Relative Pay-off Concerns
and Risk-taking
How does a social ranking influence choice behavior
for decisions under risk?
Thesis by Esmée Zwolsman (11141018)
Supervised by Prof. Dr. Joep Sonnemans
MSc Economics
Track: Behavioural Economics and Game Theory
15 ECTS
Abstract. This paper investigates whether risk attitudes are influenced by relative payoff concerns. In an online experiment participants make lottery choices that differ in risk for which the earnings count towards a balance that is presented in a ranking together with the balances of earnings of two peers. As the ranking is not pay-off relevant, decision-making behaviour is likely motivated by a concern for status.
Comparing behaviour between an individual condition and a ranking condition, this paper examined whether subjects change their decision conditional on their position in the ranking.
The results show that participants are relatively less risk averse when placed first or last in the ranking. Whilst participants are more risk averse when placed second in the ranking.
1 Introduction
Scholars have long considered relative wealth and status concerns to be an important driver of human behaviour. According to Veblen (1899), people can only appreciate own income through a comparison with the incomes of their peers. He notes that people have relative income concerns as they participate in conspicuous consumption as a means to signal social status by impressing others. Yet, traditional economic models have focused primarily on economic behaviour where individuals derive utility or well-being only from absolute income and absolute consumption levels.
In the last two decades, economics literature is challenging this traditional view by also considering the role of social comparison and relative income concerns for individual well-being. For instance, research shows that relative income concerns influence happiness (Vendrik & Woltjer, 2007; Luttmer, 2004) and affect job performance (Gneezy & Rus-tichini, 2000) as well as job satisfaction (Card et al., 2012). Relative income concerns have also been examined in numerous laboratory experiments, from which many social preferences models have been introduced to explain the observed behaviour. Fehr and Schmidt’s (1999) well-known model of inequity aversion, for example, shows that most individuals dislike earning less and/or dislike earning more than others. Today, the focus of research has advanced on how relative concerns influences decision-making behaviour, in particular on decisions under risk.
The importance of understanding risk-taking behaviour motivated by relative concerns is emphasized by the excessive risk-taking in the financial industry in the run-up to the financial crisis, for which the bonus culture and the tournament incentives in this industry have been identified as one of the causes (Rajan, 2006; Diamond & Rajan, 2009). However, it is not just risk attitudes of financial professionals that are affected by relative concerns. Also private investors are found to be influenced by their peers when purchasing risky assets. A paper by Brown et al. (2008) for example, shows that households are more likely to participate in the stock market if their neighbours do. This suggests that risk attitudes are influenced by what others do and by what others have.
Statement of Originality
This document is written by Esmée Zwolsman 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 supervision of completion of the work, not for the contents.
Despite empirical evidence on the influence of relative income concerns on risk-taking be-haviour, the understanding of how and for whom these concerns influence risk attitudes is still limited. In line with Veblen (1899), this paper posits that relative income concerns are driven by an aspiration for social status, where status depends on an ordinal distri-bution of earnings. Besides the utility derived out of absolute earnings, higher earnings may therefore also increase utility through higher social status.
This paper investigates experimentally whether risk attitudes are influenced by the earn-ings of others. By providing an ordinal rank of earnearn-ings that includes the earnearn-ings of two peers, it examines how one’s position in a social ranking of earnings affects risk-taking behaviour through a concern for status. As such, this paper predicts that participants on the bottom of the ranking are risk seeking in order to achieve higher status, and that participants on the top of the ranking are risk averse in order to keep their high status. It furthermore predicts that those in the middle of the ranking will be relatively risk averse to try to avoid falling into the last place.
Risk attitudes are measured by letting participants choose between ten lottery pairs, once with and once without a social ranking. The social ranking provides the balances of earnings, which are based on the accumulated earnings of previous questions. Since the ranking is not pay-off relevant, that is, participants will be paid according to their final balance and not according to their position in the ranking, behaviour is likely motivated by status concerns.
This paper finds, in contrary to the predictions, that participants are less likely to choose the safe lottery when they are in the top of the ranking. The results show that those on top and on the bottom of the ranking choose the risky lottery relatively more often. Whilst participants choose the safe lottery relatively more often when they are in the middle of the ranking. This result suggests that risk seeking behaviour occurs for individuals both in the top and in the bottom of an income distribution. Furthermore, it suggests that individuals in the middle and the bottom of the ranking try to avoid and get out of the last place respectively.
This paper is structured as follows. Section 2 discusses relevant literature and existing work on social comparison and risk-taking behaviour. The experimental design and the hypotheses are described in Section 3. Section 4 reports on the results and its limitations. Finally, Section 5 concludes and discusses possible behavioural implications of the results.
2 Related Literature
Social status is derived out of one’s position in a ranking of individuals, based on traits, assets and actions (Weiss & Fershtman, 1998), as a ranking allows a straightforward identification of one’s relative position or status. Hence, the term "rank incentives" is generally used to describe a concern for rank, which is not driven by monetary rewards that comes with a higher ranking. Instead, rank incentives are considered to be driven by a desire for social status, which may be extrinsic by signalling one’s superior status to others (Moldovanu et al., 2007), or intrinsic by improving one’s self-image (Maslow, 1943). Therefore, people may also care about their relative position in a ranking if a ranking is not financially incentivized.
Indeed, studies find that behaviour is influenced by rank incentives. Recent evidence, for example, finds that relative performance feedback improves overall performance under students and workers (Tran & Zeckhauser, 2012; Azmat & Iriberri, 2010; Blanes i Vidal & Nossol, 2011; Delfgaauw et al., 2013). Even so, little research has been done on the relationship between relative concerns and risk-taking behaviour.
Most economic literature concerning rankings focuses on tournament incentives, and how effort effects and different payment schemes affect risk-taking (Lazear & Rosen, 1979). Tournament style payment schemes are generally regarded as promoting more risk-taking among competitors. For example, it is demonstrated that winner-take all tournaments lead to participants choosing maximum risk and zero effort (Hvide, 2002)). And ex-periments in the field show that promotion tournaments increase managerial risk-taking among senior executives for both financial and non-financial firms (Kini & Williams, 2012). However, the effects of rankings on risk-taking behaviour might not solely be caused by monetary incentives, it might be motivated by a desire for social status as well. There-fore, we might observe similar risk-taking behaviour when a ranking is no longer pay-off relevant.
