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MSc Economics
Track: Behavioral Economics and Game
Theory
Master Thesis
A bezzle in the haystack:
alterations of the perception of total wealth affecting trust and
investments.
by
Daniele Di Nepi
11815965
August 2018
15 ECTS
Supervisor/Examiner:
Dr. T.J.S. Offerman
Department of Economics
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Statement of Originality
This document is written by Student Daniele Di Nepi 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.
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Table of contents
I.
Introduction and motivation...p.4
II.
Literature...p.7
III.
Experimental Design...p.11
IV.
Research and theoretical hypothesis...p.14
V.
Data and results...p.19
VI.
Comment and Conclusions...p.30
VII. References...p.32
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A bezzle in the haystack:
alterations of the perception of total wealth affecting trust and investments.
Abstract
The bezzle is the sum of all the money individuals in the society think to have, that is actually not in their possession anymore, due to the illegal actions of others, such as frauds, or to their own biased perception, in case of self-delusion and mistakes. Previous researches were trying to find a relation between the business cycle status and the size of the bezzle, growing in booms and shrinking after crashes. The objective of this article is to analyze the effect of perceived scarcity and abundance in altering the awareness of an uncertain income and the later consequences on trust and decision-making in investment circumstances by using an empirical method that was not previously employed. The experiment is built up focusing on trying to induce abundance and scarcity states into subjects, following the definitions from the literature on the topic. The results are mainly going towards the predicted direction, even if they are not, in their entirety, statistically different from the control group. The main reason for that could be linked to the small sample adopted and an order effect that was not avoided in the experimental design.
I. Introduction and Motivation
After ten years from the beginning of the financial crisis, macroeconomic experts still struggle to find a solution able to restart the growth engine. In Europe the quantitative easing, a vigorous expansionary monetary policy, managed to stabilize the market and helped to overcome the sovereign debt crisis. However, the effect on growth was still too minimal when taking into account the magnitude of the intervention, that is in the order of hundreds of billions. The majority of the debate came from trying to understand at which point the chain process that should increase output, at least for the short run, was disrupted. After the balance sheets of the banks were freed by the ECB policies, then firms investments should start to increase, especially with a really low interest rate as an incentive. For some the problem was an unexpected low demand for loans by entrepreneurs, for others it was the bankers’ supply side the real problem, not conceding the investments to small and medium businesses. From an analysis by Perotti (2016), interesting data show how firms became net lenders for the economy having immobilized resources waiting for investment opportunities in a degree that was never seen before.
The main objective of this paper is to find a possible reason for the aforementioned stagnation in the decreased trust by the investors, while using an approach based on behavioral economics that could also help to explain a number of macroeconomic observations related to the absence of
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technological progress and the increased protectionism. It could be that the global financial crisis acted not only directly, in the numbers of the economy. An indirect change could also affect the behavior of its participants and their attitude towards investment opportunities, especially when considering the latest literature about the effect of scarcity and abundance on people’s way of thinking.
Investments are decisions subject to psychological influences that might have been oriented towards the same direction by the economic depression and the way it matured. The research question of this paper revolves around the effect of the two states of the business cycle, sustained growth and sudden crash, together with the two mental states of abundance and scarcity deriving from those economic conditions. These variables affect investments more indirectly than the interest rate and are more difficult to quantitatively detect as their predicted consequence is a movement in trust, rate of fraud and their discovery. Therefore it must be clear that the paper does not concern the reason of cooperative and reciprocal behavior by humans, instead, it is mainly concerned to its sensibility to a context of growth and crisis.
Figure 1: Gross saving in blue and gross investments in red of companies between 1960 and 2013.
Taken from Perotti 2016
The experimental design applied to the study is a trust game as seen in Berg et al. (1995), with the addition of another decision available to the trustor that will have the possibility to pay for
controls and avoid an unfair division of payoff or just accept the decision of the trustee while having an higher level of earnings in case of fair division. In this way, they both have to formulate expectations regarding their partner behavior. The method to induce a state of abundance will be applied by giving subjects in the treatment group a lump sum of 5 and 10 euros in the two rounds of growth, while in the case of scarcity, by subtracting 30 euros from their total earnings in the crisis round. The effect on trust will be observed from the participants’ choices and how they are distributed in the different rounds, together with the beliefs they declared about the actions of the other player in the couple.
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The inspiration came from a commentary of the great crash of 1929 and from one of the most important researchers of that period J.K. Galbraith (1955). In describing the dynamics of the crisis, the author talks about the embezzlement, a really interesting crime since it involves a time factor in which the fraud is yet to be discovered by the victim, even if already perpetrated by the
fraudster, causing an increased perception of total wealth between the two parts. In fact, at any time in an economy, there exists a “bezzle”, an artificial sense of abundance, that temporarily increases the perception of total wealth between individuals.
More importantly, the bezzle is said to vary with the business cycle. In good times when “people are relaxed, trusting and money is plentiful”1, the rate of embezzlement increases, the rate of
discovery falls and a lot of people think to be richer and more successful than they actually are, as the crime still has to be found out. What happens, instead, with the crash that follows is the exact opposite, with “money watched with a narrow, suspicious eye”2, people assumed to be dishonest
and the controls of audits being far more penetrating. The situation is described as a switch from “universal trust” to “universal suspicion”.
There is not a right or wrong choice in the decision to have more or fewer controls. Nevertheless, the way this choice is influenced by the business cycle, or its altered perception by the amount of bezzle, could cause a number of problems. In fact, if everyone is more or less trusting because of an artificial increase in the amount of wealth, this might have a strong impact on the actual
investment and growth or cause stagnation after a crash. This inconsistency in the behavior and in the preferences of the participants could also tell something more about the behavior of other variables affecting trust, such as reciprocity. The study here proposed tries to identify an effect on the decision-making process of evaluating what the other person ethical behavior will be. In the experiment, the bezzle will be measured by the choices of the participants and the number of decision that have been done in order to keep all the money by the trustees while its effects of alteration will be brought more directly by the exogenous shocks to the economy that at first will be giving money to subjects, and then take away even more from their previous earnings. The fact that subjects will not know about their result until the end of the four rounds means that they will have to formulate positive or negative expectations about the other person in the couple.
Therefore, the study is not about the creation of the bezzle, but on its effects on trust and investments, assuming it has the same effect of an increased wealth. In this sense, the consequences on abundance would be related to making the participants more exposed to embezzlement decisions in the growth rounds, while investing more carefully or not investing at all in the depression case. The results of the experiment are not fully consistent with the research hypothesis for the growth treatments, although showing a decreased number of control decisions together with more unfair divisions overall. Data have more insights when looking at the crisis treatment, with more controls and out options being selected. Moreover, an interesting effect on the belief of the trustee is highlighted: in becoming less confident of an investment decision by the
1 Galbraith,J.K. (1955) pp.152-153 2 Ibidem
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trustor, they seem to increase the importance of reciprocal concerns for the ones actually investing, with a number of fair divisions choices higher than previous rounds.
