Most importantly, these instructions stressed that the experiment had to be completed in one sitting and told the respondents to remain focussed throughout the experiment. The experiment was set up in the following way. After reading the instructions respondents had to complete the first task, a 10 item quiz. Upon completion, their belief about placing in the top half of quiz-takers was elicited. The belief elicitation was followed by the second task. After the second task, beliefs about placing in the top half of this task were elicited. The experiment was concluded after respondents filled out a short questionnaire.
In total, the respondents could earn up to 50 points throughout the ex-periment. They were told that every right answer would increase their score by one point and that every point would be converted to 50 cents. Therefore, respondents could earn up to 25 euros from their score alone. In addition, the
respondents could earn 5 euros for the belief-elicitation questions. The out-come of one of these questions would be added to their total earnings. This means that respondents could earn a maximum of 30 euros by participating in the experiment. Respondents were informed that after all responses were collected, 5 respondents would be randomly selected to be paid according to their performance.
On average, the randomly selected respondents earned 18.3 euros.
3.2
First task - Quiz
The first task consisted of 10 Raven matrices. These type of questions are often used in IQ tests and have been developed to measure a person’s logical reasoning skills. Respondents were randomly selected into either the hard or the easy group. The only difference between these two groups was the difficulty of the first quiz 2. Overall, the setup of the first task is similar to
the setup of the first part of the experiment by Barron and Gravert (2018). There does exist one significant difference. In this experiment, respondents only had 60 seconds per question before being automatically moved to the next question. Respondents saw an example question before the start of the quiz to familiarize them with the type of question. After this example they were once again reminded of the time constraint per question.
The time constraint was implemented to limit the difference in time spend on the first task between the two groups. During a test-stage of the experi-ment it became clear that those who had been assigned the hard quiz were spending much more time on the first task than those who had been assigned the easy quiz (30 minutes and 10 minutes respectively). Since this difference could possibly influence the behaviour and judgement of the participants in the second part of the experiment, the decision was made to implement a time constraint. This implementation had two consequences. First, because the respondents were automatically moved to the next question after 60 sec-onds, some respondents might be too slow to select an answer. This created the opportunity for respondents to behave strategically. The strategy of se-lecting the first answer that seems correct and using the remaining time to verify the validity of this intuition ensures that no question goes unanswered. Respondents that used this strategy or a similar one might feel like they out-smarted others which could inflate their confidence of performing well on the
quiz. Second, the time constraint made both the hard and the easy quiz more difficult. However, this effect was stronger for the hard quiz than for the easy quiz. The benefit of ensuring that both groups spend the same amount of time on the first task outweighed these two small negative consequences.
The reason to use Raven matrices as a first task is twofold. First, Raven matrices are used to test, to a certain extent, intelligence. It is likely that most respondents like to think of themselves as intelligent as this is generally considered to be a desirable quality. Therefore, respondents have an intrinsic motivation to do well in this task. Furthermore, the fact that intelligence is a desired personal trait increases the likelihood that there will be a difference in confidence between the hard and easy group after the quiz3. Second, Raven
matrices have been used often by experimental economists (Schwardmann & Van der Weele, 2016; Mobius et al., 2011). More specifically, they have been used before in order to experimentally influence confidence (Barron & Gravert, 2018).
3.3
Second task - Cognitive slider task
The second task, which was the same for all respondents, was a novel adap-tation of the slider task that was originally developed by Gill and Prowse (2012). In the adaptation of this task, respondents had to position sliders such that the final position of each slider was exactly equal to the answer of the sum that was shown in front of the slider. An example can be seen in Figure 1. The instructions for this task stressed that this task should be done with a computer mouse. However, if the respondents had no mouse, it said a trackpad could be used too. After these instructions and three practice sliders, respondents had three minutes to position as many slider correctly as possible. In total, there were 40 sliders on the page, this number was chosen to ensure that nobody would finish all 40 sliders. Out of the 136 respon-dents, only one respondent managed to correctly position all 40 sliders. On average respondents positioned 23 sliders correctly. Approximately 56% of the respondents used a mouse (76 out of 136).