More recently, literature has focused on rankings and its influence on risk-taking through a concern for status. In a theoretical model, Roussanov (2010) shows that the desire to "get ahead of the Joneses" is triggered by a concern for social status and that this causes a lower aversion to idiosyncratic risk than to aggregate risk. Krasny (2011) models the impact of status seeking among investors on portfolio choices. The author shows that low-status investors invest in highly risky assets that optimize their chances to move up the ladder, while high-status investors hedge against the assets chosen by the low-status investors out of concern to lose their high status.
Two experiments by Dijk et al. (2014) and Kirchler et al. (2017) study tournament incent-ives and portfolio choices and investigate whether rank incentincent-ives persist when a ranking
is not pay-off relevant. In both experiments subjects make portfolio choices between as-sets for multiple periods, while after each period subjects’ portfolio profits are compared with others in a ranking. The authors compare risk-taking behaviour by varying rank in-centives between treatments; a tournament treatment where only the top half in the rank distribution receives a pay-off, and a ranking treatment where the ranking is not monet-ary incentivized but where the pay-offs are a linear function of a subject’s accumulated profits. A treatment without rank incentives is also included to serve as a baseline. Dijk et al. (2014) find no difference in risk-taking behaviour between treatments. Even without monetary rank incentives, under-performers choose the positively skewed (risky) assets more often while over-performers mainly choose the negatively skewed (safe) assets. The authors conclude that the main driver of social competition in tournaments might not be the extrinsic monetary reward that comes with winning a competition, but the intrinsic desire for status. Conducting an experiment with financial professionals, Kirchler et al. (2017) also find no difference in risk-taking between treatments. They find that under-performers take more risk even when the ranking is not monetary incentivized.
The above-mentioned results indicate that individual’s preferences are also driven by relative status concerns and not by preferences over absolute earnings alone. However, Kirchler et al. (2017) replicate their experiment with a student subject-pool and find, in contrast to financial professionals, that students are not affected by rank incentives. They find that under-performing students take more risk only when the ranking is pay-off relevant. Kirchler et al. (2017) suggest that the different results for subject-pools might be explained by a higher concern for relative performance of financial professionals. This may be so, given the strong social competition and emphasis on performance in the financial industry.
The experimental results also report that finance professionals are more risk seeking in the baseline treatment. This could indicate that the different results of Kirchler et al. (2017) are driven by different risk preferences between subject-pools instead of different concerns for rank. Furthermore, during the experiment the finance professionals were aware that all other participants were finance professionals as well. According to Festinger (1954), social comparison is motivated by the similarities that individuals share, where the motivation to compare increases with similarity. One can imagine that finance professionals have more in common than students with different study backgrounds. As such, rank incentives might be stronger in the experiment with finance professionals.
When comparing the results of Kirchler et al. (2017) and Dijk et al. (2014), the latter do show identical behaviour of risk-taking for students in the ranking and tournament treatment. However, the results of Dijk et al. (2014) may also be explained by two aspects in which their paper differs. First, Dijk et al. (2014) let subjects choose between assets
that differ in skewness, while the assets in the experiment of Kirchler et al. (2017) differ in variance. And second, Dijk et al. (2014) do not control for preceding asset returns, while Kirchler et al. (2017) do.
According to Weber & Camerer (1998) investors are more likely to hold on to assets with negative returns than to assets with positive returns. A rational investor should do the exact opposite, as assets with negative returns are more likely to stay in a downward trend. This behavioural anomaly is called the disposition effect1, which is caused by a strong dislike for losses and an investor’s tendency to hold on to a losing asset in the hopes for higher future returns (Weber & Camerer, 1998). Therefore, as Dijk et al. (2014) do not control for asset returns, their results may be biased towards stronger rank incentives. In particular, because more risky or positive skewed assets increase the chance of being in the bottom of the ranking in case of negative returns, subjects may subsequently hold on to that risky asset in the hope for a turn-around in profits. The observed risk-taking behaviour of under-performers may therefore also be explained by the disposition effect. A closely related experiment by Kuziemko et al. (2014) also combines rank incentives and risk-taking. In their experiment a ranking of six participants is established by an initial distribution of money, after which all subjects choose between a risk-free and a risky lottery. While both options have the same expected value, the risky lottery comes with a possibility to move a place up in the rank. The authors find no difference between risk-taking for subjects across rank positions, except for subjects placed last in the ranking. Subjects placed last choose the risky lottery significantly more often. A result which the authors ascribe to last-place aversion.
The aforementioned experiments on rank incentives and risk-taking give incoherent res-ults. While Dijk et al. (2014) do find rank incentives to be robust when the ranking is not monetary incentivized, that is, under-performers taking more risk than over-performers, Kirchler et al. (2017) find similar results with financial professionals, but cannot replicate them with a student subject-pool. Moreover, Kuziemko et al. (2014) find that only par-ticipants placed last in the ranking take more risk, while parpar-ticipants placed above them in the ranking do not differ in risk-taking behaviour. This raises the question whether relative pay-off concerns are as prevailing when it comes to risk-taking behaviour, as rank incentives appear to be subsidiary to other factors such as private risk attitudes and perceived similarity between subjects.
Besides literature on rank incentives, a different strand of literature may also explain decision-making behaviour through relative income concerns, specifically, if the earnings of a peer serve as a social reference point.
The concept of a social reference point originates from Prospect Theory (Kahneman
& Tversky, 1979). For individual decision-making Prospect Theory suggests that risk attitudes depend on a reference point, often being current earnings. Specifically, people evaluate outcomes in losses and gains relative to a reference point, rather than focusing on absolute outcomes. The main prediction of Prospect Theory is called the reflection effect. This effect suggests that, relative to a reference point, individuals tend to be risk averse in the gain domain and risk loving in the loss domain. The reflection effect is mainly caused by loss aversion, the tendency to take on more risk to avoid a loss than to acquire an equal gain. In line with Prospect Theory, if earnings of a peer serve as a social reference point, a subject should exhibit risk seeking behaviour when own pay-off is less than a peer. Conversely, when own pay-off is above that of a peer, a subject should exhibit risk averse behaviour. However, experimental evidence on the validity and effects of social reference points is quite mixed.
A paper by Linde & Sonnemans (2012) examine whether the reflection effect is exhibited relative to the earnings of a peer. In their experiment subjects face binary lottery choices while being given the fixed earnings of a peer. When choosing, a subject could earn at most as much as their peer, establishing a loss situation, or at least as much as their peer, establishing a gain situation. However, their results do not support the predictions of Prospect Theory when applied to a social context, as Linde & Sonnemans (2012) find that subjects are risk averse in all choice situations, even more so when they can earn at most as much as their peer (when a subject is placed in a loss situation).
