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How do risk attitudes affect pro-social behavior? Theory and experiment

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Abstract

We explore how risk preferences affect pro-social behavior under uncertainty. We analyze a modified dictator game in which the dictator can, by reducing her own sure payoff, increase the odds that an unknown recipient wins a lottery. We first augment a standard social preferences model with reference-dependent risk attitudes and then test the model’s predictions for the dictator’s giving behavior using a laboratory experiment. Consistent with the predictions of the model, we find that the relationship between giving behavior and a giver’s loss aversion is mediated by the strength of the giver’s pro-social preferences. Among more (less) pro-social dictators, an increase in loss aversion increases (decreases) the likelihood that a dictator contributes to a recipient.

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  • 26 November 2020

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  1. Another strand of experiments has investigated whether individual risk preferences predict trusting decisions. Several studies have failed to find a systematic association between the two (see, e.g., Eckel and Wilson (2004) and Houser et al. (2010)).

  2. Our approach is not intended to reconcile the seemingly contradictory findings in the existing literature. That task is outside the scope of this paper. Whereas the results described above emerged from a disparate array of games and settings, we concentrate here on the dictator game and study one specific configuration of this game in detail.

  3. In our empirical analysis, we also make a limited attempt to account for the role of non-linear probability weighting, another important component of risk attitudes.

  4. For an excellent summary of recent work, see Sprenger (2015).

  5. Saito (2013) extended Fehr and Schmidt’s (1999) inequality aversion model to investigate the trade-off between equality of opportunity and equality of outcome when outcomes are risky. His model, however, assumes risk neutrality.

  6. Our focus on the interaction between social preferences and risk attitudes also differentiates our work from that of Fornasari et al. (2020), who study risky choices with social spillovers with an emphasis on decision-making on behalf of others. Although the authors, like us, take a model-driven approach, they neglect considerations about risk attitudes and focus exclusively on the role of social preferences.

  7. As we illustrate in Online Appendix A.2, such a social welfare function encompasses the utility formulations of most well-known models of social preferences, including Fehr and Schmidt’s (1999) inequality aversion model; Charness and Rabin’s (2002) model of social-welfare or quasi-maximin preferences; and Cox et al. (2007) model of ego-centric altruism.

  8. Note that the linearity of U implies that all risk aversion comes from loss aversion. This assumption relies on Rabin’s (2000) “calibration theorem,” which demonstrates that the substantial risk aversion commonly observed in small- or modest-stakes experiments cannot be explained by curvature of the utility function over wealth: “The theorem shows that, within the expected-utility model, anything but virtual risk neutrality over modest stakes implies manifestly unrealistic risk aversion over large stakes. The theorem is entirely ‘nonparametric,’ assuming nothing about the utility function except concavity” (pp. 1281–1282). Rabin conjectured that loss aversion “provides a direct explanation for modest-scale risk aversion” (p. 1288).

  9. Note this reference point nests the two degenerate possibilities that \(\widehat{P}\equiv 1\) or \(\widehat{P}\equiv 0\). When \(\widehat{P}\equiv 0\), the dictator believes the recipient always evaluates her final payoff relative to her initial wealth (i.e., her wealth before participating in the experiment), as in prospect theory (Kahneman and Tversky 1979; Tversky and Kahneman 1992). When \(\widehat{P} \equiv 1\), the dictator believes the recipient always evaluates her final payoff relative to the lottery prize.

  10. In the experiment, subjects received a 10,000 COP attendance fee in addition to their payment from the experimental tasks. To avoid notational clutter, we exclude the attendance fee from all the equations in the paper. This has no effect on our results.

  11. If the dictator did not regard the pool of tokens as part of her endowment, the referent would be given by her original endowment of 20,000 COP. This implies that tokens allocated to the recipient would not entail a loss, but instead would simply reduce a gain. Therefore, the implications for the dictator’s giving behavior would be the same as when her reference point is \(R_{\text{ wealth }}^{\text{ dict }}\).

  12. Therefore, our approach does not conflict with the findings from a few studies which suggest that loss aversion is lower when individuals make risky decisions on behalf of others than when they decide for themselves. See Eriksen et al. (2020) for a review of this research.

  13. We remind the reader that Proposition 1 holds for any social welfare function W that is concave in direct utilities. If, in addition, W is linear in direct utilities, and therefore linear in the number of tokens given, then Proposition 1 applies more generally to the amount of tokens given. The relationship between \(\lambda\) and the amount of tokens given is ambiguous, however, for some non-linear functional forms of W.

  14. While Person 1 subjects completed these allocation tasks, Person 2 subjects completed other tasks which were not monetarily incentivized.

  15. By ensuring that a dictator’s choices were fully transparent to the recipient, we eliminated the possibility that a dictator could exploit “moral wiggle room” (Dana et al. 2007) or “hide” her selfishness behind risk (Andreoni and Bernheim 2009).

