MSc Economics
Track:
Behavioural Economics and Game Theory
The Effects of Global Risk on Risk-Seeking and Emotions:
An investigation of an additional loss factor in an investment game
by
Alex Wouters
10035656
June 2016
15 ECTS
Supervisor
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STATEMENT OF ORIGINALITY
This document is written by Student Alex Wouters who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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ABSTRACT
The experiment conducted in this paper is aimed to provide additional insight in the role of ‘Global Risk’ on an investment decision. In the decision problem studied, subjects distribute hypothetical money to a safe and a risky option in an investment game. Global Risk is introduced as an additional chance factor, which can result in losing all earnings. This study of Global Risk has two major purposes: (1) to study the effect of a small Global Risk of 1/6 on investment in a risky option (2) to investigate the role of emotions (elicited by this Global Risk) on investment decisions. The results suggest that a Global Risk of 1/6 increases risk-taking. These results cannot be explained by Expected Utility Theory nor are they in line with relevant literature. Explanations are offered by taking experienced emotions and Cumulative Prospect Theory into account.
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TABLE OF CONTENTS
Introduction ... 5
I. Decision Problem ... 7
II. Economic Theory and Hypothesis ... 9
2.1 Economic Theory on Risk Taking ... 9
2.2 Behavioural Economic Theory ... 11
2.3 The effects of an increase in rounds played ... 14
III. Experimental procedure ... 14
IV. Methodology ... 17
4.1 Investment ... 17
4.2 Emotions ... 17
V. Results ... 19
5.1 Investment Results ... 19
5.2 Emotions and Investment ... 22
VI. Cumulative Prospect Theory ... 29
VII. Discussion... 31
7.1 Related Studies ... 31
7.2 Topics for Future Research ... 34
VIII. Conclusion ... 34
Reference List ... 36
Appendix A ... 39
Appendix B ... 40
Instructions Experiment Group BL ... 41
Instructions Experiment Group GR ... 43
Payoff Table ... 45
Decision Form BL ... 46
Decision Form GR ... 53
Appendix C ... 60
Panel Regression round 3 & 4 ... 60
Panel Regression Output BL ... 61
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INTRODUCTION
Global risk is an additional risk that is extremely hard or impossible to avoid. It is an external risk that is outside the influence of a decision-maker. The resolution of global risk could result in losing one’s resources. A real world example of a global risk is the possibility of a financial crisis. A financial crisis could result in the loss of all savings and risky investments, which imposes an additional risk on top of the risk of the investment. Other examples include terrorist attacks, whereby feelings of anxiety and fear are nourished because something bad could happen that cannot be avoided. In economic experiments, global risk is an additional chance factor that could result in losing all earnings at the end of an investment game. The effect of global risk in an economic experiment is investigated by Bosman and van Winden (2010).
In their one-shot laboratory investment experiment Bosman and van Winden (2010) find that, when introducing a global risk chance factor of 1/3 (0.333) whereby all earnings can be lost, investment decreases compared to a control group that does not face this global risk. These results cannot be explained by classic economic theory.1 In the analysis of their results, Bosman and van Winden (2010) take account of emotions that were gathered with self-reports. They find that the differences in distribution of investment can be explained by taking the relationship between investment and situation anxiety and investment and irritation into account.
Caplin and Leahy (2001) however mention that ‘many decisions are sensitive to the possibility rather than the probability of negative outcomes’ (p. 70). The research of Bosman and van Winden therefore raises the question to what extend their observed effect of global risk is due to the possibility of losing everything, or due to the size of the probability of the global risk. This makes it interesting to study the effect of a smaller global risk than the 1/3 used by Bosman and van Winden.2 This might also shed more light on whether the effect of
global risk is caused by an increase in the complexity of the decision problem. Furthermore,
1 According to Expected Utility Theory, the probability of a global risk that is equally spread between two
possibilities (two investment opportunities), should not influence investment decisions. Simply because the probability affects the expected utility of both outcomes in the same way.
2 Bosman and van Winden (2010) already studied the effect of a larger global risk of 2/3 (0.667). With a global
risk of 2/3, they find that investment is again lower than in the control group, although no longer significantly. By using a smaller global risk, the point raised by Caplin and Leahy can be carefully studied and a more complete analysis of the effects of global risk can be provided.
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the emotions described in Bosman and van Winden (2010) possibly lack connection with the described global risk. In their experiment, subjects were only asked to rate their emotions during the experiment. Since emotions were not elicited before the experiment, it is possible that the emotions reported are merely linked to the affective state the subjects had before entering the experiment, and not to the global risk. As a result, the findings of Bosman and van Winden (2010) on emotions may not be robust. By also measuring the emotions of the subjects before the start of the experiment, this problem can be circumvented.
To investigate the point made by Caplin and Leahy (2001), the focus of this research is on the effects of a relatively smaller global risk. A second objective is to investigate the relationship between global risk, investment and emotions. First, a dynamic multi-stage investment experiment is conducted with a significant smaller global risk. That is, a global risk with the probability of 1/6 (0.167). Multiple statistical tests are conducted to check if the results differ from the predictions of Expected Utility Theory and if the results are in line with the findings of Bosman and van Winden (2010). Second, ratings about experienced emotions (gathered by self-reports) are investigated. Examined is whether emotions are affected by the possible global risk and if investment is driven by the change of these emotions.
The effect of emotions is investigated because global risk itself can trigger emotions like anxiety, irritation and hope, which on their turn can affect investment behaviour (at least) in the short run (Ortony et al., 1988; OECD 2002; Samuelson 2004). The recent terrorist attacks in Paris and Brussels and the financial meltdown of 2008 made this type of risk also socially relevant again. The rise of IS, today’s financial globalization and possible country defaults make the fear of a global risk more prominent nowadays. A careful investigation of the effects of global risk and the role of emotions can provide additional insights to these matters. By conducting a laboratory experiment with global risk, the effect of global risk can be isolated and linked to experienced emotions and investment. The laboratory setting ensures a controlled study that can be replicated.
In the experiment, subjects are asked to allocate an endowment over a safe and a risky option. As it is an investment experiment, the global risk in this experiment can be interpreted as a financial crisis in which the global risk could result in losing all accumulated earnings of both a safe and a risky option. Emotions are measured by self-reports before, and during the experiment. This adds robustness to the emotion measurements and allows for a close investigation of the relationship between experienced emotions and investment.
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The organization of the paper is as follows. Section I describes the decision problem, followed by an overview of economic theory and hypotheses in section II. Section III gives the experimental procedure. In section IV, the methodology is outlined. The results of the experiment are presented in section V, followed by an additional explanation of the results in section VI. Section VII provides a discussion of relevant literature and section VIII presents a conclusion to this paper.