In contrast, a related paper by Gamba et al. (2017) shows that subjects are less risk averse when put in a loss situation compared to a small social gain situation. In their experiment participants are paired and given a low or a high wage at the end of completing the same work task. Informed about own and the wage of the other, participants then choose between lotteries that are presented in a multiple price list2. The choice outcome
is subsequently framed as a bonus on top of their wage. Their setup makes it possible to compare risk attitudes in large social gain situations (the other is allocated a lower wage), to risk attitudes in small social gain situations (the other is allocated the same wage) and to risk attitudes in loss situations (the other is allocated a higher wage).
Compared to subjects that received the same wage as their peer, Gamba et al. (2017) find subjects who received lower wages and subjects who received higher wages to choose the risky lottery more often. Given that this result indicates that risk seeking behaviour can occur in both social losses and social gains, their findings differ greatly from the results of Linde & Sonnemans (2012), as they find subjects to be predominantly risk averse in both the social loss and the social gain domain.
Gamba et al. (2017) point out that risk attitudes towards private reference points are
likely to interact with risk attitudes towards social reference points. In the experiment of Linde & Sonnemans (2012) the private reference points are not fixed, as subjects observe four possible lottery outcomes that, at the same time, serve as private reference points. This makes it harder to establish the reference point which a subject compares to. If the lowest outcome of the risky lottery acts as the main private reference point for example, choosing the safe lottery with a higher minimum and lower maximum outcome provides a certain gain. Whilst, the risky lottery with a lower minimum and higher maximum provides an uncertain gain. Given that people prefer certainty over uncertainty, this could help explain why subjects chose the safe lottery over the risky lottery more often. Hence, providing multiple private reference points may make a social reference point less relevant.
Nevertheless, as the aforementioned papers find behaviour to be either risk seeking or risk averse in both directions of a social reference point, it suggests that applying Prospect Theory to a social context may not explain relative pay-off concerns and risk-taking behaviour as hypothesized. However, what the experiments of Linde & Sonnemans (2012) and Gamba et al. (2017) have in common is that subjects cannot reverse the social ranking; they cannot earn more (less) than the other when they are behind (ahead). At most, when set in a loss situation, subjects can earn the same as their matched partner. Since a subject cannot change his or her absolute position in a social ranking, their experiments may be missing an important aspect that drives social behaviour, that is, a concern for status (Weiss & Fershtman, 1998).
According to Eaton & Eswaran (2003) a concern for rank is likely to be a direct result of evolution, as higher ranked individuals had better access to food and better chances to reproduce. Neurological evidence supports this claim with respect to relative pay-off concerns, as it shows that people react more strongly to advantageous inequality than disadvantageous inequality (Fliessbach et al., 2007; Bault et al., 2008). Including a concern for rank may therefore be an important aspect in explaining human behaviour in a social environment.
To my knowledge there is only one study that examines the effects of a social reference point where a social ranking can be reversed, a study by Schwerter (2013). In Schwerter’s experiment, subjects choose among lotteries while keeping the earnings of a peer fixed. These fixed earnings could either be high or low. The more risk a subject takes the higher the possible earnings, making it possible to outperform a peer. Schwerter (2013) finds that participants take on average more risk when confronted with a peer who receives a high fixed payment than when confronted with a peer that receives a low fixed payment. This finding is consistent with the hypothesis that a social reference point induces risk-taking behaviour as predicted by Prospect Theory. The author therefore interprets this
finding in favour of social loss aversion, as subjects are more likely to take risk when they can surpass their peer than they would if they are already ahead of their peer.
This paper extends existing work on the effects of social comparison and risk-taking behaviour by adding a ranking component that can be reversed. Following literature on social influences, an important motivation for individuals to compare own outcome with outcomes of others is whether those outcomes of others are considered to be relevant (Trautmann & Vieider, 2012). This paper attempts to strengthen relevance of others through a concern for rank. In addition, it examines whether risk-taking behaviour is distinctive for those who are in the middle of a ranking, by including a ranking where subjects’ earnings are presented together with the earnings of two others instead of one. Furthermore, this paper distinguishes itself from previous studies on rank incentives, as it compares risk attitudes in a social context to risk attitudes in an individual context. Therefore, it refrains from investigating whether rank incentives persist if a ranking is no longer pay-off relevant. Since participants choose between lotteries instead of assets, this paper eliminates the possibility that behaviour is influenced by the disposition effect.
3 Methodology
This paper studies the effects of a social ranking on risk-taking behaviour by conducting an experiment. In this section the experimental design, the hypotheses to be tested and the experimental procedures will be described.
3.1 Experimental Design
The experiment aims to examine the effects of a social ranking on risk-taking behaviour, using a within-subject design. It consists of two treatments, an individual treatment and a ranking treatment. In each treatment participants face ten choice-situations where they are asked to choose between two lotteries, a risky lottery and a safe lottery. The lotteries that participants face in the individual treatment are presented in a different order and are slightly altered in values from the lotteries used in the ranking treatment, but have equivalent variances to compare risk-taking between treatments. Three lottery pairs with negative earnings are included to compare decision-making behaviour between positive and negative outcomes. The lottery choices can be found in Appendix A.
In each choice-situation a subject is asked to choose between two lotteries, a risky lottery with a lower minimum and higher maximum outcome, and a safe lottery with a higher minimum and lower maximum outcome. Past research has found that most individuals
are risk averse (Holt et al., 2002). Therefore, six out of ten lottery pairs have a higher expected value when choosing the risky lottery compared to the safe lottery.
Participants partake in the individual treatment first, where after each choice, a parti-cipant is informed of the outcome of the chosen lottery. The lottery outcome is sub-sequently added to a balance of earnings. This balance of earnings accumulates between choices and is displayed on every screen throughout the treatment. Participants are in-formed of their final balance of earnings after the last choice-situation.
After the individual treatment participants take part in the ranking treatment. The dif-ference of the ranking treatment compared to the individual treatment is that participants are also, from beginning to end, exposed to the balances of earnings of two peers. As in the individual treatment, participants choose between ten lottery pairs and after each choice they are informed of its outcome. To examine if rank incentives have an effect on decision-making behaviour, participant’s earnings accumulate between choices and are presented in an ordinal ranking with the balances of earnings of two peers. The subject with the highest balance is listed on top of the rank and the subject with the lowest balance is listed on the bottom of the rank. A screenshot of the ranking treatment is included in Appendix B.