3This claim is based on experimental literature that shows that following good or bad
information about their ability, people generally update their beliefs about a certain skill or trait more if they care about this skill or trait (Eil & Rao, 2011; Mobius et al., 2011). However, there is no clear consensus on this phenomenon as Coutts et al., (2018) provide evidence that disputes these earlier findings.
Figure 1: Example slider
In the original slider task, subjects were asked to position as many slid-ers on precisely on the number 50 in two minutes. The slider task in this experiment differed slightly in two respects. First, subjects had to solve a (simple) sum to determine where the slider should be positioned to increase their score by one point. Second, due to this sum, subjects had to position the slider to a different number each time, as opposed to the same number every time in the original setup of the task.
This adaptation of the slider task was designed to add a small, cognitive element to the task. Some of the literature discussed in the previous section showed that professionals tend to become overconfident after a success (Billet & Qian, 2008; Puetz & Ruenzi, 2011). This shows that an increase in con-fidence about performance in a task influences judgement in a subsequent, similar task. Since success in the first task of the experiment is dependent on the cognitive ability of the subject, their confidence about their cogni-tive abilities is most likely affected. Therefore, adding a cognicogni-tive element to the slider task increases the likelihood of a confidence spillover. How-ever, the amount of cognitive ability needed to do well in the second task is deliberately kept at a minimum. After all, the main research question is whether overconfidence spills over to unrelated tasks. Furthermore, due to the minimal cognitive strain of the second task, performance in this task is still mostly determined by the amount of effort the respondent exerts. This enables the analysis of a possible relationship between confidence and effort. Due to the online nature of the experiment, the slider taks was one of the few options to measure said relationship. Furthermore, the task is simple to explain and requires no pre-existing knowledge, making it ideal for an online experiment.
3.4
Belief-elicitation
Beliefs were elicited using a simplified version of the Becker-DeGroot-Marschak procedure which is also known as the “crossover method” or “reservation probabilities method”. The normal procedure works in the following way. First, subjects are made aware of two possibilities:
1. You win 5 euros if your score is in the top 50% 2. You win 5 euros with probability z
Subjects then indicate their subjective probabilities of placing in the top 50% which is denoted as x. Next, a random number is drawn to determine the value for z. This number is drawn from a uniform distribution of all probabilities. If the drawn value for z is lower than x, the subject is paid 5 euros if their score was in the top 50%. If the drawn value for z is higher than x, the subject is entered into a lottery where they win 5 euros with probability z. This procedure ensures that subjects maximize their payoff by truthfully reporting their subjective probability of placing in the top 50%, regardless of their risk-preferences4. Other belief-elicitation mechanisms that
are often used, such as the quadratic-scoring rule, make the assumption that the subjects are risk-neutral, which is widely known not to be the case for most individuals (Rieger et al., 2014). Moreover, Hollard et al., (2010) com-pared the reservation probabilities method with the quadratic-scoring rule and found that former yielded more accurate beliefs.
Although the reservation probabilities mechanism is theoretically optimal, there are some practical problems related to it. First and foremost, the mechanism is difficult to understand. Explaining the mechanism to students to a point of understanding takes approximately 15 minutes (Buser et al., 2018). However, many respondents in this study are not students and have not been exposed to any form of statistics for years. Fully explaining the mechanism would therefore take too long and possibly make the subjects frustrated or confused. Ultimately there was no guarantee that the subjects completely understood the mechanism since they could not ask questions. Therefore, respondents were not given a full explanation. Rather, they were simply asked to indicate how likely they thought it was that their score put them in the top 50% of all respondents5. It was stressed that being truthful
4Proof for this claim is given in Appendix A.
maximized their chance of adding 5 euros to their accumulated earnings. At the very end of the experiment respondents could follow a link with a full explanation as well as the mathematical proof.
This implementation of the mechanism is not ideal. However, in order for the data to be usable, the respondents do not need to fully comprehend the mechanism. Important is that their stated probabilities reflect their true subjective probabilities. Due to the phrasing of the questions, respondents had no monetary incentive to report anything other than their true subjective probabilities.