II. Literature
The idea of the bezzle was not only related to the 1929 great crash. Another important economist, John Kay (2015), recently took back Galbraith’s portrait to describe what happened before and after the financial crisis of 2008. The same characteristics of the embezzlement are seen in different areas of interest. Kay cites Charlie Munger, a business partner of Warren Buffett that extended the concept of bezzle to non-illegal situations. Mistakes and self-delusion can, in fact, have the same effect of wealth creation described by Galbraith for the embezzlement. If a person expects to become rich, as in periods of speculation, is difficult to “stand in the way of the
crowds”3 and their trust decisions are directly affected. The author brings a number of interesting
cases to prove this point, such as the one of Enron under Jeffrey Skelling, a gas company that started to trade gas contracts in the same way as it was going on with mortgages at that time, with a mark to market accounting use. This resulted in a price reflecting the profits that might accrue in the future with this possibility being ultimately defined by “what the market thinks”4, in this case,
to become rich. Enron titles were being bought in quantity, although not closely understood, before the crash that came in 2001. The hypothesis advanced is that there might have been an increase in negligence by the operators generated by a form of legal bezzle. Kay describes more expressions of this carelessness and how the “financialization” that started in the 80s brought these behaviors with “investors knowing less or nothing about mortgages they were investing on” and “asset-backed securities sold in the ignorance of the quality of the underlying assets5”.
Moreover, in his historical analysis of the crisis of the late twentieth century there is a recurrent pattern: the origin is a genuine change in the economic environment, positive events with
prospects of growth and profits such as “the success of emerging economies, the development of the internet, innovation in financial instruments and the adoption of a European common
currency”6. Those events trigger the “good times” of Galbraith with an abundance of money and
investment opportunities, however, followed by more carelessness and a lower discovery rates of frauds, inflating the growth. In fact, as Kay describes “early spotters make profits, a herd mentality among traders attracts more and more people and money into the asset class concerned. Asset mispricing becomes acute”7. The finale is well known with emerging markets debt problems, the
new economy bubble, defaults on asset-backed securities and the sovereign debt crisis. In the middle, a store of transitory wealth or “bezzle” generated from profits earned in overpriced stocks and other titles, from operations that can be nearly defined as frauds, even if originated from a completely legal human reaction.
3 Kay,J.(2015). p.127. 4 Ibidem p.128 5 Ibidem pp 86-87 6 Ibidem. Pp.41-42 7 Ibidem p.42
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Other academic articles, inspired by Galbraith, tried to test the relation of corruption and business cycle status and found contrasting results. Gokcekus and Suzuki (2011) built up a model in order to confirm Galbraith intuition in econometrics terms, using panel data estimation from 1995 to 2007 in 39 countries. The parameters estimated measure the effect of permanent and transitory income variations on the corruption perception index (CPI). The results end up supporting the initial assertion with a positive significant relation between transitory income, reflecting the business cycle status and measured as deviation from average income in the sample, and corruption. The bezzle grows during booms and shrinks in depressions. Kéita and Laurila (2016) replicated the previous study with a bigger dataset and found opposite results. This time the countries included were 113 and the years from 1998 to 2013. The model is the same, with an additional measure for corruption, the control of corruption index. From the results, it would seem that both transitory and permanent income have a positive influence on integrity and commercial morality. It must be underlined, though, that it is difficult to find a quantitative measure of the bezzle, as it is complex to calculate and, by definition, it comes unnoticed during the time is present, that is, from Galbraith’s point of view, during booms and discovered during recessions. Moreover, an index of corruption or perceived corruption in affairs, may not be the right mirror of the variable, as it is also said by Kéita and Laurila. This measure would not be taking into account mistakes and self-delusion, with all the other form of “legal bezzle” coming from overpricing, mistakes and inattention, whose importance was previously described. Besides, another limitation of the study is that a bigger sample of countries was not followed by controls for classes of
income. In fact, a lot of the countries being introduced in the dataset are developing countries and this could be causing the difference in the conclusions.
Trust in itself has been analyzed in many different ways. From an empirical point of view, many articles tried to explain why individuals tend to take an action that does not assume self-interest from the other person. In Berg et al. (1995), one of the main references for the trust game, trust is seen as what facilitates an exchange and makes it possible to achieve a better result for the group even by turning down a better individual payoff and it is therefore at the basis of developed societies. The experimental design was thought in order to highlight reciprocal behavior concerns, without looking at reputational factors or other opportunistic reasons. In fact, the trustee knows that the money he obtained can be the result of trust only. Therefore, sending back an amount would be a sign of reciprocating the trust he just received. The results of the study demonstrate that participants are sensible to reciprocity, and social history of the previous behavior of the other person in the couple does not negatively influence the choice to trust while, instead, it increases the average payback of trustees. Variations to this study showed how behavior changes, together with the willingness to reciprocate, in different contexts. For example an higher
monetary prize assigned to the self-interest option, as in Guth et al.(1997), decreases the average payback by trustees. In the case of Anderhub et al. (2002), the focus is on the effect of reputation with the introduction of repeated rounds, to study if in this case reciprocal behavior is present or the choices are just the result of opportunism. The new neuroeconomics perspective provides other insights, as in Delgado et al. (2005), describing how prior moral and social information about a trustee affects the neural circuitry of reward and activity in the caudate nucleus region. This area
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is linked with trial and error learning and activity seems to decrease when the quality of
predictions starts to improve. In previous studies, this reaction was also found in repeated trust games with the caudate nucleus activity going down when behavior started to be predictable, while producing a higher response at the beginning of the game. In this article, the authors wanted instead to avoid reputational concerns and trial and error learning, while studying the relevance of moral beliefs, that were also cited in Berg’s paper as an important influence for the final choice. Participants were in fact provided with 3 fictional partners to play with together with a description of each of those being morally positive, negative or neutral. The descriptions could have left the situation unchanged or generated expectations on the behavior of the other person, that if respected or not, should activate the caudate region for trial and error learning. Another possibility, would be to remain faithful to the descriptions, even when the partner’s behavior is incoherent, and ignore the trial and error completely. Trustors decided to share more when coupled with a positive character, however, if in the case of a neutral description the choice seemed more motivated by trial and error learning with activation of the caudate region, for negative and positive profiles there was an absent or non-significant response to feedback. This means that even if the actual behavior contrasted with the moral description, the decisions to share stayed high in the case of a morally good partner. The conclusion is that trust is externally influenced by the perceived morality of the other person, even more than from the actual feedback received. This is particularly important for this research, as it introduces a possible alteration of the behavioral responses, in this case due to morality. Moreover, the decreased reaction to the actual feedback could also happen with states of the business cycle, motivating the decisions more than past experience.
In addition to this, trust was studied as a source of economic growth, in the literature related to social capital and Putnam hypothesis, that view social ties and associations as a source of economic efficiency. However, the opposite relation was never studied especially in empirical papers. In a recent study by Stevenson and Wolfers (2011), they attempted to understand the coincidence of the decline of trust in American public institutions and the great recession, and underlined how “there is little existing literature documenting the cyclicality of trust” and that “our understanding of the links between economic performance and trust leaves much to be desired”. In their research, the attempt is to link the answers to surveys about trust in institutions to the business cycle status. The results, especially the one concerning banks, highlight a strong negative relation with unemployment, meaning a substantial procyclical behavior.
