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Theory and Decision

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29.06.2016

Social comparison and risk taking behavior

verfasst von: Astrid Gamba, Elena Manzoni, Luca Stanca

Erschienen in: Theory and Decision | Ausgabe 2/2017

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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.

Vorheriger Artikel Gender differences in ambiguity aversion under different outcome correlation structures

Nächster Artikel The efficiency of crackdowns: a lab-in-the-field experiment in public transportations

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See, e.g., Committee of European Banking Supervisors (2010) and Office of the Comptroller of the Currency et al. (2010).

See, e.g., Abel (1990) and Galí (1994).

See Gill and Stone (2010) for an analysis of the effects of perceived inequality on effort levels.

Models of reference-dependent preferences that differ from Prospect Theory are proposed, for example, in Koszegi and Rabin (2006, (2007), Masatlioglu and Ok (2005) and Munro and Sugden (2003).

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.

This effect is in line with findings about risk aversion being decreasing in wealth. See, for example, Dohmen et al. (2011) and Guiso and Paiella (2008).

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 model by Fehr and Schmidt (1999) admits that individuals dislike both social losses and social gains so that it is not compatible with a $g(\cdot )$ increasing in x. In Sect. 5, we discuss how our experimental results relate to existing inequity aversion models.

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.

See also Sullivan and Kida (1995), Ordóñez et al. (2000) and Koop and Johnson (2012), for experimental evidence.

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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Titel: Social comparison and risk taking behavior
verfasst von: Astrid Gamba
Elena Manzoni
Luca Stanca
Publikationsdatum: 29.06.2016
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 2/2017
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-016-9562-z

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