Abstract
This paper studies the effects of social comparison on risk taking behavior. In our theoretical framework, decision makers evaluate the consequences of their choices relative to both their own and their peers’ conditions. We test experimentally whether the position in the social ranking affects risk attitudes. Subjects interact in a simulated workplace environment where they perform a work task, receive possibly different wages, and then undertake a risky decision that may produce an extra gain. We find that social comparison matters for risk attitudes. Subjects are more risk averse in the presence of small social gain than social loss. In addition, risk aversion is decreasing in the size of the social gain.
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Notes
See Gill and Stone (2010) for an analysis of the effects of perceived inequality on effort levels.
In a closely related study, Linde and Sonnemans (2015) show that in a setting where agents’ choices only affect their own earnings, the presence of a social reference point does not affect risk taking behavior in contrast with the predictions of standard social preferences models.
Schmidt et al. (2014) study the effects of social comparison on risk taking in a setting where the social reference point is state-dependent. This assumption allows the authors to study how social comparison affects (gender specific) risk attitudes when risks are either idiosyncratic or correlated.
The keeping up with the winners effect is supported empirically by Fafchamps et al. (2015). Among other findings, their multi-round experiment on asset integration indicates that subjects who are asked to invest an initial endowment that is smaller than the endowment received by other subjects are more willing to take risks.
Notice that the representation in Eq. (1) encompasses as special cases many functional forms that have been adopted to study, for example, relative income concerns in the macroeconomic literature (e.g., Abel 1990) and in the empirical literature (e.g., Ferrer-i-Carbonell 2005). Different specifications of Eq. (1) can be found in Clark and Oswald (1998), Fehr and Schmidt (1999), and in recent experimental studies, such as Lahno and Serra-Garcia (2015) and Schwerter (2013).
Notice that the same behavior is predicted by a utility function as in Eq. (1) if the private component is linear and the social component has prospect theory features, i.e., concave for social gain and convex for social loss.
We could perform the same analysis by considering a more general utility function such as: \(v(x,r,s)=u(x)+h(x-r)+g(x-s)\). This, however, would not provide additional insights about the effects of social comparison.
Subjects were paid for only one of the two parts, randomly drawn by the computer at the end of the experiment, with a probability of 0.1 and 0.9, respectively.
These are the same stakes as in Holt and Laury (2002). We also kept the same payment structure: if the risk task was paid out, the computer randomly selected one row out of ten and played the lottery chosen by the subject in that row.
We implemented two repetitions of a small-scale letter-combination task to double the probability of writing combinations already used by the coworker. This procedure allows us to enhance the salience of the social environment, without increasing excessively the difficulty of the task and the rate of failure—as it would be the case with a single repetition of a large-scale letter-combination task.
In every session, we allocated contracts in such a way that half of the subjects could obtain a wage of 2 ECU and the other half a wage of 10 ECU by completing the task (subjects received this information in the instructions). Note that this contract allocation scheme ensured an ex ante procedurally fair wage distribution among all participants within sessions and between coworkers within pairs.
In the bonus task, lottery A pays either 4.00 or 3.20 ECU, while lottery B pays either 7.70 or 0.20 ECU. These are the same stakes as in Laury and Holt (2005). As in the first part of the experiment, lottery A is safer than lottery B, the first choice assigns probability 1 to the unfavorable outcome, a rational decision maker would prefer lottery A in the first choice and a risk neutral individual would switch exactly after the fifth row.
The German wording for the notice about wages on the top of the screen in the bonus task was: “Ihr biheriger Lohn beträgt 10 ECU. Des bisherige Lohn Ihres Kollegen beträgt 10 ECU”. “Project” was “Projekt”.
As the identity of the worker who received the bonus was revealed only at the end of the experiment, both workers could focus on the bonus task as if it had economic consequences. This procedure allowed us to set the coworker’s wage as the social reference point.
If a worker has the same wage as his coworker or the highest wage in the pair, his final earnings including the bonus would be certainly larger than his coworker’s final earnings. It is possible that reversing the social ranking affects risky behavior. However, our focus is on how the relative position in the social ranking per se affects the risk attitudes of the decision maker.
This hypothesis implies either that we can represent the argument of the private utility as \((x-r),\) or that private utility is u(x) but it displays constant risk aversion. In both cases, private risk aversion does not vary across treatments, hence we can focus on social risk aversion.
Note that Theorem 5 in Pratt (1964) applies to our framework since our utility function is additive in its two components and both components are increasing in own outcomes. Essentially, the theorem states that the sum of two functions that are constantly or decreasingly risk averse is decreasingly risk averse. We assumed that the social component is decreasingly risk averse; the private component is constant across social conditions since by design its argument \((x-r)\) is constant.