I. DECISION PROBLEM
In this experiment, subjects are confronted with a dynamic decision problem similar to the problem described in Bosman and van Winden (2010). The decision problem investigated differentiates between two treatments: The Baseline (BL) treatment and the Global Risk (GR) treatment:
BL: subjects receive an endowment z at the start of each round and distribute this endowment over a safe option and a risky option. The safe option gives a certain return of z – x (where x is the amount invested in the risky option). The risky option gives a return of 2.5x or 0, both with probability ½. The game is played for four rounds. The total hypothetical amount of money the subject can make are the earnings that are gathered over all four rounds.
GR: subjects play the game in the same way as in BL, except for the introduction of a global risk. Global risk introduces a probability pgr that could result in losing all
accumulated earnings in round 2 and 4.
The most important difference between this decision problem and the one described in Bosman and van Winden (2010) is that the probability of the global risk, pgr, is set at 1/6
(0.167) instead of 1/3 (0.333). Setting a lower probability of global risk allows me to draw inferences about whether the results of Bosman and van Winden (2010) are due to size of the global risk or due to the possibility of losing everything. An additional difference between both problems is the amount of rounds played. In this decision problem the subjects play four rounds, whereas the subjects in Bosman and van Winden (2010) only play one round. By
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playing four rounds a more robust measurement of both experienced emotions and investment can be obtained. The decision problem and the two treatments are described in more detail below.
The decision problem in the GR treatment goes as follows. There is a sequence of four rounds, r = 1,..,4, in which for each round an investment decision is made. On entering any round r, the subject receives an endowment, which is the hypothetical amount of money
z. The subject has the choice to divide this amount z over two options: she can invest an
amount x (where 0 ≤ x ≤ z) in a risky option while leaving the remainder (z – x) for a safe option. The risky option yields a return of either 2,5x or 0, both with probability ½. The safe option yields neither gain nor loss. The return on investment, together with the amount in the safe option, will give the closing balance for that round r. The subject proceeds to the subsequent round and again receives the endowment z. The subject again divides the amount
z over the two options (she is not allowed to reinvest her earnings). This decision problem is
played for four rounds. The total hypothetical amount of money the subject can earn is the sum of all closing balances of each round r. However, after the outcome of the lottery of the investment decision in round 2 and 4, the subject faces global risk. The global risk can result in the loss of all accumulated earnings. The probability of losing all earnings in round 2 and 4, conditional of entering it, is based on the global risk, pgr (where 0 < pgr < 1). The subject is
informed beforehand about this probability. With a probability of pgr she will lose all
earnings, while with the probability of 1 - pgr the subject keeps her earnings and can make a
hypothetical profit. If the subject is struck by the global risk, the experiment ends and she receives a payoff of zero.
The Global Risk treatment will be compared to the Baseline treatment. In BL the subject also receives the hypothetical endowment z at the start of every round, which has to be distributed between the risky and the safe option. Opposed to the decision problem in GR, the subject in BL does not face global risk. That is, the subject does not face the risk that all earnings will disappear with probability pgr in any round.
The two cases are illustrated by the decision trees in Figures 1 and 2. The first decision knot represents the decision whether to invest or not. The second and third knot in figure 2 represent the different outcomes after the investment decision is made for the case when global risk occurs (prob. pgr), and when it does not (prob. 1 – pgr).
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FIGURE 1. Decision tree for Baseline.
FIGURE 2. Decision tree for Global Risk.
II. ECONOMIC THEORY AND HYPOTHESES
2.1 Economic theory on risk-taking
In this decision task, participants are confronted with the concern of allocating money to two projects where all possible outcomes and associated probabilities are known. To analyze and interpret the potential outcomes of this decision task, I therefore start with the predictions derived from the classic economic theory of decision making under risk: Expected Utility Theory (EU).
Hypothesis 1
The introduction of a global risk of 1/6 has no effect on investment decisions.
z + 1.5x 0 0 z – x 1 3 2 1/2 1/2 1 - Pgr Pgr 1 - Pgr Pgr 1 x
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EU states that the decision maker decides between different risky or uncertain prospects by comparing their expected utility values, i.e., the weighted sums obtained by adding the utility values of outcomes multiplied by their respective probabilities (Davis et al. 1997). If the decision problem described in figure 1 is played for round 1, and subjects consider hypothetical wealth as utility, expected utility maximizers are predicted to invest the full endowment z in the risky option. Full investment (x = z) is assumed, because the expected utility from investment in the risky option exceeds the expected utility of investment in the safe option: (1/2(z – x + 1.5x) + 1/2(z – x)) = z + 0.25x > z.
For the decision problem described in figure 2, the global risk pgr, is equally
distributed between the chance nodes 2 and 3. According to Expected Utility Theory, the probability of a global risk that is equally spread between two possibilities (two investment opportunities), should not influence investment decisions. Simply because the probability affects the expected utility of both outcomes in the same way. The expected utility of the risky option is (pgr)(1/2(z – x + 1.5x) + 1/2(z – x)) and the expected utility of the safe option is
(pgr)z. The expected utility from investment in the risky option again exceeds the expected
utility of investment in the safe option, as: (pgr)(z + 0.25x) > (pgr)z = z + 0.25x > z. This is the
same result as in the BL treatment. Consequently, investment should not be influenced by the global risk and investment in GR is also forecasted to concentrate at x = z.
The same outcomes are also expected for the remaining rounds in both treatment groups. An expected utility maximizer evaluates each round individually and independently. Since the outcome of the lotteries in the three remaining rounds are independent of the outcome in the first round, an expected utility maximizer is, irrespective of which treatment group she is in, predicted to invest everything in the risky option in every separate round r. Also, since global risk is distributed equally between outcomes in round 2 and 4, it will show no differences in individual investment compared to rounds 1 and 3. EU therefore predicts that investment will not differ significantly between rounds and will concentrate at x = z in every round r.
Although risk-aversion could lead to more conservative investment decisions, Rabin (2000) states that expected utility maximizers are (almost everywhere) arbitrarily close to risk neutral when stakes concerning wealth are arbitrarily small. He finds that within the expected-utility framework, for any concave utility function, even very little risk aversion over modest stakes implies an absurd degree of risk aversion over large stakes. Therefore, when the stakes are small, people are approximately risk neutral. The fact that this experiment is conducted with hypothetical wealth and a potential small monetary prize could
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lead to risk-taking levels that are in accordance with Rabin’s findings and thus lead to the prediction of x = z derived above.
2.2 Behavioural economic theory
Besides testing the predictions of EU on risk taking with global risk, the aim of this experiment is to do additional research on the relationship between experienced emotions, investment and global risk. In this experiment, research is done on the emotions happiness, hope, anxiety, fear, irritation and anger. Based on emotions that subjects report after making their investment decisions, predictions about the effect of global risk on emotions and (therefore indirectly on) investment can be made.