Lastly, after the second task, respondents were asked to report the sub-jective probability of placing in the top half of those who used the same tool for the second task as them. It is easier to position sliders correctly when using a mouse compared to a trackpad. If respondents that used a track-pad would compare themselves also to those who used a mouse, it would be rational for them to lower their estimates. Similarly, those who used a mouse would rationally shift their subjective probability upwards. Speci-fying that they would only be compared to those who used the same tool ensured that there was no significant difference in beliefs between those who used a mouse (M = 63.67, SD = 21.10) and those who used a trackpad (M = 60.82SD = 24.00); t(120.13) = 0.073, p = 0.469.
3.5
Questionnaire
Finally, after the subjects reported their beliefs for the second time, they were presented with a short questionnaire. This questionnaire contained questions about personal characteristics such as gender, age, nationality, and the mood of the respondent throughout the experiment. Furthermore, the questionnaire contained a question where the respondents could indicate the difficulty of the two tasks on a scale of 1 to 10. The answers to these questions showed that on average the hard test (M = 8.59, SD = 1.38) was rated significantly harder than the easy test (M = 6.15, SD = 1.97); t(133.158) = 8.475, p < 0, 001. After answering all the questions the respon-dents were thanked for their participation and were shown a link that directed them to the full explanation of the payoff mechanism for the belief-elicitation questions.
4
Hypotheses
With this experimental design, three hypotheses will be tested. First, since overplacement is usually found after easy tasks, and hard tasks have been found to lead to underplacement, it is expected that there will be a difference between the average stated beliefs between respondents that faced that hard quiz and respondents that faced the easy quiz during the first part of the experiment.
Hypothesis 1: The average subjective probability of placing in the top half in the first task will be significantly higher for those who faced the easy quiz.
The second hypothesis relates to the spillover effect of overconfidence. The extensive psychological work by Brinol et al. (2010) shows that confidence can lead to a bias in judgement. Confidence leads to more positive thoughts and it increases the validity of self-relevant thoughts. Therefore, confident individuals that have to indicate the probability with which they placed in the top half of respondents, are likely to report a higher probability than those with less confidence. Furthermore, it has been shown that affirming an unrelated aspect of an individual increases the confidence of said individual (Binol et al., 2007; Mcgregor et al., 2001). Ultimately, if the first hypothesis is confirmed and the first quiz lead to a difference in confidence between the two treatment groups, it is likely that respondents in the easy group will report a higher average subjective probability of placing in the top half in the second task.
Hypothesis 2: The average subjective probability of placing in the top half of the second task will be significantly higher for those who faced the easy quiz.
The third and final hypothesis relates to the relationship between confidence and performance. The existing literature is ambiguous about this relation-ship. The theoretical model by Compte and Postlewaite (2004) predicts a positive relationship. According to this model, overconfident individuals ex-ert more effort in tasks than non-overconfident individuals. Therefore, this model predicts that respondents in the easy group who experienced an up-ward shift in their confidence, will exert more effort in the second task. Since performance in this task is almost entirely dependent on effort, respondents
in the easy group should perform better than those in the hard group. How-ever, experimental evidence contradicts this theoretical prediction. Barron and Gravert (2018) found that an exogenous shift in confidence did not affect the amount of effort subjects exerted. Since the experimental design of this research is similar to that of Barron and Gravert, it is expected that there will be no difference in performance between the hard and the easy group.
Hypothesis 3: Those who faced the easy quiz will not perform differently in the second task from those who faced the hard quiz.
5
Results
5.1
Treatment effect
The 136 respondents were randomly faced with either the hard or the easy version of the first task. From this point these groups will be referred to as the “hard group” and “easy group” respectively. Table 3 in the appendix presents a summary of the core characteristics of these groups. Panel A shows that the percentage of Dutch speakers and women was identical across groups. Likewise, the average age did not differ between the groups. However, the table also shows that the easy group is bigger than the hard group by 14 respondents. This is probably due to people not completing the experiment because they found the first task too difficult. The possible ramifications of this difference will be discussed in the next section.