Given that, the attempt is to see if this effect on trust is related to institutions only, as more involved in the economy of the country and its outcomes, or it concerns also the single individuals in an investment relation, during different business cycle periods. Recent literature about the effects of scarcity and abundance on people decision making can clarify this point, as they are a parallel of the states of sustained growth and sudden depression being studied and have important psychological consequences on the individuals, similar to the ones described by Galbraith. As explained by Mullainathan and Shafir (2013) in the book “Scarcity”, a state of abundance is generated by unused resources, as the space left empty while preparing a big luggage that allows to simply throw in clothes and other things without thinking too much about
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saving space, while scarcity is the necessity to make compromises, being forced to do that by the limited resource as in the case of leaving something out of a smaller luggage. This can be applied to different dimensions from money to time and social relations representing the space at disposal.
Scarcity has multiple effects on us. First of all, it makes us concentrate and efficient on what there is scarcity of. The book provides multiple experimental studies that prove this “focus dividend”. For example in an article by Shah, Mullainathan and Shafir (2012), subjects where playing a modified version of the popular video game “angry birds”, called “angry blueberries”, in which they had to fire shots from a slingshot to gain points. Scarcity and abundance states were induced by endowing them with more or fewer shots to throw. The participants with more shots were earning more points while, on the other hand, they were also spending less time aiming. In fact, the less endowed were more precise and earned more points per shot, with 2.31 instead of 1.67 on average. A proof that “Having less elicits greater focus”8. The following experiment from the
same article presented another famous game, family feud, in which the subject had to give as many answers as possible to a number of general questions with multiple responses, without one being right or wrong (e.g. what is the best movie in history?). Answers that were more popular and given by more people earned more points for the participants, and, therefore, the key to winning was to predict what the others were thinking. Again, individuals were divided into scarcity and abundance treatment groups, measured by the time they had at their disposal to give answers, 300 seconds versus 1000. Second per second participants with less time were again more efficient than the one with more time, sometimes even with 50% more answers.
That said, scarcity also brings drawbacks. It causes not only a focus dividend, but also a “tunnel effect”. The concentration becomes so strong that everything unrelated to the scarce resource becomes blurred. For example, the student with no money to pay his rent may put less care on studying and exams. In general, people could make choices that, in the long run, cause even more scarcity of the resource they are missing. This is because the person becomes much more present-oriented and wants to solve his issue immediately.
The effect is a kind of tax imposition on our cognitive capacity and self-control. This is also what the authors find, a pervasive effect, also calculated by using IQ test exercises such as Raven’s progressive matrices. In an experiment by Mani, Mullainathan, Shafir and Zhao (2013), subjects were divided into rich and poor by using the median income they declared to the researchers. Then both of them were randomized into two treatment groups of scarcity and abundance, characterized by a situation they proposed to them on a piece of paper. It was just a question about spending for full repairs after a car malfunctioning or repair what you could with the money from insurance and going on with the risk of more damages. The difference was that in the
scarcity treatment the amount to be paid was much higher, 3000 dollars instead of 300. After that, participants had to complete a Raven’s matrix test. If in the 300 dollars treatment the
performance of rich and poor was the same, in the 3000 dollars a huge gap was created in terms
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of results in Raven’s test of IQ. Money mattered much more and left the subjects with less cognitive power. Even with just the thought of a 3000 dollars reparation bill, the effect on fluid intelligence was already visible.
That said, is not only scarcity that causes these issues. This happens even more in states of abundance. Too much on the scarcity side and there is distraction, inattention, lower cognitive ability and capacity to plan. Too much on the abundance side and there is procrastination,
laziness, inefficiency and mistakes in spending, mainly because there are so much time and money that every mistake is not felt too much. Abundance is in fact characterized by unused resources, the possibility to make mistakes and do not feel the presence of trade-offs, as what is being lost has a really low value. In the investment context studied in this research, it is related to periods of high profits and sustained growth when losing something in a market operation is felt as less painful. Problem is that the result is inefficiency and waste, as money is consumed with ease. More importantly, the idea is to think what happens when the state of abundance is artificial, with an increased perception of total wealth caused only by forms of “bezzle” as frauds, mistakes in pricing or over-excitement, and what are the consequences when this is discovered after a market crash.
“The seeds of the scarcity trap” are in these periods with relative abundance at disposal. Besides, when a resource is abundant, it is common to see it wasted9. The conclusion is that there might be
a relationship between the amount of resource and performance that reaches a maximum with enough unused resources, to not feel the negative effects of scarcity, and falls down at the extremes. The same thing could go on with investment’s decisions and trust between the parts.
III. Experimental Design
The experimental structure is briefly summarized in the game tree of figure 2. It is built up starting from a typical trust game as a parallel of the investment relation, however, it has a clear
difference, as player 1 has access to an additional decision node. All participants are randomly assigned to two roles of trustor and trustee and organized in couples, that will stay the same for the duration of the experiment. If the player starts as a trustor, he will always participate in that role, coupled with the same trustee. The objective is to concentrate on the effects of abundance and scarcity, that will be induced in the treatment group, on the choices available to the players in the game.
First of all, the trustor receives an initial endowment of four euros and has to decide whether to invest the money in the trustee, multiplying the amount to twenty euros, or keeping the 4 euros ending the round. If the trustor decided to invest, the trustee can choose what to do with the 20 euros. He has access to two actions, labeled give and keep. Choosing give means to equally divide the money resulting in 10 euros for both, while keep causes an unequal division, with 19 euros remaining with the trustee and the trustor receiving only 1 euro. Give and keep would represent the possibility open to the trustee to fraud his counterpart, without him knowing. In fact, the
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trustor will not be directly informed of the choice of the trustee, as represented in the game tree with a dashed line. In addition to this baseline setting, another decision node for the trustor was designed, to have a measure of the rate of discovery and audit choices in the different treatments. The two possible actions are called costly check and free pass. The former works as an insurance for the trustor as it limits the damages if the trustee was defrauding him, while it is also expensive if the investment was instead going well. The free pass option is just the opposite, leaving the situation as it was after the trustee choice. It wants to symbolize the decision between a careful, although, expensive analysis in terms of money and time or a cheaper one, but also riskier.
Figure 2: Game tree with payoff of player 1 on the left and payoff of player 2 on the right. In each decision
node the number represents which player is the one making a choice.
The payoffs associated to an equal division without check would be 10 euros for both players, if, instead, the trustor decided to check, his earnings would go down to 5 euros reflecting the expense for an audit or other types of control on investment. When the trustee was instead choosing the unequal division, if the trustor is not checking, he would earn 1 euro while the trustee would be getting 19. Otherwise, if the trustor decided to be more cautious and pay for controls he would get 3 euros, that is less than what he would have received by staying out and not investing on the trustee, which is also a better situation in reality. However, he would still get more compared to playing pass. The trustee instead would earn 2 euros, that results in his worse possible outcome, as he is being caught defrauding. At the end of the round, participants are also asked to estimate the probability of the other players’ decisions, in order to have an idea of their beliefs. The experiment is made of 4 rounds and this base structure is common to both the treatment and the control group.