Hypothesis 2
Emotions are affected by the global risk and these emotions have a significant effect on investment behaviour.
Bosman and van Winden (2010) were the first to investigate global risk, investment, and emotions. The focus of their study is on the behavioural effects of global risk in an investment experiment. Their experiment was conducted with 64 students and later repeated with an additional 65 students. The subjects were divided in 2 treatment groups; the BL group and the GR group, where in the latter the subjects could lose all earnings due to global risk. Self-reports were filled in by the subjects to measure the emotions experienced during the experiment. Subjects were asked to report their experienced emotions right after the investment decision was made, but before the possible resolution of global risk. Bosman and van Winden found that the introduction of GR decreases investment. They also found that the majority (75%) showed risk-averse behaviour by putting part of the endowment in the safe option.
Concerning emotions, Bosman and van Winden found that anxiety experienced after the investment decision, but before the resolution of the investment risk, is positively related to the amount invested in the BL treatment. The positive relation of anxiety is not in line with previous research, which indicate that anxiety should have a negative relation with investment (Raghunathan and Pham, 1999; Lerner and Keltner, 2001; Loewenstein et al,
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2001).3 Bosman and van Winden claim that their result could be explained by a two-way relationship between investment and anxiety. Investment itself may generate anxiety. Anxiety can therefore be split in decision anxiety and situation anxiety. ‘Decision anxiety’, relates to the investment decision made by the subject and is positively correlated with investment (as it increases when you put a higher investment at stake). ‘Situation anxiety’ is caused by the situation prior to the investment, and is negatively correlated with investment. It causes subjects to be biased towards low-risk options. Situation anxiety per unit of investment increases due the presence of global risk (Ortony et al., 1988). Decision anxiety on the other hand, depends on the amount invested. As the situation anxiety in GR is higher, investment in this treatment group decreases. As a result, decision anxiety also decreases. So the introduction of global risk and the negative effect on investment due to situation anxiety, induces less decision anxiety, which may cause the overall level of anxiety in the GR treatment to stay constant. Taking the different kinds of anxiety into account, Bosman and van Winden found a positive relationship between investment and anxiety in BL, but no relationship between investment and anxiety in GR. Another finding of their experiment is that the global risk appears to induce irritation, which is an emotion related to anger.
Anger and irritation can account for excessive risk taking (Leith and Baumeister, 1996). These emotions are known to induce optimistic risk estimates and risk-seeking choices. Leith and Baumeister (1996) conducted an experiment on the effect of bad moods on risk-taking behaviour under 129 psychology students. In their experiment, the subjects were divided in 3 groups. The happy group was primed by watching 2 comedy clips, whereas the control group got to watch a neutral advertisement. The negatively primed group had to sing an egoistic song in front of the experimenter to create a feeling of embarrassment. To elicit a feeling of anger, they were told that the recorder didn’t record the first time and that they had to do it all over again. Also, the happy group had to write a short story about something good that happened to them in the past and the negative group something that angered them. After these tasks, the students were asked to rate their emotions and make two lottery questions. Study participants who experienced “frustrated anger” were more likely to choose a high risk, high reward option in a lottery. Albeit elicited emotions in their research, other experimental research finds similar outcomes (Loewenstein et al, 2003; Lerner and Keltner, 2001). The fact that global risk induces anger like emotions and that anger can lead to excessive risk
3 This finding is found by experimental (Raghunathan and Pham, 1999; Lerner and Keltner, 2001) and
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taking could lead to a positive relation between anger and investment in global risk. The opposing effects of anger and anxiety induced by global risk help explain the U-shaped distribution of investment that was found in GR by Bosman and van Winden (2010). For BL, Bosman and van Winden find a more inverted U-shaped distribution.
The emotion fear is found to have a negative impact on risk-taking. Cohn et al (2014) performed an investment experiment with financial professionals, whereby the subjects had to distribute an endowment over a risky option and a risk-free safe option. To induce a feeling of fear, Cohn et al (2014) exposed the subjects to random electric shocks during the investment task. The findings of their experiment are in line with previous psychological papers about risk and fear (Lerner and Keltner, 2001): higher levels of fear lead to more investment in the save option and to more risk-averse behaviour. This resembles the findings of Bosman and van Winden (2010), who claim that situation anxiety induced by the global risk could have a negative impact on investment.
The affective emotion hope is associated with happiness (Park and Peterson, 2006). Hope and happiness can lead to more optimism about the probability of winning (Kaplanski et al, 2015, Isen and Patrick, 1983), which could have a positive effect on risk taking. The effect is however not certain. Isen and Patrick (1983) found that happy participants placed riskier bets in a hypothetical gambling situation. However, the same participants placed less risky bets when real money was at stake. They explain this finding by suggesting that happy subjects have more to lose and that losing a real bet would decrease their mood. This is known as the mood-maintenance theory. Related experimental research find similar results (Arkes, Herren, and Isen, 1988; Isen, Nygren, and Ashby, 1988). Nygren and Isen (1996) find that despite being relatively more optimistic, positive affected people tend to be conservative or self-protective in choice situations where there is a reasonable chance that a real loss may occur. The effect of happiness and hope on investment is therefore ambiguous. The intensity ratings of hope and happiness in the GR treatment group on the other hand are expected to be lower as a results of the increased probability of losing one’s earning.
Based on relevant behavioural economic literature, hypothesized is that due to higher situation anxiety, anxiety ratings are higher in the GR treatment. Outliers in anxiety ratings are expected in round 2 and 4 because the global risk is more ‘real’ in these rounds. The same holds for irritation. In addition, expected is that fear and anxiety show a negative relationship with investment. Anger and irritation, are expected to show a positive relationship with investment.
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2.3 The effects of an increase in rounds played
Besides the lower global risk, the experiment conducted in this paper differs from Bosman and van Winden in that there are four rounds played instead of one. As described above, the rounds are independent and the increase in rounds should have no effect on investment behaviour. There are however two possible complications that must be taken into consideration when analyzing an experiment with multiple rounds. Myopic loss aversion could occur. Myopic loss aversion results in a greater sensitivity to losses when outcomes are evaluated more frequently (Thaler et al, 1997). Although the rounds are independent, the immediate feedback of the lottery at the end of each round creates a moment of evaluation which could lead to less risk-taking in subsequent rounds. Another implication of the increase in rounds is the experience the subjects gain over the course of the experiment. Playing a single-shot investment game may not be enough time for the subjects to learn the true incentives. By playing four rounds subjects should have played enough repetitions to familiarize themselves with the incentive scheme, which could lead to investment behaviour that is in line with rational decision making (EU). In public goods for example, it is often observed that repeated games cause for behavioural shifts that can be explained by (several factors including) learning (Andreoni, 1988). There is however no experimental evidence about whether subjects tend to move closer to the predictions of EU in an investment experiment similar to the one conducted in this research. As the effects described above move in opposite directions, the possible effect of an increase in the amount of rounds played is ambiguous. The effects of an increase in rounds played will be discussed in greater detail in section VII.