The first hypothesis was based on the hard-easy effect and stated that the average belief of placing in the top half of the first task would be higher in the easy group. Figure 2 shows these beliefs. The hard-easy effect was indeed present. On average, those who were faced with the easy quiz stated a significantly higher average belief (M = 55.39, SD = 24.00) than those who faced the hard quiz (M = 26.52, SD = 21.66); t(134.50) = 7.368, p < 0, 01. The manipulation of relative confidence of the two groups was therefore effective and the first hypothesis is confirmed. However, the stated beliefs of both groups did not constitute overconfidence. In the easy group, a small majority of 56% believed they placed in the top half. Although this means that some of the people held an inflated belief and were overconfident in their performance, tests showed that there was no real overplacement in the
easy group6. Moreover, the average belief of the easy group is statistically
indistinguishable from 50 (two-sided t-test; t(74) = 1.947, p = 0.055). Figure 2: Mean belief first task
Note: Vertical lines indicate 95% CI around the mean
In the hard group, only 15% of the respondents believed that they placed in the top half with the average belief of placing in the top half being ap-proximately 27%. Therefore, there is apparent underplacement in the hard group. In the appendix the reported beliefs of the hard group are tested for ”real” underplacement. Real underplacement is present if the reported beliefs can not be rationalized in a Bayesian manner, indicating irrational beliefs. Appendix D shows that the hard group indeed exhibited real under-placement.
To verify that the treatment of facing a more difficult quiz caused the difference in the average reported belief between the two groups, an OLS regression was performed. The results of two specifications can be found in Table 1 in columns 1 and 2. In both regressions, the dependent variable was the reported belief of placing in the top half of the first quiz, expressed as a percentage.
The first column shows the output of a simple regression where the only explanatory variable is a dummy variable that equals one if the respondent was in the hard group. The significantly negative coefficient shows the nega-tive relationship between being in the hard group and reported belief. In the second column, the simple regression is extended with additional explanatory variables. The variables Dutch and Female are both dummy variables that take the value of one if the respondent is Dutch or female respectively. The third added variable captures the age of the respondents.
Following, there are four dummy variables that capture the mood of the respondents throughout the experiment. The effect of each mood is always compared to the respondents that felt neutral. Lastly, the variable Top indicates whether or not a respondent truly placed in the top half of their respective quiz.
This specification shows a negative relationship between age and reported belief. Older respondents reported a significantly lower belief, with a differ-ence of approximately 1 point per four years. Unsurprisingly, respondents that truly did place in the top half of their quiz reported a higher belief than those who placed in the bottom half. Most importantly however, after adding these variables the treatment effect remains. Ceteris paribus, respon-dents that made the hard quiz reported a belief that was, on average, 24 points lower than those who made the easy quiz. The effects of gender and mood are discussed in subsections 5.4 and 5.5 respectively.
The third and final column in Table 1 shows the output of a logistic regression in which the dependent variable is the dummy variable Top. This column shows which variables impacted the chance of placing in top half of the first task. The insignificant coefficient for the Hard variable shows that respondents in the hard group did not face a lower probability of placing in the top half, even though they believed they did. Furthermore, it shows that only the age of the respondents impacted the chance of placing in the top half. The coefficient for the Age variable is significantly negative, indicating that older respondents were less likely to place in the top half of quiz-takers. This finding rationalizes the negative relationship between age and reported belief that was mentioned earlier.
5.2
Spillover effect
signifi-Table 1: First task regressions
(1) (2) (3) Belief Belief Top
OLS OLS Logit Hard -28.9∗∗∗ -24.0∗∗∗ -0.28 (3.92) (3.59) (0.42) Female -8.88∗ -0.39 (3.69) (0.41) Age -0.24∗ -0.057∗∗∗ (0.10) (0.014) Dutch 0.28 0.081 (4.79) (0.52) Frustrated -9.48 -0.82 (5.68) (0.66) Happy 17.3∗∗ -1.44 (6.00) (0.90) Stressed -4.12 -1.12 (4.66) (0.68) Bored -11.9 -1.34 (6.59) (1.13) Top 16.7∗∗∗ (3.87) cons 55.4∗∗∗ 62.6∗∗∗ 2.29∗∗∗ (2.77) (6.98) (0.67) N 136 136 136 R2 0.284 0.555 Robust standard errors in parentheses
the two groups was therefore successfully manipulated.
