We first analyzed the impact of a social reference point when rank cannot be affected and, hence, focused on a possible impact of the distance to the social reference point on risk-taking. More specifically, we investigated Conjectures 1a, 1b, and 1c by comparing risk-taking in the social loss (Below) and social gain (Above) conditions with risk-taking in the isolated condition. Next, we turned to the impact of a social reference point when rank can be either improved or lost in the catch-up (Catch-Up) condition. Conjectures 2a and 2b describe the behavior if people are only concerned about rank. Last, we investigated the heterogeneity of individual behavior and categorized subjects into the following behavioral types based on the experimental results: (i) only rank matters; (ii) only distance matters and the respondent is status motivated; (iii) only distance matters and the subject is guilt motivated; and (iv) the social context does not matter.
Risk-taking when rank is given
As risk-aversion in isolation matters for behavioral conjectures, we separated subjects into three categories: risk-averse, risk-neutral, and risk-seeking. Subjects were classified as risk-neutral if their lowest preferred certain amount was either 50 or 55 (implying a total amount of 100 or 105 with the endowment). A risk-neutral subject should be indifferent between a certain pay of 50 or the lottery; however, as they do not have the option of being indifferent, the lowest preferred certain amount would have to be either 50 or 55. Thus, risk-averse subjects have switching points below 50 and risk-seeking subjects have switching points above 55. As can be seen in Table 3 below, 26.5% are categorized as risk-averse, 38.1% risk-neutral and 35.4% risk-seeking, while a certainty equivalent of 55.292 shows that individuals on average are risk-neutral. In Table 3, we also show the descriptive statistics from the same categorization of individuals for the other three conditions. To analyze our research questions, we need to investigate within individual changes between conditions.Footnote 16
We began to investigate the impact of a social reference point when the distance between own outcome and the reference point can be affected but rank is given. Remember that risk-taking should not be affected if only rank matters to the subject. If distance to the outcome of the other also matters, risk-averse individuals should be less risk-averse and risk-seeking individuals less risk-seeking in the social loss (Below) condition compared to in Isolation. In the social gain (Above) condition, guilt-motivated risk-averse individuals should be more risk-averse and guilt-motivated risk-seeking individuals more risk-seeking than in Isolation. Status-motivated risk-averse individuals should be less risk-averse, and status motivated risk-seeking individuals less risk-seeking than in Isolation. Hence, to investigate the impact of the social reference point on risk-taking we need to condition on risk-taking in isolation, that is without a social reference point. Figure 1 and Table 4 compare risk-taking in the social gain (Above) and the social loss (Below) conditions, respectively, with risk-taking in Isolation, while formal testing by using regressions are shown in Table 5.
In Fig. 1 the x-axis measures risk attitudes in terms of the sum of certainty equivalent and the fixed endowment of 50 without a social reference point (Isolation) and the y-axis measures risk attitudes in terms of the sum of certainty equivalent and the fixed endowment of 50 with a social reference point. The dots are frequency weighted. The 45-degree line indicates the same choices in both conditions. Dots above the 45-degree line indicate riskier decisions with a social reference point, and dots below the line indicate less risky choices with a social reference point. The vertical dotted lines divide people into risk-averse (to the left), risk-neutral (in the middle), and risk-seeking (to the right) in isolation. Table 4 shows the shares of each risk type in isolation (risk-averse, risk-neutral, or risk-seeking) who either increase risk-taking, do not change risk-taking, or decrease risk-taking in the social contexts. There is substantial individual heterogeneity. Still, it is clear from both Fig. 1 and Table 4 that people who are risk-averse in Isolation more often increase than decrease risk-taking in the social conditions. The risk-neutral people change their risk-taking decisions less often than do others. Though the difference in risk-taking decisions for risk-seeking people is less clear from the figure than is the difference for risk-averse people, they more often decrease than increase risk-taking, especially when being behind others. This pattern of behavior in the social context is in line with Conjectures 1b and 1c, but not with Conjecture 1a, according to which there should be no systematic impact of the social context when rank is given. Thus, our results favor a model where distance to the social reference point affects utility. Moreover, risk-averse individuals are less risk-averse and risk-seeking individuals less risk-seeking in the social gain context compared to in the case without social comparison. This suggests that people like to be ahead of others, or, in other words, that β is positive.
Table 5 presents results from regressions comparing risk-taking in the social gain (Above) and social loss contexts (Below) with the comparison condition without a social reference point (Isolation) for risk-averse, risk-neutral, and risk-seeking individuals. All regressions use individual fixed effects.
Regression results support the patterns found in Fig. 1 and Table 4. Individuals who are risk-averse in isolation increase risk-taking in both the social loss and the social gain context, whereas individuals who are risk-seeking in isolation decrease risk-taking in both social contexts. There is no systematic impact of the social reference point on risk-neutral individuals. These results are in line with utility from deviations between own income and a social reference point, where people get positive utility (status) from being ahead of others and disutility (envy) from being behind of others. The results are not in line with a model either where the social reference point matters only through rank or where social preferences do not matter.