If placed last, participants may be more likely to choose the risky lottery to try to move a place up in the ranking. And, if placed first, participants may be more likely to choose the safe lottery to avoid moving a place down in the ranking. To separate rank incentives from monetary incentives, participants, if chosen for payment, are paid their final balance of earnings regardless of their place in the ranking. Explicit language or numbers to indicate places in the ranking are absent to dampen the effect that they will experience it too much as a game. Figure 1 gives a presentation of the outcome page between questions.
In the ranking treatment only the balances of earnings of the two peers are given and not the choice-decisions nor their earnings. This will make it highly unlikely for a participant to imitate behaviour of a peer. Furthermore, as rankings are private, decision-making behaviour is unlikely to be provoked by social pressure or an extrinsic desire for social status. Also, risks are not correlated between participants to better establish differences in rank. Therefore, given that a participant chooses the same lottery as a peer, he or she can still move in opposite directions of the ranking.
The two peers that participants face during the ranking treatment are randomly drawn out of a group of five. They did not participate in the experiment, but were asked to choose between the same lottery pairs that were used in the ranking treatment before the experiment was conducted3. This simple design has an additional benefit of controlling for possible interaction effects between subjects in the ranking treatment. Specifically, a participants can only react to what their peers earn, but the two peers cannot react to what participants earns.
3.2 Hypotheses
The principle hypothesis of this paper focuses on decision-making behaviour in the ranking treatment, compared to behaviour in the individual treatment. As literature has shown, starting with Lazear & Rosen (1979), rank-order tournaments increase overall risk-taking. If relative pay-off concerns or rank incentives have a similar effect on decision-making behaviour, it is likely that subjects will exhibit more competitive choice behaviour. Spe-cifically, we would expect subjects to choose the risky lottery more often in the ranking treatment compared to the individual treatment. Therefore, we would expect overall risk-taking to increase in the ranking treatment.
H1: Participants will be more likely to choose the risky lottery in the ranking treatment
compared to the individual treatment.
The primary goal of this paper is to investigate whether there are behavioural differences in risk-taking of a person placed last, second or first in a ranking. Literature on rank incentives typically involves a ranking that is financially incentivized, showing that those on the bottom take more risk than those on the top. Stripping the rank of financial rewards, Dijk et al. (2014) find that similar risk-taking behaviour persists, likely due to a concern for relative status concerns. The authors show that subjects who are on top of a ranking choose relatively safe portfolios to protect themselves for losing their top position, while subjects on the bottom choose risky portfolios for the possibility to improve their
3Peers’ choice outcomes and balances of earnings were also established before the experiment was
position in the ranking. Likewise, Kuziemko et al. (2014) provide evidence that people try to avoid being in the last place and will take more risk to do so.
Furthermore, the earnings of others may also serve as an aspiration or reference point when a person finds these others to be relevant. If so, then being in last place is equivalent to being in a social loss situation if you compare own earnings with the earnings of those above. Due to the reflection effect as mentioned in section 2, last-place participants may therefore be more likely to choose the risky lottery. Likewise, being in a social gain situation, first-place participants may be more likely to choose the safe lottery (Linde & Sonnemans, 2012). Therefore,we would expect subjects that are placed last in the ranking to choose the risky lottery more often than subjects that are placed first in the ranking.
H2: Participants that are placed last in the ranking will be more likely to choose the risky
lottery than participants that are placed first in the ranking.
Predicting behaviour of second-place participants is more complicated, as it is difficult to assess whether the possibility of being in first place looms larger than the possibility of falling to the last place of the ranking.
Kuziemko et al. (2014) provide evidence for the latter, as they show that second-to-last-place participants try to avoid ending up in the last place of a ranking. In their experiment, they study participants’ preferences for a redistribution of income after a social ranking is established. They show that second-to-last-place participants were less likely to give a portion of their earnings to those that are placed last in the ranking, while participants in all other rank positions gave a portion of their earnings to those below them in the ranking. Thus the authors conclude that people try to avoid being in last place, as for those ranked second-to-last, giving a portion of their earnings to last-place participants increases the chances considerably of ending up in the last last-place of the ranking. In line with the results of Kuziemko et al. (2014), we would therefore expect second-place participants in this experiment to choose the safe lottery more often, as it reduces their chance of ending up in the last place of the ranking.
H3 : Participants placed second in the ranking will be more likely to choose the safe lottery.
The experiment also includes lottery pairs with negative outcomes. As Prospect Theory suggests, individuals are more sensitive to perceived losses than gains. Therefore, we would expect subjects to be risk seeking when faced with negative outcomes or losses.
H4 : Participants will be more likely to choose the risky lottery when lottery outcomes are
3.3 Procedures
The experiment was run on a website, where anyone with access to its link could parti-cipate. The experiment was online from September 27, 2016 until October 10, 2016. As subjects participated via an online website, decision times were registered to control for environmental conditions as well as to make sure that subject were not using a calculator when making decisions.
Subjects were recruited via Facebook and other social networks, which lead to 83 subjects taking part in the experiment. There were 49 male participants and 34 female participants. Ages varied between 19 and 60 years old with an average age of 33 across all participants. The occupation of participants varied from business consultant and analyst to musician and other professions in the art industry. Only 9 of the 83 participants were students. During the experiment one randomly selected participant would receive the amount earned. The maximum amount that a subject could earn was € 52,90 in the individual treatment and € 52,00 in the ranking treatment. Only the final balance of one randomly selected treatment counted towards payment. The earnings were paid out by bank trans-fer on October 11, 2016, to the participant that was randomly selected for payment using a random number generator. This participant was informed of being selected for payment on the e-mail address he or she provided before participating in the experiment.
4 Results
Section 4.1 first presents a summary of the statistics and preliminary results on decision-making and switching behaviour between treatments. Results on risk-taking behaviour for each rank position are discussed in in section 4.2. After, the results of a regression analysis will be reviewed in section 4.3. Lastly, in section 4.4 the limitations of the experiment will be discussed.
4.1 Summary Statistics
In total 83 people participated in the experiment. 7 participants did not complete the choice tasks or spent on average more than 1.5 minutes per choice-situation and are there-fore omitted from the sample. The data consists of 1500 observations from 75 participants. Table 1 gives a summary of the choices and earnings per treatment. The presented data on earnings are based on participant’s accumulated earnings after the final choice made at the end of each treatment.