In the post-experimental questionnaire, we collected sociodemographic characteristics, such as age, gender, height, weekly budget, as well as feedbacks on the experimental instructions and tasks.
The largest number of mistakes was made in the first task, where 11 subjects made multiple switches between the lotteries, and one of them also started from the dominated lottery in the first row. In the bonus task only 6 subjects switched multiple times (5 of which also showed inconsistencies in the first task), while no subject started from the dominated lottery. Therefore, only 12 subjects displayed one or more of these inconsistencies, and were eliminated from the sample. This finding is particularly interesting if one considers, for example, that in Laury and Holt (2005) 44 subjects out of 157 present multiple switches.
Overall, only 19 subjects were dropped from the sample, since one of the subjects with zero wage was also in the group of subjects with inconsistencies in the first risk task.
A Pearson \(\chi ^2\) test does not reject the hypothesis that the distribution of subjects in the three categories is the same under the two measures of risk attitudes (\(p = 0.46\)).
See Harrison et al. (2005) for a discussion of the MPL format.
Table 6 in Appendix 2 provides descriptive statistics for the explanatory variables. In the questionnaire, we also asked subjects to report their weekly budget. However, since we inferred from their implausible answers that they did not understand the question, we do not consider this variable as a meaningful individual control. If included, the variable budget is significant with coefficient 0.0002, but none of the other results change.
For example, Saito (2013) axiomatizes the expected inequality averse model, which applied to our social reference point s, can be rewritten as follows:
$$\begin{aligned} V(x,s)=\delta U\left( \mathbb {E}(x),\mathbb {E}(s)\right) +(1-\delta )\mathbb {E} \left( U(x,s)\right) , \end{aligned}$$where \(U(x,s)=x-\alpha \max \{s-x,0\}-\beta \max \{x-s,0\}\). If we limit our attention to social gain, we can rewrite the above equation as \( U(x,s)=x-\beta (x-s)\) which is linear. Hence, \(U\left( \mathbb {E}(x),\mathbb {E} (s)\right) =\mathbb {E}\left( U(x,s)\right) \); moreover, V(x, s) becomes linear and cannot explain the finding that risk attitudes vary within the social gain domain.
Their paper also provides results on the neutral condition. However, such condition differs from gains and losses as the decision maker chooses which lottery will be played not only for himself but also for the other person.
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Acknowledgments
We are grateful to the Max Planck Institute of Economics (Jena) for financial support, Ria Stangneth and Claudia Zellman for technical assistance in the lab. We thank Madhav Aney, Lorenzo Cappellari, Andrew Clark, Anna Conte, Anna De Paoli, Werner Güth, Jona Linde, Fabio Maccheroni, Aldo Rustichini and participants to the Thurgau Experimental Economics Meeting 2013 (Konstanz), FUR 2014 (Rotterdam) and ESA 2014 (Prague) for useful suggestions. The usual disclaimer applies. Elena Manzoni gratefully acknowledges financial support from PRIN 2010-2011 “New Approaches to political economy”.
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Appendices
Appendix 1: Experimental instructions
[Translated from German]
Welcome and thank you for your participation! Please read carefully the following instructions.
Please note that you are not allowed to talk with other participants during the entire experiment. If you have any questions, please raise your hand. We will come to you and answer your question personally. If you violate these rules, we will be forced to interrupt the experiment. Please turn off your mobile phones and keep notes, books and food out of your cabin.
The experiment will last about 45 min. You will be paid a participation fee of 2,50 EURO for completing the experiment. Your final earnings today will depend on your own actions and some element of chance. Earnings will be computed in ECU (Experimental Currency Unit) where
The experiment will consist of TWO PARTS. At the start of each part you will receive instructions about that part. Only one part will affect your final earnings: the first part has \(10\,\%\) of chances of being paid, while the second part has \(90\,\%\) of chance of being paid. At the end of the experiment, the computer will determine which part you will be paid for. Since you cannot know in advance which part will be drawn for your payment, we recommend to focus on each part as if it was the part which will determine your earnings. You will be paid in cash at the end of the experiment, after answering a questionnaire.
Instructions for PART I
The first part of the experiment will consist of a decision task.
The decision task consists of ten choices between Option A and Option B; each option is a lottery that can give you randomly either a favorable monetary outcome or an unfavorable monetary outcome. The favorable and the unfavorable outcomes of Option A and the favorable and the unfavorable outcomes of Option B are represented in a bar graph on the top of the screen. An outcome is identified by a bar whose size reflects the amount you can earn, which is also indicated with numbers in the picture.