To avoid any effect of reputation, participants are informed of the results only at the end of the experiment and no communication is allowed between the players in the couples, with no
information provided between the rounds. Although this excludes important factors in generating trust, such as reputation building between the parts and learning, it is also true that a lot of investments nowadays do not involve knowing the other person or the development of a relation. In most of the cases, a click on brokers platform is enough. At the same time, it removes any effect
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caused by previous responses and allows to isolate the effect of the two treatments being studied of abundance and scarcity on the choices in game. Those two would be induced in round two, three and four of the treatment group as exogenous shocks from the rest of the economy. The idea is to follow the definition contained in Mullainathan and Shafir (2012) and generate unused resources for the subjects. In round two, both of the parts receive 5 euros that will not be involved in the game and do not risk to be lost, described as profits from other activities and not related to this particular game. This is an attempt to generate “a bigger luggage” at disposal for the
participants and see if this has an effect on their choices and behavior, even without being the result of the their partner choices. In the third round, both parts receive 10 euros that, as before, are for them to keep and are not involved in the game. Having more than one round of abundance reflects the fact that usually those periods are more gradual and last longer as opposed to the crash that is sudden and tend to be strong and fast. Therefore, in the last and fourth round,
participants will face the market meltdown and lose 30 euros from their accumulated earnings and then play the same game again. Scarcity is made of trade-offs and compromises and in this case, subjects will have to choose considering they could be finishing the experiment earning nothing. Even though is not the best way to induce scarcity in this context and other ideas were considered, this is the easiest one for an online design and makes the game direct and clear. If the trustor chooses not to check, he knows that now his mistake will matter and a possible fraud from the trustee will be felt much more as it could potentially lead to zero earnings. This is already a good feature coming from the “possibility to make mistakes” typical of abundance and the more severe consequences to false steps associated with scarcity. It would be interesting, in subsequent
attempts, to introduce prizes for each earning level, representing the different expenses that each level of income allows to make and, more importantly, the decreasing marginal utility of income. Another possible feature to add would be to let the players know their previous results after the crash treatment, so as to represent what happens after discovering a fraud.
A between subjects design was implemented, with a control group made of different players, also playing four rounds with the same structure, however, without any exogenous shock to their earnings. This will be the term of comparison for the results, to see what is the effect of the treatments proposed. Even if this design does not control for the individual fixed effects, it
removes any order effect between the two groups, which, in this case, would cause a confounding factor in the analysis.
Given the characteristics of the experiment, it was thought to build it up on the internet, in order to have access to more observations. Without the need for any interaction, a strategy method was implemented, with every player just making conditional decisions at every information set. This means that subjects will not know directly what the other person in the couple chose. Instead, they will give their decision as if their partner took a certain response. With this experimental structure and the incomplete information of the trustor, the only decision where the strategy method makes a difference is the one of the trustee, that plays as if the trustor chose to invest. At the same time, if this is not the case and the trustor chose to stay out, without strategy methods, the trustee would have not played, while in this case is just making a choice that will not be
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effective. Even if the trustee will have a less emotional reaction that would support more
reciprocity, this condition will stay the same in all the rounds, without causing variations. Since the interest of the analysis is in the reaction caused by the treatments, this feature of the strategy method should not cause any issue. For what concerns the trustor decisions, since the information of the last decision node is imperfect, they answer without knowing what their partner did.
Both Gorilla and Qualtrics platforms were used for the experiment. Subjects were incentivized with a possible monetary reward that was assigned to two randomly chosen participants and equal to their final earnings in the game, that was, in the end, equal to 5 and 8 euros. Participants were recruited via direct link or social network. Platforms such as survey circle were also used to try to increase the number of subjects obtained. Data were only included after the correct answer of a pair of control questions about the game before the task. If wrong and with the impossibility to contact the participant again the data were discarded.
IV. Research and theoretical hypothesis
A game theoretical analysis can be advanced, as the task is a typical dynamic game with imperfect information.
The trustor does not know if he is on the fair or the unequal division side of the game tree and this generates an information set that contains both give and keep as previous histories. First thing to do is to look for Nash equilibria, in order to find the rational beliefs that players should have to reach a sequential equilibrium.
From now on the keep option for player 1 will be called “out” to avoid confusion with keep for player 2. It is possible to find two pure Nash equilibria by listing the strategies and find the one best responding to each other, and those are Out,Check;Keep and Out,Pass;Keep that are
straightforward as the probability of give is equal to zero and there is no possibility for the trustor to get something more than four euros of the out option from the investment choice.
GIVE KEEP
IN-CHECK 5;10 3;2
IN-PASS 10;10 1;19
OUT-CHECK 4;0 4;0
OUT-PASS 4;0 4;0
Table 1: Strategic form of the game with the list of the strategies available to player 1 on the left and to
player 2 on the right. Since there is an information set, player 1 cannot condition on player 2 action.
To look for mixed strategy Nash equilibria, it is necessary to list the expected utilities of the different actions. For player 2:
15 𝐸𝑢(𝐺) = 10𝑝(𝐼, 𝐶) + 10𝑝(𝐼, 𝑃) 𝐸𝑢(𝐾) = 2𝑝(𝐼, 𝐶) + 19𝑝(𝐼, 𝑃) And equating: 8𝑝(𝐼, 𝐶) = 9𝑝(𝐼, 𝑃) 𝑝(𝐼, 𝑃) =8 9𝑝(𝐼, 𝐶)
Where p(I,C) is the probability of Invest,Check and p(I,P) is the probability of Invest,Pass As all the possible combinations of Invest and Keep must be considered, the relation is expressed with one probability in terms of the other.
For player 1 the expected utilities of pass, check and out are instead: 𝐸𝑢(𝐼, 𝐶) = 5𝑝(𝐺) + 3(1 − 𝑝(𝐺)) = 3 + 2𝑝(𝐺)
𝐸𝑢(𝐼, 𝑃) = 10𝑝(𝐺) + (1 − 𝑝(𝐺)) = 1 + 9𝑝(𝐺)
𝐸𝑢(𝑂, 𝐶) = 4 = 𝐸𝑢(𝑂, 𝑃) Equating check and pass: 3 + 2𝑝(𝐺) = 1 + 9𝑝(𝐺)
2 = 7𝑝(𝐺)
𝑝(𝐺) =2 7 Equating check and out: 3 + 2𝑝(𝐺) = 4
𝑝(𝐺) =1 2
Equating pass and out: 1 + 9𝑝(𝐺) = 4
𝑝(𝐺) =1 3
Before p(G)=1/3 is better to stay out and after is better to play pass. To be indifferent between check and pass (red and blue lines), the probability of give must be equal to 2/7, but, in that case, player 1 would be better off in the out option, as it has an higher expected utility. To find all the equilibria, the analysis will start from the cases in which the trustor is still playing invest in his strategies.
If the p(G) is higher than 1/3 there is no mixed strategy NE as the trustor is better off playing I;P, but in this case the trustee would be always playing keep and there is no way for the trustor to be unpredictable and rational at the same time.