Earnings Safe Choice Risky Choice N Average Min Max Individual Treatment 425 (56.7%) 325 (43.3%) 750 € 18.88 € 6.45 € 38.60 Ranking Treatment 404 (53.9%) 346 (46.1%) 750 € 18.79 €2.15 €42.45 Overall 829 (55.3%) 671 (44.7%) 1500
Table 1: Summary of treatments.
Across treatments, participants chose the safe lottery more often than the risky lottery (binomial test, p < .001). This is in line with past experimental findings, which shows that people tend to be risk averse (Holt et al., 2002). As was predicted, participants chose the risky lottery more often in the ranking treatment compared to the individual treatment. The difference in risk-taking however is not significant (binomial test, p = .224). Therefore
the hypothesis that risk-taking increases when rank incentives are present cannot be confirmed.
Comparing the choices in the individual treatment with the choices in the ranking treat-ment, of the 750 observations (75 participants and 10 choice-situations per treatment) in 249 cases (33.2%) subjects switch choices from the individual treatment to the ranking treatment. Specifically, in 135 occasions (54.2%) participants switch from the safe choice to the risky choice and in 114 occasions (45.8%) participants switch from the risky choice to the safe choice. Hence, participants switch more often to the risky lottery than to the safe lottery. However, a paired Wilcoxon signed rank test shows that the direction of switching between treatments is not significantly different (p = .183).
Studying the effect of rank incentives for each participant individually, 35 participants (46.7%) make more risky choices and 22 participants (29.9%) make more safe choices in the ranking treatment compared to the individual treatment. The majority of participants therefore switch to the risky lottery more often than to the safe lottery, but this finding is only significant at the ten percent level (binomial test p = .056). For 18 participants (24%) there are no specific effects of choice behaviour between treatments. They either switched in both directions an equal number of times (15 participants) or did not change lottery choices (3 participants). The 3 participants that did not switch choices at all will be excluded from the analyses in the sections that follow.
Of the 20 lottery pairs six included negative earnings, three lottery pairs for each treat-ment. In contrast to the expectation that participants are risk seeking with choices that concern negative outcomes, participants chose the safe lottery slightly more often. Of the 450 observations containing negative lotteries, participants chose the safe lottery in
231 occasions (51.3%). Subdividing choice behaviour between treatments, risky choices increase for negative lottery pairs in the ranking treatment. Of the 225 negative lottery pairs, participants’ choices increase from 102 (45.3%) to 117 (52%) risky choices. Accord-ing to a Wilcoxon signed rank test, the difference between treatments in lottery choices containing negative outcomes is significant (p = .047). Performing a Wilcoxon signed rank test on choices containing positive lotteries shows no significant difference in choices between treatments (p = .665).
Although risk-taking behaviour between treatments is not found to be significantly dif-ferent, the results indicate that including non-monetary rank incentives does increase risk-taking on average and on the level of participants. The increase of risky choices in the ranking treatment is partly due to subjects’ switching behaviour for questions with negative outcomes, because for negative lotteries the risky lottery is chosen more often in the ranking treatment compared to the individual treatment. Still, as the result on the increase of risk-taking is not significant, the first hypothesis is rejected.
Result 1: Risk-taking does not differ across treatments.
4.2 Risk-taking behaviour for each rank position
Figure 2 presents the average percentages of subjects choosing the risky lottery for each position in the ranking (rank-ties are excluded from the analysis). The rank positions are based on participants’ balances of earnings so far where losses and gains accumulate between choice situations. Participants placed first in the ranking chose the risky lot-tery most often, of the 156 observations they chose the risky lotlot-tery in 84 cases (53.9%). Second-place participants chose the risky lottery in 57 cases (48.3%) of the 118 observa-tions. And last-place participants preferred the risky lottery in 136 cases (47.2%) of the 288 observations. Comparing risk-taking between rank positions, there is no significant difference in lottery choices between rank 1 and rank 2 (Chi-squared test, p = .364), between rank 1 and rank 3 (Chi-squared test, p = .183) or between rank 2 and rank 3 (Chi-squared test, p = .843).
Despite the choices between rank positions not being significantly different, these results portray a different choice pattern than was predicted. If rank incentives have an effect on choice behaviour, we would expect the level of risk-taking to be highest for last-place participants. Yet, the results show that first-place participants chose the risky lottery most often. As for second-place participants, the frequency of choosing the risky lottery lies in between the two other rank positions, closer to the frequency of last-place participants. However, these results are solely based on the average choices made per position in the ranking treatment. They do not take into account individual preferences, as some
parti-Figure 2: Percentage of risky choices for the first, second and third position in the ranking.
cipants may be more risk averse than others. Risk neutral or risk seeking participants will be more likely to choose the risky lottery regardless of their rank position. Furthermore, because the majority of lottery pairs involves a higher expected value for the risky lottery, risk-neutral participants will be more likely to choose the risky lottery. Choosing the risky lottery in turn, will likely lead to higher gains and a higher rank position. Therefore, it is difficult to assess if choice behaviour is influenced by the position participants obtain in the ranking, or if the position in the ranking is a result of participants’ risk attitudes. This makes it crucial to analyse if and in which direction participants switch between treatments conditional on their position in the ranking.
Participants’ switching behaviour between treatments for each rank position is illustrated in figure 3 (see table 5 in Appendix D for summary statistics). Looking at the figure it immediately stands out that of the first-place participants choosing the risky lottery, about half did not choose the risky lottery in the individual treatment. A McNemar test confirms that first-place participants switch significantly more towards the risky lottery (p = .013). When looking at switching behaviour of second-place participants most switched towards the safe lottery. According to a McNemar test however the difference in switching is not significant (p = .430). Lastly, a slight majority of last-place participants chose the safe lottery. Yet, observing switching behaviour, they switched more often towards the risky lottery than the safe lottery with respect to the individual treatment. This would be in line with the hypothesized risk seeking behaviour for last-place participants. However, according to a McNemar test there is also no significant difference in switching direction for last-place participants (p = .426).
Figure 3: Switching behaviour in percentages with respect to the individual treatment.
Taking the choices of the individual treatment into account the results show that rank incentives have the opposite effect than was predicted for first-place participants, as they are more likely to switch to the risky lottery than to the safe lottery. Second-place participants switch, as predicted, more often towards the safe lottery than the risky lottery, but this difference is not significant. Last-place participants switch slightly more often towards the risky lottery as predicted, but the difference in switching direction is also not significant.