The second hypothesis stated that the easy group would report a higher average belief of placing in the top half of the second task than the hard group. This would be evidence of a spillover effect of confidence. The average belief of the hard group (M = 63.51, SD = 21.15) does not significantly differ from the average stated belief of the easy group (M = 61.52, SD = 23.45); t(134.58) = 0.520, p = 0.605). The difference in confidence that was induced by the first task did not manifest itself in the beliefs of the respondents about their performance in the second task. To further verify this conclusion, an OLS regression was performed.
The results from the regression can be found in Table 2. The first column shows that there is indeed no relationship between the stated belief of placing in the top half in the second task and facing the hard quiz during the first task. The regression with only the Hard variable as explanatory variable is, as a whole, insignificant; F (1, 134) = 0.27, p = 0.605. Column 2 shows that extending this regression with the same set of variables as before, with the addition of the dummy variable Mouse which equals one if the respondent used a mouse during the second task, does not change the conclusion about the treatment effect. According to the second hypothesis the coefficient of the Hard variable should be significantly negative. However, the coefficient remains positive and insignificant. There is therefore no statistical evidence that the confidence manipulation from the first task persisted into beliefs about performance in the second task and the second hypothesis is rejected. Similar to before, column 3 shows the output of a logistic regression with the dummy variable Top as dependent variable. Naturally, in this case this variable equals one if a respondent placed in the top half of the second task. Column 3 shows that respondents in the hard group were equally likely to place in the top half as respondents in the easy group. It also shows that, just like before, the chance of placing in the top half decreased with age. Interestingly, older respondents did not report a lower subjective probability of placing in the top half.
5.3
Effect on performance
The third hypothesis stated that there would be no difference in perfor-mance between the hard and the easy group. A comparison of the means shows that this is most likely the case. The average score of the hard group
Table 2: Second task regressions
(1) (2) (3) (4) Belief Belief Top Score
OLS OLS Logit OLS Hard 1.99 7.16 0.26 2.76∗ (3.87) (3.76) (0.44) (1.06) Female -9.81∗∗ -0.31 -1.85 (3.34) (0.41) (1.09) Age 0.18 -0.053∗∗∗ -0.21∗∗∗ (0.11) (0.015) (0.032) Dutch -2.45 -0.032 -0.0047 (4.65) (0.57) (1.66) Mouse 1.93 0.75 5.21∗∗∗ (3.83) (0.45) (1.03) Frustrated -0.086 -1.92∗ -4.16∗∗ (6.43) (0.83) (1.44) Happy 18.6∗∗∗ 1.21 5.41∗ (4.45) (0.93) (2.24) Stressed -3.73 0.83 1.40 (4.39) (0.54) (1.38) Bored -23.3∗∗ 1.00 4.67 (8.85) (1.00) (4.08) Top 21.4∗∗∗ (3.28) cons 61.5∗∗∗ 48.9∗∗∗ 1.54∗ 28.6∗∗∗ (2.59) (6.32) (0.65) (1.84) N 136 136 136 136 R2 0.002 0.370 0.419 Robust standard errors in parentheses
not significantly different from each other; t(132.22) = 0.327, p = 0.745. However, a regression analysis shows that this conclusion is premature. The fourth column in Table 2 shows the result of an OLS regression with the score in the second task as dependent variable. The coefficient for the Hard variable is positively significant. This indicates that the respondents in the hard group scored better in the second task than those in the easy group, seemingly contradicting the earlier finding that the average score of the two groups is the same. The explanation for this paradoxical result lies in the Mouse variable. Using a mouse during the second task has a positive ef-fect on the obtained score, as is shown by the significant coefficient for the Mouse variable. Furthermore, Table 3 shows that the percentage of people that used a mouse is significantly higher in the easy group. Therefore, the average score of the easy group was shifted upward due to the higher mouse usage in said group. After controlling for this effect the true effect of the treatment remains, which is positive. Lastly, the regression output shows that frustrated respondents scored lower and happy respondents higher than their neutral counterparts.