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If the p(G)=1/3, there could be a group of mixed strategy Nash equilibria in which the trustor is mixing Invest and out in all the possible combinations while maintaining the probability of
Invest;Pass equal to 8/9 of the probability of Invest;Check, making the trustee indifferent between give and keep. However, when playing pass with a probability of 8/17 and check with a probability of 9/17 the trustor would not be best responding to the trustee playing give with probability 1/3 This point is of particular interest because the trustor is able to make the trustee consider to play give but he would not maximize his own payoff. Therefore, in this case there is no mixed strategy Nash equilibrium, aside one in which the probability of I;C and I;P is set to 0 and the trustor is always choosing out, never reaching the second decision node. In this case, in fact, it is possible to both play optimally and make the trustee indifferent as the payoff is not affected, resulting in the mixed strategy Nash equilibria of {I;C=0, I;P=0, O;P=p, O;C=1-p, G=1/3, K=2/3}, with p and 1-p keeping p(I;P)=(8/9)p(I;C). This can be easily extended to all the situations in which is optimal to play out, that is, when the trustee is playing give with a probability lower than 1/3. In all those cases and as long the same condition keeping the trustee indifferent is maintained, the players would be best responding to each other. Therefore the set of mixed strategy Nash equilibria is equal to {I;C=0, I;P=0, O;P=p, O;C=1-p, G≤1/3, K≥2/3} with p(I;P)=(8/9)p(I;C).
Y axis: Expected utility
X axis (probability of give) Figure 3: Graph representing how the expected utilities of Invest;check in red, Invest; Pass in blue and of
Out in green change with the increase of the probability of give. Best responses are Out before 1/3 and Invest;pass after.
Next step is to look for the weak sequential equilibria, given the Nash equilibria that have been found. Considering the equilibria in pure strategy Out;Check,Keep, with a belief of give equal to 0 it is not possible to rationalize it and have a weak sequential equilibrium. In fact, when the trustor believes that the trustee will always keep, he will best respond by staying out. At the same time, though, the probabilities on the other side of the game tree must now be considered, and lead to
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the trustee always choosing keep, and the trustor best responding with check. This would mean that the trustee is not choosing his optimal action and would be better off with give. Therefore, there is no weak sequential equilibrium in this case.
When looking at the other pure strategy Out;Pass,Keep, also with a belief of give equal to 0, it is again not possible to reach a weak sequential equilibria. While the trustor is optimizing by staying out, on the other side of the game tree he is believing the trustee will never choose the fair division and, even so, he is still playing pass, and not best responding with a check.
For what concerns the mixed strategy Nash equilibria, when the probability of give is equal to 1/3, a different reasoning from previous one must be followed as all the game tree is now taken under consideration. Even if the trustor has all the possible combinations of Out;Check and Out;Pass to choose from, a probability of pass equal to 8/17 and the one of check equal to 9/17 is needed to make the trustee indifferent, and play give with a probability of 1/3. This makes the initial belief rational, but the trustor will not be maximizing his final payoff, as the best response is to always play pass without mixing with check. This now represents a problem as, even when a decision node will never be reached, the choice must be optimal in there too, in order to have a weak sequential equilibria.
When looking at the cases with a belief of the probability of give less than 1/3, the best response for the trustor is again to stay out. Therefore, to see if this results in any weak sequential
equilibria, there must be still optimality in both of the sides of the game tree. The only viable belief for player 1 is the one that makes him indifferent between check and pass, as if he becomes predictable, given his belief, the action taken by player 2 will be always the opposite of what he thought. For example, if the belief of give is close to 0 the trustor will nearly always check and in that case the best response for the trustee is to play give more, in contrast with the initial belief. If, instead, the belief of give for player 1 is equal to 2/7, he will mix between check and pass so that also player 2 will be indifferent between give and keep. This results in a probability of pass equal to 8/17 and a probability of check equal to 9/17 while on the trustee side the probability of give and keep are equal to the trustor beliefs of 2/7 and 5/7 respectively. The result is the weak sequential equilibrium (Out:1,Inv:0,Pass:8/17,Check 9/17; Give:2/7, Keep 5/7) with beliefs µ=(p(g):2/7,p(k):5/7).
This means that with this payoffs, player 1 should never invest in equilibrium, as the decision to check is always dominated by out. This scenario was selected on the basis of both the latest experiments related to costly punishments regarding the choice to play Invest,Check and the fact that the theoretical equilibrium of the trust game itself is already against the decisions to play Invest, Pass. About the first line of reasoning, for example, in the ultimatum game rejecting an unfair offer is theoretically always worse than accepting it, assuming an income maximizing individual, as the refusal always gives 0 while by accepting the responder can at least win something. What those two situations have in common, is that checking is always worse than staying out with a belief of give lower than 2/7. The position of the responder is close to the one of the trustor in deciding to stay out or check because with the first option he would just take the
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money while with the second he would directly punish a trustee who chose the unfair division, while earning less monetary payoff. The difference in the case of the ultimatum game is in the clear separation of a monetary and emotional payoff and the fact of knowing for sure what the other person did, without having to formulate beliefs. For what concerns the experimental results, subsequent pieces of evidence as in Thaler (1988), showed that the percentages of refusals of low offers by responders were near to 50% and half of the proposals were equal divisions, against the theoretical hypothesis. An explanation of this might come from recent neuroeconomics research as in Sanfey et al. (2003), and the idea that a different non-monetary type of payoff is paid to participants punishing the individualistic proposer. Results of neuroimaging analysis show how unfair offers activate both insula and pre-frontal cortex, areas respectively related to negative emotions and executive control, and when a rejection was chosen, the activity in the insula was prevalent while the pre-frontal cortex was dominant for acceptance cases. This could be an evidence of the conflict between a negative emotion, generated by the unfair proposal, and the cognitive processes connected to the goal of maximizing income, and that in certain circumstances the conflict is resolved in favor of actively turning down a monetary reward. Moreover, as in Xiao and Houser (2005), it seems that venting a negative emotion is a way to signal to the other player disapproval in absence of other channels of communication. Responders seem to have a demand or a need to express an emotion in whatever way it is possible and an action that works as a signal or that contains the possibility of a punishment might be more valuable for this reason, even if less rewarding in monetary terms. Although the situation is different in this experiment, something similar could give value to the action of costly check, as there is no communication between the parts, and it has this capacity to express a negative emotion aside his monetary payoff, in the case the belief of the trustor is for an unfair division by the trustee. Moreover, this is common to other games as in Singer et al. (2006), where there is evidence of how seeing a prisoner’s dilemma defector under shock activates the reward circuitry of the other player, mirroring a “sweet
revenge” feeling. The idea is that, by applying a higher payoff to the costly check outcomes, there would be both a financial and emotional reason to take that decision and the behavioral responses would be all oriented on that choice. As the interest is not in this reaction, whereas, on the effect of the abundance and scarcity treatments, the attempt is to avoid any unbalance between the actions.