The experiment also included negative lotteries. In general, participants are found to be more risk seeking with negative gambles compared to positive gambles. It might be possible that risk attitudes differ per rank position towards negative lotteries compared to positive lotteries. The lottery choices for positive and negative questions per rank can be found in table 6 in Appendix D. Comparing rank incentives for negative lotteries, there is a significant difference in switching behaviour observed only for first-place participants. They switch towards the risky lottery in 13 occasions compared to 3 occasions where they switch towards the safe lottery (McNemar test, p = .021). The direction of switching for negative lotteries does not differ for rank 2 nor for rank 3. As table 6 in Appendix D reports, there are also no significant differences between treatments in choice behaviour per rank position for positive lotteries.
Performing non-parametric tests on rank incentives, no significant effects of rank incent-ives for second and last-place participants are found. Only for first-place participants the results show that they switch to the risky lottery more often than to the safe lottery. This increase in risk-taking is partly caused by their preference for the risky lottery when the lottery outcomes are negative.
Result 2: Participants placed first are relatively more likely to choose the risky lottery,
especially when the lotteries involve negative earnings.
So far, risk-taking behaviour of participants placed second in the ranking seems ambigu-ous, as there is no large difference in choice or switching direction. Following the notion that people are more likely to compare with others that are similar, second-place par-ticipants’ choice behaviour could be dependent on the relative distance of own earnings compared to the earnings of first and last-place participants. Furthermore, if earnings are closer to the participant that is placed last, choosing the safe lottery will provide a better chance to avoid ending up in the last place. To examine whether choice behaviour is affected by the relative distance in earnings, the differences between second-place parti-cipants’ accumulated earnings and the accumulated mean earnings of previous questions are computed for every choice-situation5.
Choice Distance To Mean Earnings
(+) (-) Total
Safe 19 42 61
Risky 22 35 57
Total 41 77 118
Chi-squared test: p = .396
Table 2: Choice count of participants in rank 2.
Switch Distance To Mean Earnings
(+) (-) Safe-Safe 11 27 Risky-Safe 8 15 Safe-Risky 8 9 Risky-Risky 14 26 Total 41 77 McNemar test: p = 1 p = .307
Table 3: Switching behaviour of participants in rank 2.
5The distance between own and mean earnings are positive when a participant is relatively closer in
earnings to the first-place participant. Likewise, this distance is negative when a participant is closer to the last-place participant.
Table 2 and table 3 report on the choice decisions for second-place participants. Column (+) denotes the choices of participants ranked second that are closer in earnings to first-place participants. Column (-) denotes the choices of participants ranked second that are closer in earnings to last-place participants. For participants that are closer to first-place participants (+), the results show no substantial difference between lottery choices. Second-place participants that are relatively closer to last-place participants (-) exhibit behaviour as predicted. Although not significant, they chose the safe lottery more often than the risky lottery. This result remains when taking into account the choices made in the individual treatment by looking at switching behaviour. A result that indicates that participants are more risk averse to avoid being in last place. However, given that the results are not significant, we cannot confirm the hypothesis that participants placed second in the ranking are more likely to choose the safe lottery.
4.3 Regression Analyses
In this section the results of a regression analysis will be discussed to see if the previous results hold when controlling for other factors. A logistic regression model is applied, as the primary measure of this study is a binary variable, that is, whether a participant chooses the risky lottery or not. Table 4 reports on the logistic regression. The variables
Rank 2 and Rank 3 are dummy variables. Hence the effects of the independent variables
should be interpreted as a change in the likelihood of choosing the risky lottery for par-ticipants in rank 1, and the interaction terms should be interpreted as relative effects of participants in rank 2 and rank 3 with respect to participants in rank 1. Data points from choices of the last question in the ranking treatment are excluded from the regression to control for end-effects6.
The regression reports that all control variables have the expected sign and are at least significant at the 10 percent level, except for the variable that controls for the difference in variance between the risky and safe lottery (∆ Var between lotteries). The independent variables show that the likelihood of choosing the risky lottery increases when the risky lottery has a higher expected value, when the probability of the best outcome increases and when the lottery outcomes are negatives. The variable Switch is a dummy vari-able, assigned a value of 1 if a participant switched choices between treatments. When controlling for other factors, the variable Switch shows that participants on top of the ranking are 2.35 times more likely to switch to the risky lottery. The effect is significant and confirms earlier findings, that first-place participants choose the risky lottery more often if they switch choices with respect to the individual treatment.
6A regression including the last question can be found in Appendix E. Excluding the last question
Coefficient S.E. Odds Ratio Switch 0.856** 0.434 2.35 Higher EV of risky lottery 1.712*** 0.649 5.54 ∆ Var between lotteries -0.006 0.066 0.99 Higher probability of best outcome 0.118*** 0.039 1.13 Negative lottery 0.899* 0.532 2.46 Period -0.218* 0.112 0.80 Rank 2 -2.652 4.293 0.07 Rank 2 * Switch -1.376** 0.669 0.25 Rank 2 * Higher EV of risky lottery 0.862 1.437 2.37 Rank 2 * ∆ Var between lotteries 0.044 0.130 1.04 Rank 2 * Higher probability of best outcome -0.059 0.062 0.94 Rank 2 * Negative lottery 0.569 1.142 1.77 Rank 2 * Period 0.699*** 0.218 2.01 Rank 3 2.850 2.369 17.29 Rank 3 * Switch -0.634 0.528 0.53 Rank 3 * Higher EV of risky lottery -0.487 0.792 0.61 Rank 3 * ∆ Var between lotteries -0.044 0.082 0.95 Rank 3 * Higher probability of best outcome -0.077 0.047 0.92 Rank 3 * Negative lottery 0.187 0.652 1.20 Rank 3 * Period 0.147 0.135 1.16
Observations 492
McFadden Pseudo-R2 0.1809
Table 4: Logistic regression with the probability of choosing the risky lottery as the de-pendent variable.
* Significant at the 10% level. ** Significant at the 5% level. *** Significant at the 1% level.
Comparing risk-taking between rank 1 and rank 2, the interaction terms with the variable
Rank 2 report two significant differences. First, the interaction term with Switch shows
that participants in rank 2 are relatively less likely to choose the risky lottery. This is in line with earlier results, that participants in second place chose the safe lottery more often if they switch choices compared to first-place participants. Second, the interaction term with Period shows that subjects placed second in the ranking chose the risky lottery more often the more questions have passed. An interesting result, as the period variable shows that first-place participants chose the safe lottery more often towards the end of the treatment. This result may be interpreted as first-place participants trying to defend their lead in the ranking, while second-place participants are trying to obtain the top position in the ranking towards the end of the ranking treatment.