When rank cannot be affected, risk-averse individuals make riskier choices and risk-seeking individuals less risky choices than in isolation in both the social loss context and the social gain context. This is in line with a model where people get negative utility from negative deviations from the social reference point (envy) (Conjecture 1b) and positive utility from positive deviations (status) (Conjecture 1c). It is not in line with a model where people get utility of rank only (Conjecture 1a).
Risk-taking when rank can change
Next, we investigate the Catch-up condition where rank is not given. There is a 0.5 probability of improving rank in a lottery choice, while the individual know if rank is improved or not for certain outcomes. We first investigate Conjectures 2a and 2b, that is, if risk choices are in accordance with the rank-utility model. Individuals who are motivated by rank and who chose at least some certain outcome below the social reference point in Isolation should increase risk-taking and thereby increase the possibility to catch up. However, the most risk-seeking individuals, who only choose certain outcomes above the social reference point in Isolation should decrease risk-taking and thereby be certain of catching up for more choices. Figure 2 and Table 6 compare risk-taking in the Catch-up condition both with risk-taking in the Isolation and in the Below condition.
The dashed vertical line in Fig. 2 is the social reference point of 125. Both Fig. 2 and Table 6 show the same results. It is clear that the most risk-taking subjects, who can increase the possibility of improving rank by reducing risk-taking, often do so. For the less risk-taking subjects, who can increase the possibility of improving rank by increasing risk-taking, the pattern is less clear. In Fig. 2 we see that many of them choose the approximately risk-neutral choice throughout. Table 7 shows the regression results of the same comparison as in Fig. 2 and Table 6, where separate regressions are run on those who can increase the possibility of catching up by increased risk-taking and those who can do so by decreased risk-taking.
In line with Conjecture 2a and 2b, we find that individuals who can catch up by taking more risks do so, whereas individuals who increase the possibility to catch up if they take less risk do this. In the latter case, the effect is large and statistically significant. In the former case, the effect is smaller and only statistically significant when the comparison condition is Isolation.
Even if results are in line with our conjectures where only rank matters, they are also in line with models where deviations from the social reference point matters. In Table 8, we divide the group of individuals who can increase their possibility to get ahead by increasing risk-taking into subgroups of risk-averse, risk-neutral, and weakly risk-seeking in Isolation. We refer to subjects who can increase their possibility to get ahead by decreasing risk-taking as strongly risk-seeking. This allows us to investigate how well the utility from deviations model can explain results in the Catch-up condition. The weakly risk-seeking individuals decrease risk-taking, even though this should decrease their possibility of catching up with the social reference point. The risk-neutral individuals remain risk-neutral, even if they can increase their possibilities to catch up by taking more risk. This result is more in line with the utility from deviations model than with the utility from rank model. In particular, it is in line with the utility from deviations model with \(\beta \approx -\propto\).
The last two columns in Table 7 compare the Catch-up condition with the social loss condition (Below). The fact that there are effects of the Catch-up condition in this comparison could be taken to suggest that the possibility to change rank matters. However, without more precise knowledge of \(\propto\) and \(\beta\), we do not know how risk-taking differs between the Catch-up and the two social loss conditions (Above and Below) in the utility from deviations model. Hence, the utility from deviations model could potentially explain these results even without a jump at the social reference point. Hence, while we can infer that the risk-taking decisions of subjects are in line with a model where they care about distance to the social reference point and are status motivated, we do not know if there is also a jump at the social reference point.
When rank can be affected, risk behavior is affected in the same way as when rank cannot be affected. This is in line with a model where people get negative utility from negative deviations from the social reference point and positive utility from positive deviations.
Figures 1 and 2 show substantial heterogeneity in behavior. We here investigate individual behavior in detail. More specifically, we divide subjects into behavioral types. We categorized respondents whose responses were completely in line with either (i) only rank matters; (ii) distance matters and the respondent is status motivated; (iii) distance matters and the respondent is guilt motivated; or (iv) the social context does not matter.Footnote 17 In total, 34.3% of the respondents had responses completely in line with at least one of these types. Among risk-neutral respondents, we cannot distinguish between types (ii) to (iv), as these types will choose the risk-neutral choice throughout. Among the risk-neutral subjects who can be categorized, 16% care only about rank, whereas 84% either care about distance to the social reference point or do not care about the social context. For the risk-averse and risk-seeking individuals we can categorize into each of the four types: 41.1% care about distance and are status motivated, 39.3% are not affected by the social context at all, 10.7% care only about rank, and 8.9% care about distance to the social reference point and are guilt-motivated. Among respondents who did not answer in accordance with any of these four types, two patterns stood out as being common. In all, 21.7% of the remaining risk-neutral or risk-seeking individuals always chose more risk in a social context, and 12.3% of the remaining risk-averse or risk-neutral individuals always chose less risk in a social context. To sum up, there is large heterogeneity in behavior, but distance seems to be more important than rank in our sample.