III. EXPERIMENTAL PROCEDURE
The experiment is conducted with 47 students, where 27 students are randomly assigned to the GR treatment, and 20 to the BL treatment. About 40% of the subjects are students of the Faculty Economics and Business of the University of Amsterdam. The remainder of the subjects are students from various fields and colleges including Erasmus University, Vrije Universiteit and the Hogeschool van Amsterdam. The students are recruited via mailing.4 A greater part of the subjects are assigned to the GR treatment, because of the possibility to
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drop out of the experiment in round 2. The investment game is framed in a neutral way without using suggestive terms as investment and global risk. For each subject, the experiment is conducted individually and separately from other subjects and on a one-on-one basis with the experimenter.5
The procedure for the BL is as follows. The experiment starts with a general welcome. The subject is asked to rate her emotional state before she receives any instructions. When the subject is finished, the experimenter reads the instructions for the investment game out loud and provides the subject with 2 cups, a die, a payoff table and a decision form. The two cups represent the safe option (cup A) and the risky option (cup B) respectively. In addition, the experimenter will provide an example to illustrate how the game works. The subject is also informed about the possibility of winning a monetary reward, which is determined by chance among all the subjects of her treatment group.6
After 2 practice rounds, the subject is given the first endowment z, which is €10, and is asked to allocate this amount over the two cups. This investment decision is written on the decision form. Right after the investment decision, the subject is asked to rate her experienced emotions. Afterwards the subject throws the die to determine the outcome of the risky option. If the outcome is 3 or lower, the subject losses the investment in cup B. If the outcome is higher than 3, the investment in cup B is multiplied by 2.5. The total amount of hypothetical money the subject can earn in round 1 is the money in cup A plus the (potential) return of cup B. The subject writes the earnings of round 1 at the bottom of the decision form of round 1 and at the top of the decision form of round 2.
In the subsequent rounds, the subject performs the same steps as in round 1 for four rounds. Receiving and distributing €10 at the start of each round. The subject is informed about her accumulated earnings at all time, since it is written on the bottom and at the top of the decision form for each round. At the end of round 4, the subject is asked to fill in additional control questions concerning her background. The experiment ends after all control questions are filled in. The subject returns the money to the experimenter and is informed
5 To ensure that the subjects are not influenced by my presence, subjects are informed that all data will be
handled completely anonymous and confidentially.
6 At the end of the experiment the subject writes her name and total earnings on a piece of paper and puts it in a
box provided by the experimenter. After all subjects finished the experiment, the experimenter will randomly draw a ticket from the box. The person whose name is on the drawn ticket will receive the amount she actually made during the experiment.
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within 1 week about whether she won the monetary reward. For the BL treatment group, the chance of winning one’s earning is 1/20.7
The introduction of an additional loss factor in GR is the main difference between both treatments. Besides this global risk, the GR treatment set up in a similar way as the BL treatment. The subjects allocated to the GR treatment are also given a red die. The experimenter reads out loud that there is a probability of 1/6 (0.167) that the subject losses all accumulated earnings in round 2 and 4. This is determined by a throw of the red die, which is tossed at the end of those rounds. The subject is reminded about the global risk at the start of round 2 and 4. Round 1 and the start of round 2 are similar to BL. After the outcome of the lottery in round 2, the subject throws the red die to determine the possible resolution of global risk. If the subject tosses a 1, she is struck by global risk. She losses all her earnings and is not allowed to continue the rest of the game. She is asked to fill in the same control questions as the subjects in the BL treatment and the experiment ends. If the outcome is higher than 1, the subject proceeds to round 3 with her accumulated earnings and follows the same steps as in round 1. In round 4, there is again a possibility to lose all earnings. The experiment ends after round 4 either with the resolution of global risk or without it. The subject fills in the control questions and returns the money to the experimenter. She is informed within 1 week if she won the monetary reward. For the GR treatment group, the chance of winning one’s earning is 1/27.8 In table 1 in Appendix A, the sequence of events is illustrated. Appendix B includes the instructions and decision forms for the experiment for both treatment groups.
Emotions are measured with self-reports. To keep the experiment in line with Bosman and van Winden (2010), emotions are measured on a 7-point Likert scale. Subjects are asked to rate their experienced emotions before and during the experiment from ‘no emotion at all’ to ‘high intensity of the emotion’. The emotions measured after the investment decision but before the outcome of the lottery and the resolution of global risk (conditional of being in the global risk treatment group) are happiness, hope, anxiety, fear, irritation and anger.
7 The BL treatment group consists of 20 subjects.
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IV. METHODOLOGY
4.1 Investment
For both the BL treatment and the GR treatment I am going to measure the amount invested in the risky option. To compare both treatments, the average investment in BL of all four rounds is compared to the average investment of all the rounds in GR. To check if average investment over all rounds in GR is different than in BL, a Mann-Whitney test is conducted. Variances of investment are also examined. To test for differences in distribution of investment per round, a series of Kolmogorov-Smirnov tests are conducted for each round.
Also, for both the BL and the GR treatment, investment per round is compared to other rounds of the same treatment group. To check for differences between rounds, the investment means per round are compared with another Mann-Witney test. Lastly, control questions are evaluated to test if there are significant differences between women and men and if FEB students or students that have experience with CREED experiments invest differently.
4.2 Emotions
Emotions are measured right after the investment decision, but before the outcome of the lottery. The self-reports can therefore give a strong indication of the emotions that occur when actually making the investment decision. In addition, by imposing more repetitions of the decision task, I can get more insight in the role of emotions. If the subjects play more rounds, the (hypothetical) earnings and potential losses also increase, which could lead to stronger emotional reactions. This makes an analysis of the hypothesized effect of emotions on investment more reliable.
For both treatment groups, I am going the summarize and investigate experienced emotions. A Mann-Whitney test is conducted to test whether there are significant differences in average emotions between the subjects in GR and in BL. Another set of Mann-Whitney tests is conducted to check for differences per round for each treatment group separately. In addition, multiple panel regressions are run to investigate the role of experienced emotions on investment. By making use of panel regression, I can get more insight on the effect of emotions on individual behaviour, across individuals and over the course of the entire experiment. The first-difference estimator is hereby most insightful, since it uses the individual-specific one-period changes for each subject. It estimates the one-period change of investment on the one-period change in an emotion. The regressions are run with the different
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emotions as independent variables, whereby different control variables (experience, FEB background, gender, treatment group) are also taken into account. The model can be represented by the following equation:
(1) 𝒀𝒊𝒕− 𝒀𝒊,𝒕−𝟏 = (𝒙𝒊𝒕− 𝒙𝒊,𝒕−𝟏)′𝜷
Whereby Y is the amount invested, X a vector for emotions, i the subject and t the measures per round. This type of regression is run for BL, GR and for all subjects taken together. An additional control regression is run for the data of round 3 and 4 to check if the outcome of two rounds are in line with the output over the entire experiment.