Thanks to the theoretical equilibrium that has been found and the proposed research question, it is possible to formulate the research hypothesis. The effects of scarcity are more related to an after crash situation while the one of abundance to a sustained growth period. On a behavioral point of view, this means it is expected to provoke a focus dividend and a tunnel effect on subjects when taking money from them causing instinctive, together with more cautious responses, as money has a higher value, while more carelessness is expected in the growth treatment. This goes together with what was explained in Kay (2015), in most of the recent history cases in fact, after positive changes in the economy and excitement in markets comes a speculative movement and a crash, at first with the bezzle growing because of inattention and frauds and then shrinking with increased controls and suspicion. The hypothesis advanced is that the state of mind of abundance and scarcity could well be a parallel of the good and bad times of Galbraith and, therefore, having
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an effect on certain behavioral responses such as fraud, increasing or decreasing the quality of auditing, trust and negligence.
Individuals may take decisions on the basis of a wrong assumption on both their available unused resources and behavior of their partners and this opinion could be influenced by the current state of the business cycle, making people more trusting if the economy is going well, as in the case of good moral depiction in the experiment by Delgado (2005).
If the amount of unused resources increases, there should be examples of embezzlement, with more “keep” choices by the trustees and more carelessness by the trustors, with a lower
percentage of costly check and out outcomes compared to the control group with all of this more emphasized in the second round of abundance, in contrast with the theoretical equilibrium that would result only in “out” terminal histories. In the scarcity treatment, instead, the sudden revelation of having much less than expected, that is minus 15 euros of previous uncertain game earnings, should trigger the “universal suspicion” with more trustees playing give and more trustors choosing to costly check or staying out, due to the effect of believing in a lower
probability of give. In conclusion, scarcity would cause a lower rate of embezzlement and a higher rate of discoveries as Galbraith predicts, together with fewer investments ending in a 10,10 payoff division. Behavioral results of the trust game already go against the theoretical Nash equilibrium that would see the trustor to always keep its money at the beginning of the game. In this
experiment a step forward is trying to be done, to see if a situation of abundance decreases the paybacks by the trustees symbolized by give, causing a lower reciprocity while increasing the trustor belief in a fair division, reflected by more pass decisions. Scarcity instead would cause trustors to decrease their faith in reciprocity and act more in the way suggested by the rational equilibrium, choosing more out options, or by emotional payoffs, choosing more costly check while trustees would go back playing more give than before as more suspicious of a check and less willing to take risks. In conclusion, this means to test if the percentage of pass is higher in the treatment compared to the control group for round 2 and 3, whereas it is lower in round 4. On the trustee side, it will be tested if the percentage of keep by the trustee is higher in the treatment group compared to control in round 2 and 3 and if it is lower in round 4.
V. Data and Results
77 subjects participated in the experiment, 7 were not included for not answering the control questions correctly and not being in contact again. Therefore, 70 players contributed to the results: 37 played as player 1, the trustor, and 33 played as player 2, the trustee. The treatment group contained 18 players 1 and 15 players 2 while the control group 19 players 1 and 18 players 2. 30 of the participants were female and 40 were male. In describing the results, the analysis will go through the findings in line with the research hypothesis towards the weak points, all of this from a general to a more in-depth analysis of the data, taking into account the comparison with the control group and the couples in-game outcome. As already described, the objective is to find a higher percentage of Invest,Pass terminal histories by players 1, together with keep by players 2,
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in growth treatments rounds, and more Invest,Check or Out by players 1 and give by players 2 in the market meltdown case.
First of all though, is important to verify the genuine randomization in the treatment and control group. This is possible by using pre-treatment covariates, in this case, 3 demographics answers the subjects gave at the end of the experiment. When looking at gender the difference in the two groups is not statistically significant [χ2(1) = 0.78, p = 0.38] and so for education divided in high school, college graduate and postgraduate [χ2(2) = 2.47, p = 0.29] and age divided in 18-24, 25-29, 30-34,40-44 and 50-54 [χ2(4) = 5.11, p = 0.28]. Therefore it is possible to conclude that none of those covariates is a predictor of being a part of the treatment or the control group and the randomization was successful.
Given that, it is possible to start looking for the findings in line with the research hypothesis, beginning with the treatment group for players 1, with a basic presentation and analysis of the observed results. Table 1 summarizes the choices made by the trustors, distributed in the different rounds and divided into the three groups of possible terminal histories. As it is possible to see, the percentage of pass tends to stay high for the growth treatments; At first by increasing from 61% to 72% of the choices from the baseline round, and then, even if slightly falling in round 3 to 44% of total decisions, it respects the hypothetical prediction of going down even further, reaching his minimum in round 4 of just approximately 28%, substituted by check (33%) and out (39%) that could represent the passage to a more suspicious behavior and less carelessness after market crashes with the presence of scarcity. Although, at a first analysis, it seems that the results are supporting the initial prediction, there is also evidence of a possible order effect in round 3 concurrent to the influence of abundance that will be isolated more clearly with the introduction of the control group.
Table 1: Treatment group players 1 results. In green the number of passes, red the number of Out and in
blue the number of checks. Pass choices fall in the 4th round while they were higher in the previous two growth treatment rounds.
The treatment group for players 2 also provides evidence directing to a conclusion in line with the research hypothesis. What must be highlighted in this case is that the number of keep choices increases in round 3 to nearly 50% of the total, after two growth treatments and having received 5
22% 17% 28% 33% 17% 11% 28% 39% 61% 72% 44% 28% 0 2 4 6 8 10 12 14
Round 1 Round 2 (Growth) Round 3 (Growth) Round 4 (Crash)
N °o f C h ec k, O u t, P as s
Round (Treatment type)
N°of Check N°of Out N°of Pass
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and 10 euros of unused resources, while falls down again after the crash, with an increase of give choices to 67% and keep going down to 33%, reflecting the fall of the rate of embezzlement. The delay in the response of the keep choices can be reasonable, given it is the unethical option and there was only one round of growth before. It is interesting to see a correspondence for the responses of player 1 and 2 in round 4 that seems to be the one with more insights. In general, players seems to not follow the theoretical weak sequential equilibrium, as there should be always more keep than give, but also more out choices by the trustors. This could reflect the importance of reciprocity and also the effect of the exogenous shocks on the belief of give of the trustors and the actual choices of the trustee. If the rational equlibrium would only see out choices and, on the other side, behavioral responses of a classic trust game show that trustors still believe in a payback and there are trustees rewarding them by sending money back, in this case the choice to invest seems to be influenced by the number of rounds already played and the two treaments. For growth, the evidences are mixed with round 2 having the predicted higher percentage of
Invest;Pass, although, against the expectations, the paybacks are still high. In round 3 something similar goes on, with the percentage of Invest;Pass slightly falling under 50% against the
expectations coupled with the predicted response of the trustee with an increased probability of keep. For scarcity instead, the results seem to support the research hypothesis predictions, with a more “rational” behavior by trustors, choosing more out and check and trustees, on the other hand, increasing the probability of give. This last decision could have different interpretations, for example playing more give could be motivated by the desire to reward who is still investing or just take less risks being in the last round.