In conclusion, facing a hard quiz during the first stage of the experiment increased the performance during the slider task. The third hypothesis is therefore rejected.
5.4
Gender differences
The regressions in columns 2 of Table 1 and Table 2 show another, unhypoth-esized result. In both these extended regression specifications, the estimated coefficient for the dummy variable Female is significantly negative. This indicates that women reported a lower subjective probability of placing in the top half than men. The difference was slightly more pronounced after the second task, where women reported a belief that was on average almost 10 percentage points lower than that of men. After the first task women re-ported a belief that was on average nearly 9 percentage points lower. Figures 4 and 5 in the appendix show the distribution of the male and female beliefs graphically.
This finding could be rationally explained if women were really less likely to place in the top half than their male counterparts. To verify whether this was indeed the case, we again turn to the output of the two logit regressions that show which variables impacted the chance of placing in the top half of
in the third column of Table 1 and 2 respectively. The conclusion is the same for both the first and the second task. The coefficient for the Female variable is insignificant in both cases, indicating that women were not really more unlikely to place in the top half then men were.
The finding that women were less confident in their performance is consis-tent with, and adds to, the general consensus that men are more often over-confident than women that exists in the literature. For instance, men have found to be more confident in their cognitive abilities such as mathematical prowess (Ross, Scott, & Bruce, 2012), and are generally more overconfident in their chance of winning a competition (Buser, Niederle, & Oosterbeek, 2014; Niederle & Vesterlund, 2007; Niederle & Vesterlund 2011; Van Veldhuizen 2017).
5.5
Mood differences
Another auxiliary finding from the regression analysis relates to the mood of the respondents. As mentioned, the extended regression specifications included the mood of the respondents as a dummy variable. These vari-ables were included because the mood of an individual can impact judge-ment (Angie et al., 2011). Indeed, column 2 of Table 1 shows that happy respondents reported a significantly higher belief of placing in the top half than respondents that indicated they felt neutral. Moreover, these happy respondents did not face a higher chance of placing in the top half, which is indicated by the insignificant coefficient for the Happy variable in column 3 of Table 1.
In the second task, happy respondents again reported a higher subjec-tive probability of placing in the top half. Additionally, bored respondents held a significantly lower belief of placing in the top half than their neutral counterparts. However, happy respondents were not more likely and bored respondents were not less likely to place in the top half in the second task. Rather, from column 3 in Table 2 we can see that only frustrated respondents were significantly less likely to place in the top half, a finding that was not reflected by their reported beliefs.
However, due to a possible endogeneity problem, the estimated coefficient for the mood variables should be interpreted with care. Respondents that believed that they did well (ie reported a high belief) might be happy because of this positive self-image. Similarly, respondents that performed relatively poorly, or atleast thought they did, might be more likely to indicate that they
felt frustrated or bored. Therefore, there exists reverse causality between the stated belief of placing in the top half and the mood of a respondent. The estimated coefficients for the mood variables in the regressions in column 2 of both Table 1 and Table 2 are therefore possibly biased.
Despite the possible endogeneity problem, the finding that happy respon-dents reported a higher belief is consistent with previous literature (Brinol et al., 2007; Huang & Goo, 2008; Russo & Schoemaker, 1992). However, all the respondents that indicated that they felt happy were in the easy group. This might be an alternative explanation as to why these respondents reported a higher belief after the first task. The full distribution of beliefs of the hard and the easy group is shown in Figure 3 below.
6
Discussion
6.1
Spillover effect
The findings from the previous section have led to the conclusion that the dis-crepancy in confidence created by the first task did not manifest itself in the stated beliefs about performance in the second task. The second hypothesis was therefore rejected. However, since both quizzes in the first task were per-ceived as difficult by most respondents, neither the hard nor the easy group exhibited overconfidence. The question about the existence of a spillover ef-fect of overconfidence therefore remains unanswered. Although both quizzes were perceived as difficult, respondents indicated that they found the hard quiz significantly more difficult. Consequently, respondents in the hard group reported a significantly lower average subjective probability of placing in the top half. These beliefs showed evidence of real underplacement. Therefore, the findings presented in the previous section suggest that a spillover effect of underconfidence does not exist.