For every option, the favorable outcome is the larger gain (the longer bar, which is 
, while the unfavorable outcome is the smaller gain (the shorter bar, which is 
). For example, consider the following picture, which is an example of a pair of options:
If you choose Option A, and the favorable outcome occurs, you gain the payoff written on the top of the 
bar (i.e., + 4 ECU). If the unfavorable outcome occurs, you gain the payoff written on the top of the 
bar (i.e., \(+\) 3 ECU).
Below the bar graph you will find ten decision rows; for each row you have to make a choice between Option A and Option B. The chances of the favorable outcome and of the unfavorable outcome change across rows and are represented by pie charts. The 
slice of the pie represents the chances of the favorable outcome and the 
slice of the pie represents the chances of the unfavorable outcome; next to each pie chart you will also see in percentage terms the chances of the favorable outcome written in 
and the chances of the unfavorable outcome written in 
. In the row that corresponds to each pie chart you have to select either Option A or Option B by clicking on the relevant button. In the following picture, below the bar graph, you can see an example of one of the ten decision rows you will visualize in the task:
In this decision row, in each lottery, the favorable outcome may occur with \( 30\,\,\%\) of chances and the unfavorable outcome with \(70\,\,\%\) of chances. In Option A, you may get \(+\)4 ECU with \(30\,\,\%\) of chances and \(+\)3 ECU with \(70\,\,\%\) of chances. In Option B, you may get \(+\)8 ECU with \(30\,\,\%\) of chances and \(+\)2 ECU with \(70\,\,\%\) of chances. Given this information, you have to make a choice between Option A and Option B.
To summarize, you will make ten decisions between Option A and Option B. You may choose A for some decision rows and B for other rows, and you may change your decisions and make them in any order. When you are done, you have to click on the Submit button to proceed to the following part of the experiment. The computer will allow you to submit and proceed only once you made all the ten decisions.
1.1 Payment of PART I
At the end of the whole experiment, the computer will randomly select which part of the experiment will be paid out; this part has \(10\,\%\) of chances of being paid out.
If this first part of the experiment is selected to be paid out the computer will select by chance one of your ten decision rows; each decision row has an equal chance of being drawn. Notice that even though you will make ten choices only one of your choices will end up affecting your final earnings, but you will not know in advance which choice will be used. Each choice that you make has an equal chance of being used in the end.
Finally, the computer will play the lottery corresponding to the option you chose for the decision row which has been drawn; chance determines whether you will be paid the good 
or the bad 
outcome of that option.
Instructions for PART II
1.1 General instructions for PART II
In PART II of today experiment, you will be paired at random with another subject, who will be your coworker for all the rest of the experiment. Each one of you will be assigned a contract, which determines the wage you will get for performing a certain work task. Then you will perform the work task and your wages will be computed.
After your wage is determined, you have the opportunity to gain a bonus on top of this wage by performing a decision task which is very similar to the one you faced in PART I of today experiment. Indeed, to get a bonus, you have to choose between two projects (A and B) which have two possible realizations each: a favorable and an unfavorable monetary outcome.
1.2 Detailed instructions for PART II
1.2.1 Your contract
Each one of you will be assigned either Contract E or Contract F which establish your wage for the next work task. In both contracts your wage is either 2 ECU or 10 ECU depending on the result of a computerized fair coin toss. The two contracts differ in the following sense:
-
Contract E pays 10 ECU if the result of the coin toss is HEAD, while it pays 2 ECU if the result of the coin toss is TAIL.
-
Contract F pays 2 ECU if the result of the coin toss is HEAD, while it pays 10 ECU if the result of the coin toss is TAIL.
Therefore, your wage will depend partly on your given contract and partly on chance. Suppose the result of the coin toss is HEAD, those of you with Contract E will get a wage of 10 ECU, while those of you with Contract F will get a wage of 2 ECU. Instead, if the result is TAIL, those of you with Contract E will get a wage of 2 ECU while those of you with Contract F will get a wage of 10 ECU. Notice that the two contracts are equivalent, the only difference being that one pays a high wage when HEAD and the other when TAIL.
1.2.2 Work task
This task consists of two similar parts lasting a maximum of 4 min each. NOTICE: If you do not complete both parts of the task within the time limits your contract will not be enforced and you will get a wage of 0 ECU for this work task!
The first part consists of writing 20 combinations of two letters from the set of letters
which is displayed on the top of your screen.
You have to insert each combination (for example: AE, GI, FB, ...) in an empty box (in capital letters, without commas or spaces between the letters) and then click on the ok button. You will see 20 empty boxes (with the corresponding ok buttons next to them) arranged on two columns on your screen. You will start to fill the first column and then the second, starting from the first box at the top of the left column and ending with the last box at the bottom of the right column.