Table 2: Treatment group players 2 results. In blue the number of give choices and red the number of keep.
Keep increases at the 3rd round and goes back down at the 4th round of market meltdown.
When introducing the control groups results, a more random behavior seems to be present. In fact, when looking at players 1, from the first baseline round, the number of pass decision at first goes down to 47% and then increases to 58% to then fall again to 42% of the total. Therefore, the decisions between trust, symbolized by give, and suspicion of the behavior of the other player, represented by the amount of check and keep, are quite balanced, close to a 50% division. In round 4, it is possible to see a similar pattern to the one of the treatment group and part of the variation could be caused by the fact of a higher suspicion, simply because it is the last round.
80% 80% 53% 67% 20% 20% 47% 33% 0 2 4 6 8 10 12 14
Round 1 Round 2 (Growth) Round 3 (Growth) Round 4 (Crash)
N °o f G iv e ,Kee p
Round (Treatment Type)
N°of Give N°of Keep
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Table 3: Control group players 1 results. The number of passes tend to stay at around 50% throughout the
experiment even if the trend is similar to the treatment group.
Regarding the control group for players 2, the absence of the exogenous shocks underlines the importance of the strategic considerations by the participants that might partly be the reasons for the results shown in the treatment group. Player 2 might think risking it more in the final round is worth it or that player 1 will check less in the last rounds compared to the first two and, therefore, try to maximize his earnings by keeping more in the last rounds, with or without exogenous shocks to the economy, as it is possible to see from the results with keep passing from 33% and 28% in round 1 and 2 to 58% and 50% in round 3 and 4. To verify the existence of these strategies, it was asked to the subjects to declare their beliefs after each round by estimating the probability of the other player actions. What comes out when looking at these data is that in round 2 and 3 there is no clear pattern while in round 4 the perception is of a higher probability of check and keep. This goes in the same direction of the predicted effect of scarcity, for more give and less keep, and could still constitute a possible endogeneity, to explore by introducing the beliefs as a control variable in the regression.
Table 4: Control group players 2 results. The pattern is really similar to the treatment group.
66% 72% 42% 50% 33% 28% 58% 50% 0 2 4 6 8 10 12 14
Round 1 Round 2 Round 3 Round 4
N °o f G iv e a n d Kee p Round Give Keep 11% 26% 21% 21% 21% 26% 21% 37% 68% 47% 58% 42% 0 2 4 6 8 10 12 14
Round 1 Round 2 Round 3 Round 4
N °o f C h ec k, Ke ep ,P as s Round N°Check N°of Keep N°of Pass
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Table 5: Beliefs control group players 2. In the y axis the number of probabilities estimated by subjects
favouring pass, check, keep/out or indifferent. Impression that player 1 plays check seems to increase in the last round.
The final outcomes were generated by listing the players per number and randomly extracting each of them, to create couples of players 1 and 2. This was done with a number randomizer on the internet. Looking at the research hypothesis from an outcome point of view, it would be expected to find more pass;keep in round 2 and 3, reflecting a higher rate of embezzlement, and more out and check coupled with give or keep in round 4, meaning a higher rate of discovery (check;keep), also coupled with more difficulties in finalizing the equal outcome, that is pass;give. The final results are synthesized in table 6 and 7.
Pass-Give Pass-Keep Check-Give Check-Keep Out-Give Out-Keep
Round 1 5 3 3 0 3 0
Round 2 9 1 2 2 2 0
Round 3 5 2 4 2 3 2
Round 4 2 1 4 2 3 2
Table 6: Final outcomes of treatment group. Results are organized for each of the possible outcome paths.
0 1 2 3 4 5 6 7 8
Round 1 Round 2 Round 3 Round 4
Comments favouring pass Comments favouring check Comments indifferent Comment favouring keep
0 1 2 3 4 5 6 7 8 9 10
Round 1 Round 2 Round 3 Round 4
Pass-Give Pass-Keep Check-Give Check-Keep Out-Give Out-Keep
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Pass-Give Pass-Keep Check-Give Check-Keep Out-Give Out-Keep
Round 1 8 4 2 0 2 2
Round 2 8 1 3 3 3 0
Round 3 5 5 6 1 0 4
Round 4 4 3 2 2 4 3
Table 7: Final outcomes of control group. . Results are organized for each of the possible histories of the
game.
Results are similar to the one seen for the individuals alone, especially for the difficulties, in the market crash treatment, to be able to reach pass;give with many out;give and check;give final outcomes, meaning difficulties in trusting the other player, with this effect emphasized by the presence of the exogenous shocks. Treatment and control group are again similar to each other in the final result, however, the difference to underline is in how those outcomes were reached. For example in the treatment group only 2 players 1 and 6 players 2 always played the same actions in every round, while in the control group there were 9 players 1 and 6 players 2 meaning that abundance and scarcity had an effect in switching decision.
Moving forward it is now important to statistically test the research hypothesis to verify that the variations in the probability of pass and give choices are caused by the treatment, or if, even without the exogenous shocks, there would have been the same results. Considering the fact that the outcome variable is a count of the decisions took by participants, a non-parametric test is more appropriate. The null hypothesis will be that the treatment and control group are not statistically different and the level of significance is set at 0.05. The method used is the
chi-squared homogeneity test, as other non-parametric procedures such as the Wilcoxon test require to be able to calculate differences per individuals in each group and a dependent variable
quantifiable for every subject, which, in this case, is just binary. Moreover, this test was also used in other important articles with a similar results dataset, as in Dana,Weber and Kuang (2007). For players 1, it will be tested if the distribution of pass, check or out in the treatment group is statistically different from the one in the control group for round 2,3 and 4, while for player 2 it will be between give and keep. For players 1, in round 2 [χ2(2) = 2.5, p = 0.29], round 3 [χ2(2) =
0 1 2 3 4 5 6 7 8 9
Round 1 Round 2 Round 3 Round 4
Pass-Give Pass-Keep Check-Give Check-Keep Out-Give Out-Keep
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0.71, p = 0.7] and round 4 [χ2(2) = 1.05, p = 0.59] the results are not statistically different and same goes for players 2 in round 2 [χ2(1) = 0.91, p = 0.54], in round 3 [χ2(1) = 0.22, p = 0.64] and round 4 [χ2(1) = 0.95, p = 0.43]. Even if the treatment data seem to go in the right direction, the outcomes of the statistical tests highlights two problems, one being the small samples, especially if a procedure such as the chi-squared homogeneity test is put into use, and the other being the presence of an order effect, going in the same direction as the treatments. This would require an adjustment of the experimental design, with more rounds and in different positions, so that the market crash situation is not always the last round.