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V. RESULTS
Investment results
Figures 3.1, 3.2, 3.3 and 3.4 show the distribution of investment for each separate round. The dark bars represent the BL treatment and the grey bars the GR treatment. The BL experiment group consists of 20 subjects (10 males, 10 females) which all played four rounds of the investment game. The GR experiment group consists of 27 subjects (16 males, 11 females) of which 21 subjects played all four rounds and 6 subjects only played the first two rounds of the investment game, due to the resolution of global risk in round 2.
A clear difference in distribution shows up. In all rounds but round 1, distribution in GR is significantly more skewed to the right (Kolmogorov-Smirnov tests). In BL, investment ranges from €0 to €10 with large spikes at €3 and €5 with a median of €4 and a mode of €3. Average investment over all rounds in Baseline is €4.89 (st. dev: 2.56). In GR, investment ranges from €3 to €10 with large spikes at €6 and €7. Another spike is found at full investment (€10) in round 4. This endgame effect is also observed in BL and discussed further in section VII. Average investment in the risky option over all rounds is €6.83 (st. dev 1.99). This is significantly higher than investment in BL at a 0.01 significance level (Mann-Whitney test p = 0.000, t-test, p = 0.000). Average investment in GR is 41% higher than in BL. The median has increased to €7. The mode in GR is €6. Not only is the range of investment in GR is smaller, the variance also decreased (6.58 in BL and 3.95 in GR).
For both treatment groups the investment in the risky option differs a lot from the full investment that is predicted by EU. Only 17% of the subjects invested the full amount at least one time. This 17% is either risk-neutral or risk-loving. The other 83% showed risk-averse behaviour by putting part of the endowment in option A.
It turns out that investment is affected by gender. For both treatment groups, men on average invest significantly more than women.9 This is a not surprising, since theory (Byrnes et al., 1999) predict that women are more risk-averse than men. Experience with CREED experiments or studying at the FEB does not affect investment.10,11
9 For both treatments: men invest on average €6.81, women €4.72 T-test: p = 0.000, Mann-Whitney: p = 0.000
Men invest €5.95 in BL, women €3.78 T-test: p = 0.0001, Mann-Whitney: p = 0.0008. Men invest €7.37 in GR, women €5.86. T-test: p = 0.0002, Mann-Whitney: p = 0.0004
10 Students that have experience with CREED experiment invest €6.18, student without experience €5.81. T-test:
20 FIGURE 3.1: N in BL = 20, N in GR = 27 FIGURE 3.2: N in BL = 20, N in GR = 27 Kolmogorov-Smirnov: p = 0.070 Kolmogorov-Smirnov: p = 0.002 FIGURE 3.3: N in BL = 20, N in GR = 21 FIGURE 3.4: N in BL = 20, N in GR = 21 Kolmogorov-Smirnov: p = 0.000 Kolmogorov-Smirnov: p = 0.012
11 FEB students invest on average €5.69 and non-FEB students €4.19. T-test: p = 0.876, Mann-Whitney: p =
0.984 0% 10% 20% 30% 40% 0 1 2 3 4 5 6 7 8 9 10 R e lativ e fr e q u e n cy
Amount Invested in Risky Option Distribution Of Investment Round 1
BL GR 0% 10% 20% 30% 40% 0 1 2 3 4 5 6 7 8 9 10 R e lativ e fr e q u e n cy
Amount Invested in Risky Option Distribution Of Investment Round 2
BL GR 0% 10% 20% 30% 40% 0 1 2 3 4 5 6 7 8 9 10 R e lativ e fr e q u e n cy
Amount Invested in Risky Option Distribution Of Investment Round 3
BL GR 0% 10% 20% 30% 40% 0 1 2 3 4 5 6 7 8 9 10 R e lativ e fr e q u e n cy
Amount Invested in Risky Option Distribution Of Investment Round 4
BL GR
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Average investment per round for the BL and the GR treatment is summarized in table 2. In all rounds, average investment is significantly higher in GR.12 For BL, average investment clearly increases in the last round, but no significant differences in average investment per round are found at the 0.05 level.13 For GR, average investment in round 4 is significantly
higher than in any other round in the treatment group.14 There is also an increase in average investment between round 1 and 2 and between 2 and 3, however not significant.
TABLE 2: Summary amount invested in risky option (in euro’s)
Mean Values (Standard Deviation)
Baseline Treatment Global Risk Treatment
Overalla 4.86 (2.56) 6.83 (1.99)** Round 1 4.35 (2.21) 5.67 (1.80)* Round 2 4.35 (2.37) 6.48 (1.78)** Round 3 4.65 (2.16) 6.48 (1.78)** Round 4 6.10 (3.16) 8.33 (1.59)** a N = 80 in BL. N = 96 in GR.
(For all separate rounds in BL hold n = 20. For GR, n = 27 in round 1 and 2 and n= 21 for round 3 and 4) * Significant difference (0.05 level) between Baseline and Global Risk
**Significant difference (0.01 level) between Baseline and Global Risk
12 Difference investment round 1 between BL and GR. T-test: p = 0.0292, Mann-Whitney: p = 0.0038
Difference investment round 2 between BL and GR. T-test: p = 0.0010, Mann-Whitney: p = 0.0004 Difference investment round 3 between BL and GR. T-test: p = 0.0001, Mann-Whitney: p = 0.0002 Difference investment round 4 between BL and GR. T-test: p = 0.0069, Mann-Whitney: p = 0.0216
13 Difference in investment in BL for round 3 and 4: T-test: p = 0.09, Mann-Whitney: p = 0.145
14 Difference in investment in GR for round 1 and 4: T-test: p = 0.000, Mann-Whitney: p = 0.000. Difference in
investment in GR for round 2 and 4: T-test: p = 0.0012, Mann-Whitney: p = 0.0005. Difference in investment in GR for round 3 and 4: T-test: p = 0.054, Mann-Whitney: p = 0.078 (only significant at 0.10 level).
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Even though a shift to full investment is observed in round 4, with 30% of the subjects investing the total endowment, investment in the risky option is not in line with the predictions of EU, in any round. Neither are the results in correspondence with Rabin’s predictions of risk-neutrality as the majority shows risk-averse behavior. These findings are also at odd with the findings of Bosman and van Winden (2010), who find that the introduction of GR decreases investment. The analyses of the investment distributions and investment means lead to the following conclusion about investment with global risk:
Result 1
The introduction of a global risk of 1/6 has a significant effect on investment decisions. Compared to BL, average investment increases when global risk is introduced. This holds for every round.