It should be noted that the absence of a spillover effect of underconfidence does not mean a spillover effect of overconfidence does not exist. The main reason for a possible spillover effect of overconfidence comes from the ten-dency of overconfident individuals to underestimate their mistakes, increase the validity of positive self relevant thoughts, and a desire to maintain a pos-itive self-image. However, a lack of confidence does not necessarily lead to a bias in judgement in subsequent tasks. On the contrary, individuals with a low confidence tend to process information more carefully and engage in more self-thought than their confident counterparts (Tiedens & Linton, 2001; Weary & Jacobson, 1997). This is mostly due to the fact that overconfident individuals do not feel a need to carefully examine information that could alter their current self-view. Ultimately, a spillover effect of overconfidence might therefore still exist.
6.2
Direct treatment effect
The analysis in the previous section looked at the effect of the treatment of making a harder quiz on both confidence and the performance in the second task. However, this analysis did not consider the possibility of an indirect treatment effect. If there exists a relationship between performance in the second task and confidence in the second task, and the treatment impacted
both confidence and performance, there exists an indirect treatment effect on confidence through performance. Moreover, the estimated treatment effect in column 2 of Table 2 likely suffers from omitted variable bias.
To find an accurate estimation of the direct treatment effect, the indi-rect treatment effect needs to be controlled for. A simple solution would be to add the obtained score as an explanatory variable in the regression. The output for this regression is shown in column 2 of Table 4 in the ap-pendix. This is problematic however due to the likely reverse causality that exists between performance and belief. The assumption of reversed causality is based on both theory and intuition. The idea that higher performance leads to a higher belief is quite intuitive. Moreover, the results showed that respondents that placed in the top half stated significantly higher beliefs than those who did not, which verifies this intuition. The assumption that a higher belief leads to an increase in performance comes from the theory of ’the motivational value of overconfidence’ which has been tested by Chen and Schilder-H¨orisch (2018). The estimated direct treatment effect, which is shown by the coefficient for the Hard variabel, is therefore still biased in this specification.
The reversed causality issue between performance and reported belief can be resolved by running an instrumental variable regression where the en-dogenous variable Score is instrumented by a valid instrument. I propose the dummy variable Mouse to be such an instrument. In order for an instrument to be valid it has to be both relevant and exogenous. The regression output in column 4 of Table 2 shows that the Mouse variable significantly increases the score of a respondent in the second task, making Mouse a relevant in-strument. The second condition, exogeneity, can not be tested in case of exact indentification. Still, since using a mouse only impacts beliefs through its impact on performance7, and there are no obvious, systematic differences
between people who use a mouse or a trackpad, I assume the instrument to be exogenous. With this assumption, Mouse is a valid instrument for per-formance in the second task. Furthermore, Mouse is a strong instrument. The results of the first stage regression showed that Mouse was significant with an F-statistic of 34.59, well above the rule of thumb value for strong instruments of 10.
The output of the IV regression in which Score is instrumented by Mouse is given in column 3 of Table 4. In this specification, the estimated coefficient
for the Hard variable is an accurate estimation of the direct treatment effect. The coefficient remains positive but insignificant. Therefore, after controlling for the true effect of performance on confidence, there is no strong statistical indication of a direct treatment effect. Lastly, the coefficient for the Hard variable in the first column captures both the direct and the indirect treat-ment effect. Since the coefficient in the third column only captures the direct effect, the indirect treatment effect is given by the difference between the two coefficients. The coefficient is higher in the first column, indicating that there was indeed a positive indirect treatment effect.
6.3
Selection effect
The results section mentioned that the fraction of mouse users was signif-icantly larger in the easy group. Since using a mouse is positively related to score in the slider task, the average score of the easy group was inflated. Therefore, even though a comparison of means showed no difference between performance of the groups, controlling for mouse usage in the regression anal-ysis showed an unexpected result. On average, respondents in the hard group positioned an extra three sliders correctly compared to respondents in the easy group. This finding differs from earlier findings where an exogenous shift in relative confidence did not have an impact on exerted effort (Barron & Gravert, 2018).