Rank 3 report no significant differences. Although the interaction term with Switch shows a negative relationship for choosing the risky lottery, switching behaviour is not statistically different between rank 1 and rank 3 when controlling for other factors.
Result 3: Participants in second place switch less often to the risky lottery than
parti-cipants in the first and in the last place of the ranking.
4.4 Limitations
As there are several limitations to this experiment, the conclusions of this paper should be drawn with caution. The first and foremost limitation is that the order of treatments and its questions did not vary across participants. This could have biased the data towards more risky choices in the ranking treatment, as participants might have learned that, for the majority of choice-situations, the risky lottery had a higher expected value. Given that risk-taking did not increase significantly in the ranking treatment, a substantial learning effects across treatments seems limited. Still, it poses a threat to the validity of this paper’s results if first and last-place participants in particular might have learned that taking risk pays off. If so, then the main result can also be explained by learning effects instead of rank incentives. Moreover, not controlling for order effects could also have distorted the data for choice-situations near the end of the experiment, as concentration levels of subjects might have decreased.
Second, it is impossible to ensure whether participants read the instructions thoroughly. Therefore, participants in the ranking treatment might have based their decisions on a ranking that they perceived to be pay-off relevant. As a result, it is difficult to assess whether participants made decisions motivated by rank incentives or tournament incent-ives. Given that participants who were placed second in the ranking chose the risky lottery more often as questions advanced, this could have been the case. On the other hand, we should then observe last-place participants to exhibit an even higher level of risk-taking towards the end of the ranking treatment. Nonetheless, the setup of this experiment makes it impossible to eliminate this reservation.
And lastly, the experimental design might have caused participants to experience it too much as a game. This might have influenced risk attitudes, as finishing first or last is more pronounced in game-like settings. However, if the mind-set of playing a game influenced risk attitudes, we would expect second-place participants to compete over the first place in the ranking by choosing the risky lottery more often.
5 Conclusion and Discussion
This paper investigated whether the earnings of others influences risk-taking behaviour, by conducting an experiment where subjects’ earnings are presented in an ordinal ranking with the earnings of two peers. Comparing behaviour between an individual condition where there is no rank present, and a ranking condition, this paper examined whether subjects change their decision conditional on their position in the ranking through a concern for status.
The conjecture of relative pay-off concerns through a concern for status predicts that individuals’ choice behaviour in a ranking will be similar to that when a ranking is fin-ancially incentivized. This, as earning more than others may increase utility via higher social status, along with a higher absolute pay-off.
The results show that subjects in first and last place of the ranking switch relatively more often towards the risky lottery, while subjects in the second place of the ranking switch relatively more often towards the safe lottery. Although this shows that risk attitudes are influenced by relative income concerns, the behaviour observed cannot be explained by a model of rank incentives. This, as we should have observed risk-taking to decrease with rank position. The behaviour observed can also not be explained by an extension of Prospect Theory to a social context, as subjects on top of the ranking exhibit risk seeking behaviour whilst being in the social gain domain.
The risk seeking behaviour of subjects on top of the ranking does indicate that risk aversion decreases with earnings. As Friedman & Savage (1948) suggest, people may exhibit risk seeking behaviour when moving to a higher social class in order to distinguish themselves. However, their risk seeking behaviour stems largely from choices where the lottery outcomes are negatives. This may imply that risk aversion diminishes with income particularly when choice outcomes involve losses.
The results also show that subjects in the middle of the ranking display risk averse be-haviour as predicted. This may be interpreted as subjects trying to avoid ending up in the last place of the ranking, which indicates that the possibility of being in the bottom of a distribution looms larger than the possibility of being in the top of a distribution. Furthermore, participants in last place exhibit risk seeking behaviour, possibly to try to move out of last place. This is in line with the findings of Kuziemko et al. (2014), who show that participants exhibit last-place aversion. Therefore, behaviour of those in the middle and in the bottom of the ranking might be interpreted as subjects competing over the second place in the ranking.
However, the results should be drawn with caution, as they are based on relatively few instances where subjects switch between treatments. Of the 750 observations subjects
switched in only 250 cases, indicating that the effects of relative income concerns on risk attitudes are not that extreme.
Nonetheless, these findings may have important implications for policy discussions about regulation of excessive risk-taking in competitive industries, as the findings suggest that excluding bonuses from payment schemes could still increase risk-tasking for under- and over-performers through an intrinsic concern for status. Prohibiting bonuses from pay-ment schemes might therefore not be enough to curb imprudent risk-taking. Limiting the use of explicit rankings of performance and salaries should therefore also be considered when moderating risk-taking behaviour.
Another implication is related to the distribution of income and tax policy, as the results display diminishing risk aversion for those on the top of the distribution when lottery outcomes are negative. Considering that progressive tax policies often divide households into three different income classes, these tax policies might induce households to similar risk-taking behaviour. Households within the top of an income distribution might there-fore be more likely to avoid paying taxes compared to lower income households. Reducing tax rates is often found to increase tax compliance (Clotfelter, 1983), the findings of this paper however suggest that tax compliance might also depend on one’s position in an income distribution. Future research on risk attitudes with a focus on relative income concerns and losses may therefore be useful for the improvement of taxation policies. This paper’s findings show that relative pay-off concerns influence risk-taking behaviour. By including a social ranking it finds that those on top and on the bottom of the dis-tribution are less risk averse than those in the middle of the disdis-tribution. However, the mechanisms that drive risk attitudes through relative pay-off concerns and social compar-ison are still up for debate. An interesting question for future research, for example, is to determine whether relative pay-off concerns through rankings induce similar risk attitudes when ranking information becomes public.
Appendix
A. The lottery Pairs
Lotteries: Individual Treatment
Q Prob. (%) Lottery A Safe/ Lottery B Safe/ Q*
Outcome 1 Outcome 1 Outcome 2 Risky Outcome 1 Outcome 2 Risky
1 50 4.15 0.65 R 2.95 1.35 S 4 2 33 4.55 2.85 S 6.15 1.65 R 1 3 33 -0.85 -7.85 R -2.85 -4.55 S 3 4 33 4.65 3.35 S 7.35 2.15 R 7 5 40 -1.05 -4.05 R -2.55 -3.55 S 5 6 40 7.95 4.15 S 11.15 1.35 R 6 7 50 5.00 0.50 R 3.00 2.00 S 9 8 50 -3.15 -2.15 S -4.75 -0.55 R 8 9 33 15.00 2.00 R 8.00 5.00 S 10 10 40 4.55 3.55 S 6.55 2.20 R 2
Q*: Denotes the questions that match the lottery pairs in the ranking treatment.