Emotions and investment
Emotions can, as described in section 2.2, have a big impact on decision-making. Negative emotions like anxiety and fear elicited by the threat of losing one’s resources can interfere with rational decision making. On the other hand, positive emotions felt before the start of experiment, or elicited during the experiment, can influence decision making as well. In this section, an attempt is made to explain the investment results by looking at the affective states of the subjects.
Table 3 summarizes the average intensity scores of experienced emotions for all subjects over all the rounds of the experiment. The first column shows the intensity scores for BL and the second column for GR. For both treatment groups, the positive emotions are rated highest, followed by the negative emotion anxiety. A rough comparison reveals that subjects in GR are less hopeful, less anxious, and less angry. However, they are more fearful, more irritated and oddly also happier. The positive emotion hope is significantly lower in the GR treatment (Mann-Whitney, p = 0.04). The negative emotion irritation is significantly higher in the GR treatment (Mann-Whitney, p = 0.01). For all other emotions there are no significant differences between treatment groups. This contradicts the literature described in section 2.2, which suggests that anxiety, fear, and anger should also be higher in GR.
23 TABLE 3: Intensity scores of experienced emotions
Mean Values (Standard Deviation)a
Baseline Treatment Global Risk Treatment
Emotion N = 80 N = 96 Happiness 5.11 (1.13) 5.29 (1.14) Hope 5.23 (1.34) 4.83 (1.55)* Anxiety 3.66 (1.47) 3.46 (1.48) Fear 2.33 (1.32) 2.41 (1.31) Irritation 1.87 (0.78) 2.12 (1.15)** Anger 1.45 (0.74) 1.44 (1.31)
a Intensity scores range from 1 (no emotion) to 7 (high intensity of emotion)
* Significant difference (0.05 level) between Baseline and Global Risk ** Significant difference (0.01) between Baseline and Global Risk
In addition, when taking a closer look at the differences per round for each separate treatment we find that emotions are hardly affected by playing the investment game. Table 4 and 5 show the differences of experienced emotions per round for the BL and the GR treatment respectively. For the BL treatment, only hope and anxiety increase significantly compared to round 0 (in which the affective state before the start of the experiment is rated).15 In round 4, fear is also significantly higher compared to round 0. For all other emotions there is not enough statistical evidence to say that emotions changed by playing the investment game. In the GR treatment, only irritation increases significantly in round 4. No other emotion shows any significant difference in any round compared to the affective state before the start of the experiment. There are also no significant differences per individual round for any emotion.16
15 Tested with Mann-Whitney tests.
16 The fact that emotions hardly change between rounds could have several implications. I will return to this issue in the discussion.
24 TABLE 4: Experienced emotions per round in BL
Mean Values (Standard Error)a
Round 0 Round 1 Round 2 Round 3 Round 4
Emotion N = 20 N = 20 N = 20 N = 20 N = 20 Happiness 5.30 (0.18) 4.95 (0.22) 5.05 (0.26) 4.95 (0.31) 5.30 (0.29) Hope 4.10 (0.30) 5.20 (0.25)* 5.35 (0.33)* 5.55 (0.24)* 5.95 (0.23)* Anxiety 2.75 (0.29) 3.70 (0.26)* 3.75 (0.34)* 4.05 (0.34)* 4.05 (0.34)* Fear 1.90 (0.28) 2.15 (0.26) 2.35 (0.30) 2.45 (0.29) 2.80 (0.32)* Irritation 1.70 (0.16) 1.60 (0.18) 1.55 (0.15) 1.70 (0.19) 2.00 (0.17) Anger 1.65 (0.24) 1.35 (0.15) 1.40 (0.13) 1.45 (0.15) 1.40 (0.13)
a Intensity scores range from 1 (no emotion) to 7 (high intensity of emotion)
* Significant difference (0.05 level) between experienced emotions of this particular round compared to the start of the experiment.
TABLE 5: Experienced emotions per round in GR Mean Values (Standard Error)a
Round 0 Round 1 Round 2 Round 3 Round 4
Emotion N = 27 N = 27 N = 27 N = 21 N = 21 Happiness 5.16 (0.22) 5.12 (0.23) 5.04 (0.22) 5.29 (0.24) 5.50 (0.25) Hope 5.00 (0.29) 4.48 (0.28) 4.80 (0.37) 4.71 (0.32) 5.16 (0.34) Anxiety 3.80 (0.28) 3.32 (0.29) 3.48 (0.34) 3.45 (0.32) 3.25 (0.26) Fear 2.44 (0.25) 2.24 (0.23) 2.52 (0.30) 2.50 (0.27) 2.38 (0.29) Irritation 1.78 (0.23) 1.78 (0.19) 2.26 (0.22) 2.28 (0.25) 2.67 (0.22)** Anger 1.44 (0.15) 1.56 (0.15) 1.48 (0.16) 1.41 (0.17) 1.33 (0.15)
a Intensity scores range from 1 (no emotion) to 7 (high intensity of emotion)
** Significant difference (0.01 level) between experienced emotions of this particular round compared to the start of the experiment.
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From this comparison of means we can conclude the following:
Result 2
The experienced intensity of hope is significantly lower in GR. The experienced
intensity of irritation is significantly higher in GR. There are no other differences in experienced emotions between the treatment groups.
For subjects in the BL treatment, intensity ratings for hope and anxiety increased
significantly by playing the investment game. No other emotions are significantly affected.
For subjects in the GR treatment, the intensity rating for irritation increased
significantly by playing the investment game. No other emotions are significantly affected. Emotions do not differ per round.
Additional statistical analysis is needed to make any claims about the relationship between emotions and investment behaviour. A panel regression can provide information on the effect of emotions on investment behaviour, across individuals, over the entire course of the experiment. It estimates the one-period change of investment on the one-period change in an emotion for each individual. Investment in the risky option is hereby the dependent variable and the emotions the independent variables. For the regression analysis, emotions are normalized. Normalization is necessary, because the mutual distances between scales for each person might still be unknown. Normalizing emotions makes it possible to compare variables to each other. By normalizing, the Likert scale can be translated to analyzable data by using the same scale and by adding robustness to the effect of emotions. The outcomes of the panel regression for all subjects is displayed in table 6.