The most plausible explanation for the finding that respondents in the hard group performed better than those in the easy group is a selection effect. In the previous section it was mentioned that the easy group was bigger than the hard group by 14 respondents. From personal feedback it became clear that a number of prospective respondents did not finish the experiment because they found the first quiz too difficult. Naturally, this happened more often when people were shown the harder version of the first quiz. Since respondents that were unwilling to try their best were filtered out, the hard group consisted of a higher percentage of highly motivated respondents. In turn, the highly motivated respondents exerted more effort and thus performed better in the slider task.
6.4
Online experiment
Finally, the online nature of the experiment gave rise to a couple of problems. First there was the aforementioned problem of the selection effect. Second,
there was a substantial loss of experimental control. In one of their first publications about the slider task, Gill and Prowse (2012) mention that per-formance in this task is positively related with screen size and can depend on the mouse that is used. In order to establish an even playing field, they there-fore stress the importance homogeneity in the usage of equipment amongst subjects. This could not be enforced in this research. Similarly, there was no way to verify whether the subjects remained focussed on the experiment. Lastly, explaining difficult payoff mechanisms, such as the reservation proba-bilities method, became even more challenging than it is normally. Although, the adaptation of this belief elicitation mechanism that was used should lead to similar reports as the original version of the mechanism, whether or not it did is uncertain.
7
Conclusion
This research was a first attempt to experimentally find a spillover effect of overconfidence. A spillover effect of overconfidence would exist if individu-als that have their confidence exogenously shifted upward perpetuate this positive self image in a subsequent, unrelated task. However, the confidence manipulation lead to underconfidence amongst respondents instead of over-confidence. Therefore, the question about the existence of a spillover effect of overconfidence remains unanswered. The results of this research do however suggest that a spillover effect of underconfidence does not exist.
Given the possibly large economic consequences of, and the compelling theoretical background for, the spillover effect of overconfidence, future re-search should attempt to answer this open question. The methodology from this research can easily be altered in order to be able to prove or disprove the existence of the spillover effect. For instance, using the exact same setup with easier quizzes during the first task should lead to overconfidence such that inferences about the existence of the effect can be drawn. The second task however, need not be an adaptation of the slider task. Rather, in a laboratory setting, a second task can be created such that it more closely relates to the daily tasks that managers and CEOs face.
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Appendix A. Proof Belief elicitation
The BDM belief mechanism elicits truthfull beliefs regardless of risk prefer-ences. This section will show the mathematical proof. Recall the respondents are paid according to one of the following circumstances:
1. Respondents win 5 euros if their score is in the top 50% 2. Respondents win 5 euros with probability z
The subjective probability of subjects will be denoted by x. z is a probability drawn from a uniform distribution. If z is lower than x, the subject is paid 5 euros if their score was in the top 50%. If the drawn value for z if higher than x, the subject is entered into a lottery where they win 5 euros with probability z. Therefore, the probability of winning the 5 euros is expressed by the following formula:
P (winning) = P (winning|z > x) · P (z > x) + P (T op) · P (z < x)
In this formula P (T op) indicates the probability that a particular respondent placed in the top half. Henceforth this will be denoted as y. Since z is uniformly distributed, P (z < x) = x and P (z > x) = 1 − x.Furthermore, P (winning|z > x) = 1+x2 . The formula for winning therefore becomes:
P (winning) = (1 − x) · 1+x2 + xy
Now, we can find the value of x that maximizes the chance of winning. In order to do so we take the derivative of the probability formula with respect to x and set it equal to 0:
∂P (winning)
∂x = 0 ⇒ −x + y = 0
x = y
This shows that the probability of winning is maximized if the subjective probability that the respondent coincides with their actual probibility of
plac-placing in the top half but can approximate by stating their true subjective probability. The mechanism therefore elicits truthfull believes that do not depend on risk preferences.
Appendix C. Tables and Figures
Figure 4: Belief distribution first task