Another possible statistical outcome to consider is the one of a proportions test. Considering the trustors, the relevant alternative hypothesis in round 2 and 3 is the difference between the mean of the probability of pass in control minus treatment group to be lower than 0, as the predicted outcome is to see more Invest,Pass, and in round 4 the same difference to be higher than 0, reflecting the increased suspicion and the number of Out and Invest,Check. Results of the test reject the null hypothesis in round 2 (Pr. Z<z=0.06) at the 10% significance level, while in round 3 are clearly not statistically different from 0 (Pr. Z<z=0.79) and close to a 10% significance in round 4 (Pr. Z>z=0.18). In the trustees’ case, the alternative hypotheses to study are if the difference between the mean of control and treatment group of the probability of Give is higher than 0 in round 2 and 3, considering the predicted outcome of less give decisions influenced by growth, and lower than 0 in round 4, with restored moral integrity. In round 2 the results don’t reject the null hypothesis (Pr. Z>z=0.698), as in round 3 (Pr. Z>z=0.695) and round 4, even if closer to a 10% significance (Pr. Z<z=0.167).
The results of the tests and the choices distributions described until now display a probable coexistence of a treatment effect with the individual beliefs about the actions of the other player, or an order effect linked to what the players think in every round. For this, it is possible to try to apply a Probit regression to isolate the different effects, studying the probability of pass for players 1 and the probability of give for players 2 in the treatment and control situation and check if the coefficients are statistically different from 0. This would highlight if there is an effect on the probability of pass and give caused by the treatment, allowing also to introduce, in a separate instance, the beliefs expressed by the subjects as a control variable. For the trustor, the belief will be related to a give choice by the trustee, whereas for the trustee both the belief of invest and the belief of pass are taken into account. Even if the trustee decision is relevant only if the trustor invests, the belief of receiving the money from the other player could still influence his choice, for example by thinking that investing in a specific round is improbable, he could choose to give, in order to reciprocate to one of the few investors that he anticipates are available in this round. Concerns about the participants clear understanding and thoughtful response to the question about beliefs are present, however, they will be implemented as a control variable because of the observations made about a possible order effect. First of all, the regression will test the
significance of the effect of the treatment alone and then try to distinguish if players are taking their decision in the different rounds for the presence of the exogenous shocks or because of their personal beliefs about the round number or the opponent action. Next, it will be put under test if the beliefs themselves are being influenced by the abundance and scarcity rounds, which could
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still be a relevant evidence of an indirect effect of the treatment over the probability of choosing a certain action.
For what concerns the analysis about players 1, in the abundance treatment of round 2 and 3 it is expected to see a positive coefficient, as the probability of Invest,Pass should increase during growth, while in scarcity of round 4 it is expected to see a negative coefficient, as now check and keep decisions should increase with greater suspicion of the other player. In the case of player 2, the probability of give should decrease in growth and increase in depression. The results of the regressions are in table 8 to 13.
Probit Regression Round 2 Player 1 Number of obs.:37
LR chi2 (1)= 2.4 Prob.> chi2= 0.121
Log likelihood= -23.7786 Pseudo R2= 0.048
Pass2 Coef. Std.err. Z P>IzI [95% Conf. Interval]
Treatment2 .655 .427 1.54 0.124 -.18 1.49 Cons -0.06 .288 -0.23 0.819 -.63 .498
Probit Regression Round 2 Player 1 with beliefs Number of obs.:37 LR chi2 (2)=5.32 Prob > chi2= 0.07
Log Likelihood=-22.3213 Pseudo R2=0.1064
Pass2 Coef. Std.err. Z P>IzI [95% Conf. Interval] Treatment 2 Beliefofgive2 .8209 1.8695 .4578 1.133 1.79 1.65 0.073 0.099 -.076 1.718 -.351 4.09 Cons -1.142 .727 -1.57 0.116 -2.568 .283 Table 8: Probit Regression of Round 2 player 1. Pass is a binary variable equal to 1 if the decision of the subject was pass. Treatment is a binary variable equal to 1 if the player was in the treatment group and beliefofgive is its own belief of the other player action expressed in the probability he played give. Results for round 2 are improved with the introduction of the beliefs and again significant at the 10% level, strengthening a bit the previous proportions test results. Taken from Stata.
Probit Regression Round 3 Player 1 Number of obs.:37
LR chi2 (1)= 0.67 Prob.> chi2= 0.413
Log likelihood= -25.297 Pseudo R2= 0.01
Pass3 Coef. Std.err. Z P>IzI [95% Conf. Interval]
Treatment3 -.339 .414 -0.82 0.413 -1.151 .473 Cons .199 .2896 0.69 0.492 -.368 .767
27 Probit Regression Round 3 Player 1 with beliefs Number of obs.:37
LR chi2 (2)=2.71 Prob > chi2= 0.2584
Log Likelihood=-24.2796 Pseudo R2=0.0528
Pass3 Coef. Std.err. Z P>IzI [95% Conf. Interval] Treatment 3 Beliefofgive3 -.236 1.188 .427 1.133 -0.55 1.40 0.580 0.162 -1.073 .6 -.478 2.853 Cons -0.452 .55 -0.82 0.411 -1.529 .625
Table 9: Probit Regression of Round 3 player 1. Pass is a binary variable equal to 1 if the decision of the
subject was pass. Treatment is a binary variable equal to 1 if the player was in the treatment group and beliefofgive is its own belief of the other player action expressed in the probability he played give. As highlighted in previous results in round 3 the results are more related to beliefs of the subject than to the treatment itself. It could still be that the treatment has an effect on subject’s beliefs. Taken from Stata.
Probit Regression Round 4 Player 1 Number of obs.:37
LR chi2 (1)= 0.84 Prob.> chi2= 0.3598
Log likelihood= -23.567 Pseudo R2= 0.0175
Pass4 Coef. Std.err. z P>IzI [95% Conf. Interval]
Treatment4 -.39 .428 -0.91 0.362 -1.228 .448 Cons .199 .2896 -0.69 0.492 -.767 .368
Probit Regression Round 4 Player 1 with beliefs Number of obs.:37 LR chi2 (2)=0.84 Prob > chi2= 0.6574
Log Likelihood=-23.5669 Pseudo R2=0.0175
Pass4 Coef. Std.err. z P>IzI [95% Conf. Interval] Treatment 4 Beliefofgive4 -.387 0.199 .459 0.908 -0.84 0.02 0.4 0.982 -1.287 .513 -1.759 1.8 Cons -0.21 .547 -0.38 0.702 -1.281 .863
Table 10: Probit Regression of Round 4 player 1. Pass is a binary variable equal to 1 if the decision of the
subject was pass. Treatment is a binary variable equal to 1 if the player was in the treatment group and beliefofgive is its own belief of the other player action expressed in the probability he played give. Here the coefficient on treatment has the expected negative sign. Still, it is not statistically significant. Moreover the beliefs are not significant as many players played the opposite move compared to their belief, for example risking pass even if they their belief favoured a keep by player 2. Taken from Stata.
Results of the regression for player 1 explain something more about the actual percentage of passes. In round 2, the pattern is the one expected in the research hypothesis, also with a significance of the treatment variable at the 10% level when introducing the beliefs, that have a part in contributing to the probability of pass, meaning that the individual strategic considerations also had an influence on the participants. In Round 3, instead, the beliefs are dominant for the final decision, while the treatment seems to not have a direct effect on the number of passes. In round 4 the sign of the coefficient on the treatment variable is the expected one, although not statistically significant, while the beliefs in this round seem to be irrelevant.