A Hausman test (p =0.0081), shows that the individual specific effects are correlated with the regressors. Therefore, the random effects model produces biased estimates, and a fixed effect model is preferred. For the first-difference estimator, the coefficients of happiness, hope and irritation are significant. When using the first-difference estimator, I find that a 1-point increase in irritation increases investment with €2.07, a 1-point increase in hope increases investment with €3.04 and a 1-point increase in happiness increases investment with €2.69. All other emotions are not statistically different from 0. In other words, the hypothesized effect of emotions occurs for happiness, hope and irritation, but not for the
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other emotions. Based on relevant literature (Loewenstein et al, 2003; Lerner and Keltner, 2001; Kaplanski et al, 2013) it is indeed expected that irritation, happiness and hope induce optimistic risk estimates, stimulates risk-seeking choices and increases investment. It is however not expected that none of the other emotions affect investment behavior significantly.
An additional control panel regression is run for round 3 and 4. The same coefficients turn out to be significant for the first-difference estimator, which adds robustness to the output in table 6. When running a panel regression only on the data gathered in BL, the first-difference estimator shows that only hope has a positive significant coefficient. For the data gathered in GR, the first-difference estimator shows significant results only for the coefficient on irritation.17 The regression analyses of the experienced emotions lead to the following
results:
Result 3
In BL, hope has a positive effect on investment. In GR, irritation has a positive effect on investment.
Overall, only happiness, hope and irritation have a significant effect on investment
behaviour. None of the other experienced emotions has effect on investment.
17 For the regression on round 3 and 4 and both separate treatment groups, regression results can be found in
27 TABLE 6: Panel regression over all subjects
Emotions over all rounds predicting amount invested in the risky option
Estimators Pooled Within or First Random
OLS Fixed Effects Differences Effects
Variablea Coefficients (St. Error)
Happiness 0.02 (.87) 2.71 (1.34)* 2.69 (1.23)* 0.88 (1.00) Hope 3.49 (0.97)** 3.61 (1.15)** 3.04 (1.05)** 3.38 (0.95)** Anxiety -0.95 (0.87) 1.02 (0.98) 0.75 (0.95) 0.07 (0.86) Fear -1.06 (0.95) -0.31 (1.21) -0.54 (1.09) -0.86 (1.00) Irritation 1.97 (0.81)* 3.35 (1.20)** 2.07 (1.01)* 2.21 (1.00)* Anger 0.47 (1.06) 1.36 (1.41) 1.84 (1.43) 0.90 (1.13) Gender 1.44 (0.32)** - - 1.39 (0.46)** Treatment 1.86 (0.31)** - - 1.78 (0.45)** Constant 1.89 (0.70)** 0.29 (1.08) - 0.76 (0.85) R2 Overall 0.373 0.088 0.181 0.353 R2 Within - 0.258 - 0.233 R2 Between - 0.047 - 0.429 Sigma U(t) - 2.089 - 1.181 Sigma e - 1.536 - 1.550 Rho - 0.649 - 0.372 Theta - - - 0.455 N 176 176 176 176
a All variables are normalized before running the regression
*Significant at the 0.05 level **Significant at the 0.01 level
Note:
Number of subjects: 27 Total observations: 176 Observation per subject: 2 or 4
A Hausman test (p = 0.0081), shows that the individual specific effects are correlated with the regressors. Therefore, the random effect model produces biased estimates, and a fixed effect model is preferred.
The data set is unbalanced since 6 subjects did not make it to round 3 and 4 due to the resolution of global risk in round 2.
The Treatment dummy is 0 for BL and 1 for GR. The dummies Experience with Creed and being a FEB student are not significant in GR and therefore omitted from the regression.
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If result 3 holds, the higher intensity rating of hope in BL (illustrated in table 3) would increase risk-taking compared to GR. Hence, the model would predict a smaller difference in investment (if we only account for emotions). However, investment is significantly higher in GR. I provide two explanations for why hope is higher in BL, but investment is still significantly lower than in GR. As a result, I conclude that the main driver for investment in this experiment is irritation.
Firstly, a major problem with the measurement of hope is reverse causality. It turns out that for both treatments, hope is affected by the amount invested. When running an ordered logit regression with normalized hope as dependent variable and amount invested as independent variable, I find that investment has is positively related to hope in both treatments.18 This makes sense, as people get more hopeful about winning after they invest (Lopes, 1987, p. 270). This relation is not found for irritation. As a results, it is not clear whether hope has an effect on investment, whether investment increases the intensity ratings of hope, or that hope itself is even induced by the introduction of a global risk. This indicates that with the data gathered in this experiment, and with the coefficient of hope suffering from reverse causality, the coefficient on irritation is the only significant unbiased determinant of investment. The higher irritation in the GR treatment (table 3) can than indeed be the driver behind the increase in investment for that treatment group.
Secondly, the intensity measure of hope in BL could be influenced by another emotion. Hope and happiness are strongly correlated in BL.19 This correlation is not observed in GR.20 Happy subjects are more inclined to maintain their good mood by avoiding risk-taking (Nygren and Isen, 1996). With the intensity of hope in BL being correlated with happiness, it could be that there are two opposing action tendencies for the effect of hope on investment. On the one hand there is more risk aversion induced by mood maintenance, on the other there is more risk seeking induced by more positive risk-estimates. If these two tendencies are indeed at work in BL, it would explain the higher intensity rating of hope in this treatment, but yet the relatively lower investment in the risky option.
Taking these points into account, the regression output and the comparison of means partly support hypothesis 2, as it is only statistically valid for 1 emotion. The results show that irritation indeed is affected by global risk and that irritation is a significant determinant
18 Coefficient of investment BL 0.191 (0,08), p = 0.022; Coefficient of investment GR 0.319 (0.08), p = 0.001
19 Spearman rank-order coefficient in BL 0.43 p = 0.000
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of investment. An increase in irritation causes subjects in GR to be more risk-seeking which can account for the difference in investment between the treatments. That increased irritation can be conductive to risk-seeking is in line with the literature discussed in section 2 (Leith and Baumeister, 1996) and is also found in Bosman and van Winden (2010). In the next section, an additional explanation for the result will be taken into consideration.
VI. CUMALITIVE PROSPECT THEORY
As irritation can be conductive to risk-seeking, result 2 and 3 can provide an explanation for the increase in investment in GR compared to BL. Emotions change by introducing global risk and emotions are a significant determinant of investment with global risk. Besides focusing too much on the emotional side of decision making, an explanation for the increase in investment in GR can also be provided by looking at the cognitive side of decision making. Cumulative Prospect Theory (CPT), the main contender of EU, predicts that the introduction of global risk leads to more risk-taking. Peter Wakker provided his analysis about the effects of global risk on investment to Bosman and van Winden (2010) and find that CPT predicts that if anything, global risk will enhance risk-seeking and thus lead to more investment.