You can choose whichever combination of letters; you can also choose twice the same letter in a combination (e.g., AA). There are only two restrictions:
-
1.
if you insert a combination which has been already inserted by your coworker, this combination will not be validated
-
2.
if you insert a combination you already inserted yourself, it will not be validated.
In both cases, after you press the ok button, you will receive an error message which invites you to find a new combination to fill the box with.
If instead after pressing the ok button your combination is validated, you will see a green circle on the left of the combination.
Please notice that it is very important that every time you insert a combination you press immediately the ok button, otherwise, your combination cannot be validated. Also your combinations will not be validated if you do not press the confirm button at the end of the task.
The second part of the work task is very similar to the first part, except for the set of letters you can combine: you have to fill the boxes now with 20 combinations of two letters from the new set of letters K, L, M, N, O, P, Q, R, S, T (displayed on the top of your screen). The same restrictions as above hold.
1.2.3 Payment of the work task
After you completed both parts of this work task, you will know the result of the coin toss (HEAD or TAIL) that determines your wage and the wage of your coworker. You will be informed about both wages.
1.2.4 Bonus task
You will face now a decision task which is very similar to the one you saw in the first part of the experiment. Both you and your coworker will face this task, however, only the task of one of you will be paid out. You will receive the payment of this task, the bonus pay, only if you will be selected as the team leader. You and your coworker have the same chances (\(50\,\,\%\)) of being selected as team leader, but you will not know in advance who will be the leader. The bonus pay will be added to the previous wage of the team leader only.
We describe the bonus task very briefly because it is very similar to the decision task of PART I. Indeed, the bonus task consists of ten choices between Project A and Project B; each project can be successful or unsuccessful. If a project is successful, it gives you a high bonus (represented by the 
bar). If a project is unsuccessful, it gives you a low bonus (represented by the 
bar). The possible bonuses from each project are represented in a bar graph displayed on the top of the screen.
Below the bar graph you will find ten decision rows: for each row you have to make a choice between Project A and Project B. The possible bonuses that Project A and Project B can give you are for all ten decisions those described in the bar graph; the chances of the high or the low bonuses change across rows and are described by pie charts. The 
slice of the pie represents the chances of the high bonus and 
slice of the pie represents the chances of the low bonus; chances in percentage terms are indicated next to each pie chart.
In the row that corresponds to each pie chart you have to select either Project A or Project B, given the chances of the higher and lower bonuses.
As in the decision task of PART I, in the bonus task you will make ten choices: for each decision row you will have to choose between Project A and Project B. You may choose A for some decision rows and B for other rows, and you may change your decisions and make them in any order. The computer will allow you to submit and proceed only if you made all the ten decisions.
1.2.5 Payment
At the end of the bonus task, the computer will randomly select which part of the experiment will be paid out to you and your coworker: PART II has \( 90\,\,\%\) of chances of being paid out. The random selection will be the same for the pair of you, so that if you are paid PART II, also your coworker will be paid PART II.
If PART II of the experiment is selected to be paid out the computer will select by chance either you or your coworker to be the team leader. Each one of you has \(50\,\%\) of chances of being selected as team leader. Notice no choice you made in the experiment influences the selection of the team leader that is completely random.
The computer will then select by chance one of the ten decision rows of the team leader’s decision task; each one of the team leader’s ten decision rows has an equal chance of being drawn.
Notice that even though you and your coworker will make ten choices, only the team leader will receive the bonus and only one choice of the team leader will determine this bonus, but none of you will know in advance who will be the team leader and which choice will be used.
Finally, the computer will play the lottery corresponding to the project that the team leader chose in the decision row which has been drawn; chance determines whether the team leader will be paid the high 
or the low 
bonus for that project.
If you have been selected as the team leader, your final pay is given by the show up fee, the wage from the work task and your realized bonus; your coworker’s final pay in this case consists of the show up fee and his/her wage only.
If you have not been selected as team leader your final pay is given by the show up fee and your wage only; your coworker’s final pay in this case is given by your coworker’s show up fee, his/her wage from the work task and his/her realized bonus.
You will then answer a questionnaire and be paid your final earnings in cash.
Appendix 2: Descriptive statistics
See Table 6.
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Gamba, A., Manzoni, E. & Stanca, L. Social comparison and risk taking behavior. Theory Decis 82, 221–248 (2017). https://doi.org/10.1007/s11238-016-9562-z
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DOI: https://doi.org/10.1007/s11238-016-9562-z