Lotteries: Ranking Treatment
Q Prob. (%) Lottery A Safe/ Lottery B Safe/ Outcome 1 Outcome 1 Outcome 2 Risky Outcome 1 Outcome 2 Risky
1 33 4.75 3.05 S 6.35 1.85 R 2 40 4.70 3.70 S 6.70 2.35 R 3 33 -1.35 -8.35 R -3.35 -5.05 S 4 50 4.65 1.15 R 3.45 1.85 S 5 40 -0.85 -3.85 R -2.35 -3.35 S 6 40 7.45 3.65 S 10.65 0.85 R 7 33 4.45 3.15 S 7.15 1.95 R 8 50 -3.40 -2.40 S -5.00 -0.80 R 9 50 4.75 0.25 R 2.75 1.75 S 10 33 14.75 1.75 R 7.75 4.75 S
B. Experimental Screenshot
C. Instructions
General Instructions Welcome!
Thank you for taking part in this thesis experiment about decision-making. The experiment consists of two parts and will take you about 10 to 15 minutes. During the experiment it is possible for you to earn money.
At the end of October, one participant will be randomly selected to receive his/her earn-ings dependent on the decisions made for one randomly selected part of the experiment. The participant that is selected for payment will not be made public, but will be privately contacted by e-mail and will be paid out his/her earnings by bank transfer.
Also, all information you provide and decisions you make will not be shared with others, only with the experimenter herself.
Before we start I kindly ask you to fill in your contact details on the next page
If you prefer to stay anonymous to the experimenter you can do so by filling in a different name and contact information.
Instructions Part I
This part of the experiment consists of 10 questions.
For each question you will be asked to choose between two options. The two options are lotteries. For each option there are two possible outcomes with given probabilities. After each choice you make the chosen lottery will be played out and the outcome will be added to your current balance of your earnings so far.
If you are selected for payment, you may receive the total balance earned at the end of this part of the experiment. Therefore, the outcomes of the decisions you make during this part of the experiment may determine what you will receive on the 10th of October. So please answer each question truthfully.
When you start the experiment please do not click on the button that leads you to the previous page in your browser, as this will invalidate your choices. If you do, you will not be eligible for payment.
Control Question
Before we proceed, please answer the following question to ensure that you understand the rules of this experiment.
The answer you give does not count towards your earnings if you will be selected for payment.
Question:
See option A and option B below. If you choose option B, what is the amount you will most likely earn based on the given probabilities (percentages)?
Please give your answer without decimals. For example, if you think the correct answer is €100,00 you may enter 100
Option A
• You earn € 20.00 with a probability of 33% • You earn € 10.00 with a probability of 67%
Option B
• You earn € 15.00 with a probability of 33% • You earn € 5.00 with a probability of 67% Your answer is:
To check your answer and start with the first part of the experiment, please click on the Next button below
> Next
Instructions Part II
This last part of the experiment also consists of 10 questions. For each question you will be asked to choose between two options. For each option there are again two possible outcomes that are determined by the given probabilities. Again, the outcome of the option you choose will be revealed after each question.
However, during this part of the experiment you will also see the current balance of earnings of two other participants in a ranking. The person with the highest earnings so far will be listed on top of the ranking and the person with the lowest earnings so far will be listed on the bottom of the ranking. Your position in the ranking has no influence on your earnings, if you are selected for payment.
The two other participants have chosen among the same lotteries in the same order at an earlier point in time, without any information about the earnings of others. The participants that you may observe in the ranking will not receive any information of your earnings. Only the experimenter herself will have access to this data.
On the 10th of October one participant will be randomly chosen to receive its total earnings of either part I or part II of this experiment. Your position in the ranking does not influence the chance of being selected for payment or your earnings.
When you continue the experiment, please do not click on the button that leads you to the previous page in your browser, as this will invalidate your choices. If you do, you will not be eligible for payment.
Please click on the button below to start with the second part of this experiment.
D. Descriptive Statistics
Rank Safe-Safe Risky-Safe Safe-Risky Risky-Risky Total
1 52 20 40 44 156 (%) (33.3) (12.8) (25.6) (28.2) 2 38 23 17 40 118 (%) (32.2) (19.5) (14.4) (33.9) 3 106 46 55 81 288 (%) (36.8) (16) (19.1) (28.1)
Table 5: Summary statistics of switching behaviour in the ranking treatment w.r.t. the individual treatment.
Rank Safe-Safe Risky-Safe Safe-Risky Risky-Risky Total McNemar test
Negative lottery questions p-values
1 25 3 13 17 58 0.021
2 14 7 7 16 44 1.000
3 28 10 12 40 90 0.832
Positive lottery questions
1 27 17 27 27 98 0.174
2 24 16 10 24 74 0.327
3 78 36 43 41 198 0.500
Table 6: Switching behaviour between treatments for negative and positive lotteries per rank.
E. Additional Regression
Coefficient S.E. Odds Ratio
Switch 0.657 0.403 1.93
Higher EV of risky lottery 2.012*** 0.495 7.48 ∆ Var between lotteries 0.032 0.032 1.03 Higher probability of best outcome 0.123*** 0.038 1.13 Negative lottery 0.992** 0.493 2.70 Period -0.218* 0.112 0.80
Rank 2 0.053 1.691 1.06
Rank 3 2.208 2.003 9.10
Rank 2 * Switch -1.528*** 0.628 0.22 Rank 2 * Higher EV of risky lottery -0.206 0.801 0.81 Rank 2 * ∆ Var between lotteries -0.079* 0.037 0.92 Rank 2 * Higher probability of best outcome -0.070 0.057 0.93 Rank 2 * Negative lottery -0.159 0.781 0.85 Rank 2 * Period 0.622*** 0.188 1.86 Rank 3 * Switch -0.328 0.487 0.72 Rank 3 * Higher EV of risky lottery -0.313 0.608 0.73 Rank 3 * ∆ Var between lotteries -0.014 0.037 0.99 Rank 3 * Higher probability of best outcome -0.072 0.045 0.93 Rank 3 * Negative lottery 0.388 0.602 1.47 Rank 3 * Period 0.137 0.135 1.15
Observations 563
McFadden Pseudo-R2 0.1564
Table 7: Logistic regression with the probability of choosing the risky lottery as the de-pendent variable.
* Significant at the 10% level. ** Significant at the 5% level. *** Significant at the 1% level.
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