The main observation of CPT is that people tend to think of possible outcomes relative to a certain reference point or status quo, and have different risk attitudes towards this reference point. For outcomes with high probability, people tend to be risk averse for gains and risk seeking for losses, whereas for outcomes with low probability, people are risk seeking for gains and risk averse for losses. In addition, people tend to overweight extreme, but unlikely events, but underweight moderate and high probabilities. CPT also accounts for loss aversion. In CPT, risk aversion and risk seeking are determined jointly by the value function and by the capacities, the cumulative weighting functions. General CPT assumes that a value function is concave for gains, and convex for losses. Utility is determined by these gains and losses, and not by final wealth as is described by EU. The difference between the capacities of the events in where an outcome is ‘at least as good’ as the reference point and ‘strictly better’ than the reference point is denoted by the weighting function
π
i+. Thedecision weight
π
i- is associated with a negative outcome, which are ‘at least as bad’ or30
outcome is multiplied by the decision weight and compared to the initial reference point. Peter Wakker provided an analysis based on the mentioned characteristics of CPT.
The analysis the decision problem in figure 2 goes as follows. Subjects enter the experiment with a reference point of 0, as they don’t receive any money. As a result, people view every outcome as a gain towards the reference point. Therefore, when considering the decision problem described in figure 2 with CPT and a reference point of 0, the lottery (z + 1.5x, p/2; z – x, p/2; 0, 1 - p) is evaluated as π1U(z + 1.5x) + π2U(z – x) + π3U(0), where π1 =
w(p/2), π2 = w(p) – w(p/2) and π3 = 1 – w(p) for a probability weighting function w. When
looking at the first-order derivative of investment x, equation (2) shows that people do not want to reduce an investment x if the following holds (Bosman and van Winden (2010):
(2) 𝑈′(𝑧+2.5𝑥) 𝑈′(𝑧−𝑥)
≥
2 3 𝜋2 𝜋1Without global risk (p = 1), π1 = w(p/2) = w(1/2) ≈ 0.42 on average, according to the
weighting function described by Tversky and Kahneman (1992). With w(p) = 1, π2 = 1 – 0.42
= 0.58. This means that the RHS of (2) will approximately be equal to 0.92. With constant marginal utility, the LHS of (2) will be approximately 1, which means that people are not willing to reduce investment and all money is invested; x = z. This result is not found in this experiment, but if a power utility function is used, as is in Wakker and Zank (2002), less extreme investment predictions can be obtained.
In the case of global risk, p becomes smaller. By using the empirical finding by Tversky and Kahneman (1992) of an inverse-S probability weighting function, π1 will
become relatively larger. Consequently, π2/π1 will decrease, lowering the RHS of equation
(1). As a result, under the assumptions mentioned above, investment will increase after the introduction of global risk. This holds for every round r when considering a reference point of 0, because the value of the prospect is the same in every round. In words, the effect of GR can also be explained by the prediction of CPT that a small chance of winning enhances risk taking.
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VII. DISCUSSION
6.1 Related literature
Seeing that the differences between BL and GR can be accounted for by taking both the affective and the cognitive state into account, it is interesting to dive deeper into the differences between this experiment and the experiment by Bosman and van Winden (2010). After all, they find that GR induces more risk-aversion, which contradicts EU, CPT and the findings of this experiment. Compared to the experiment of Bosman and van Winden (2010), two alterations are made: (1) a significant smaller global risk (2) an increase in the amount of rounds played. Both will be investigated to see if the differences in experimental set-up can account for the different results. Also, an answer to the question raised in the introduction will be formulated about whether the observed effect is due to possibility of losing one’s resources, or instead due to the size of the probability of the GR.
To start off with the smaller global risk. With a global risk of 1/3, Bosman and van Winden (2010) find a U-shaped distribution of investment in GR which is due to the two opposing action tendencies of anxiety and irritation. I find that a global risk of 1/6 induces risk-taking, which results in an investment distribution that is heavily skewed to the left. Based on this result alone, one could say that the result indeed depends on the size of the probability. However, another explanation can again be provided by looking at the emotions of the subjects.
Based on the distinction of anxiety (decision anxiety and situation anxiety) found by Bosman and van Winden (2010), anxiety ratings in this experiment should be much higher in GR than in BL. The higher investment should lead to more decision anxiety and the introduction of a global risk should lead to more situation anxiety. However, anxiety ratings do not differ between treatment groups. Neither do I find the positive relationship between investment and anxiety in BL, which is observed by Bosman and van Winden (2010). When running an ordered logit regression with normalized anxiety as dependent variable and amount invested in the GR as independent variable, I however find that investment does have a positive relation to anxiety in GR.21 This implies the presence of decision anxiety in GR, as
anxiety increases when investment increases. Despite the presence of decision anxiety in GR, the intensity ratings of anxiety in the two treatment groups show no significant difference.
21 Coefficient of investment on anxiety BL -0.13 p = 0.07
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This can be an indication of less or no situation anxiety in GR. Otherwise anxiety ratings in GR should be even higher. It is possible that subjects in this experiment felt less situation anxiety in GR compared to Bosman and van Winden (2010), because of the difference in the incentive scheme.
The subjects in Bosman and van Winden (2010) received 30 guilders and had to use this as working money. If the subject was unlucky in the lottery, she actually lost her investment, which implies that she would go home with an amount less than 30 guilders. This increases loss aversion and subsequently induces situation anxiety. In this experiment, subjects do not play with their own money. There is no real fear of losing one’s income. This claim is supported by the fact that emotions in GR did not change significantly during any round in the experiment (aside from irritation in round 4). It is highly possible that a major part of anxiety in GR is induced by making the decision in the investment game, and not by the situation anxiety experienced. Decision anxiety on the other hand, could still be experienced, as the subjects play a game in which they could win or lose hypothetical money.
If there is indeed no situation anxiety in GR, the increased irritation found in this experiment (and in the experiment of Bosman and van Winden) would explain the more risk-taking behaviour in GR. Without the opposing action tendency of anxiety, the U-shaped distribution of investment in GR found by Bosman and van Winden (2010) would also change in a more left-shaped distribution of investment. Similar to the distribution observed in this experiment. If there are similar incentive schemes with real money, it is likely that situation anxiety is also observed in this experiment. It would then be possible that the opposing action tendency of anxiety would result in a similar distribution of investment as the one in Bosman and van Winden (2010). Therefore, without using similar incentive schemes, no claims can be made about whether the difference in investment is due to the size of the probability of the global risk.
This leaves the increase in rounds. As is found in the analysis of the investment results, investment does not differ per round in BL. In GR, an increase in investment is only observed for the fourth round. For any other round, investment increases, but not significantly. The (insignificant) increase in investment discards the myopic loss aversion effect described in section 2.3, which would predict a decrease in investment. Without having proper incentives, it follows logically that there is no myopic loss aversion.
As the tendency towards more investment is only significant for one round in one treatment, the statistical analysis shows that there is no learning-effect when the investment game is repeated for four rounds. If there was, more economically rational investment