  16. In addition to the setup described in Sect. 2.1, our implementation of the dictator games included one extra feature: Recipients also received an envelope. In half of the sessions, the envelope contained 20,000 COP. If the recipient won the lottery, she kept the money, and if she failed to win, she had to return the 20,000 COP to the experimenter. In the remaining half of the sessions, a recipient’s envelope was empty. If she won the lottery, she received 20,000 COP, and if she failed to win, she received nothing. As we show in Online Appendix C, this subtle manipulation did not have any effect on dictators’ behavior. Therefore, in our empirical analysis we pool the observations from all sessions.

  17. Two participants never chose Option B. To distinguish these two participants from those who first switched to Option B in the last row, we assumed their switch point was 21,000 COP.

  18. One concern is that dictators might evaluate the possible payoffs in Task 10 relative to a reference point. For instance, because the recipient receives a final payoff of 20,000 COP for sure unless the dictator chooses Option B, dictators might consider a final payoff of 20,000 COP as the reference point for the recipient’s payoff. This implies that a payoff of 0 COP to the recipient feels like a loss; therefore, a dictator’s degree of loss aversion, \(\lambda\), might also affect her valuation. Importantly, our model predicts that, holding the degree of loss aversion constant, valuations are still increasing in \(\beta\). This means that, once we control for individual differences in \(\lambda\) in the empirical analysis (using a measure that we describe below), valuations are still a good proxy for \(\beta\). We follow this strategy in our tests of Proposition 1.

  19. Similar incentivized tasks have been used in previous studies to obtain a measure of individual loss aversion. Our list draws on the lottery choice tasks used by Fehr and Goette (2007); Gächter et al. (2010); Abeler et al. (2011); and Karle et al. (2015).

  20. The assumption that E is a dictator’s reference point in Task 18 is consistent with the possibility that the dictator perceives either her initial wealth, or her experimental endowment, or her anticipated payoff as the referent in the dictator games (Tasks 1–9). Indeed, prior research has documented that reference points can vary systematically across different tasks within the same experiment. See, for example, Sprenger (2015), whose experimental design is predicated on the premise that reference points can change across certainty and probability equivalent tasks in a predictable way.

  21. An additional identifying assumption is that a dictator’s choices in Task 18 are unaffected by social comparison, that is, by positional concerns involving the recipient. We believe this is a reasonable assumption because, in most cases, the dictator did not learn the recipient’s payoff—she only knew what gamble the recipient would play. This feature of the design made positional concerns far less salient than the internal reference point, E, at this stage of the experiment. Our assumption is consistent with previous research on the influence of social comparison on risk-taking behavior, which suggests that the social referent must be salient to affect behavior (see Gamba et al. (2017) for a review).

  22. An identification strategy premised on original prospect theory, in which we ignore consumption utility and assume that participants integrate their earnings from Tasks 1–17 with their initial wealth, would yield the same ordering of individual \(\lambda\)’s as our approach.

  23. Even in the presence of non-linear probability weighting, the effect of loss aversion should still be identified in a specification with \(\widetilde{\lambda }\) that includes \(\pi \left( 0.5\right)\) as an additional control variable (the last column in Table 1). In contrast, the estimated effect of \(\pi \left( 0.5\right)\) might be biased in a regression with \(\widetilde{\lambda }\) since individual variation in \(\pi \left( 0.5\right)\) might be confounded with individual variation in \(\lambda\) that is not controlled for by \(\widetilde{\lambda }\).

  24. In a laboratory experiment, Exley (2016) showed that people sometimes use risk as an excuse to reduce giving. If the dictators in our experiment use recipients’ risk as an excuse to give less and the excuse motive is correlated with dictators’ loss aversion, then failure to control for the excuse motive in (10) might bias our results. Hence, drawing on Exley (2016), we included Tasks 11–16 to measure excuse-driven risk preferences.

  25. While our discussion of the large-stakes setting clearly holds for the widely-used formulation of social preferences that we consider in this section, we note that we have not systematically assessed the robustness of the unambiguous relationship between risk aversion and giving behavior that we sketch out here to other specifications. Nonetheless, our discussion provides an important illustration of the differences in giving behavior that may arise between situations with small or modest stakes and those with large stakes.

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Correspondence to Santiago I. Sautua.

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We thank Greg Sacks for insightful conversations at the beginning of this project, and an associate editor, two anonymous referees, Ori Heffetz, Ted O’Donoghue, Erkut Ozbay, Guillem Roig, Chad Stecher, and Kyle Woodward for helpful comments and suggestions. We also thank the audiences at the 2017 ESA World Meeting, the Experimental and Behavioral Economics Workshop at Universidad del Rosario, the Bogotá Experimental and Behavioral Economics Seminar (BEBES), Universidad Nacional de Colombia, Universidad de los Andes, and Cornell University for their feedback. Laura Correa provided excellent research assistance. For valuable assistance in the laboratory sessions, we also thank Laura Becerra and Yuliet Verbel. Sautua thanks Universidad del Rosario for financial support. Fahle acknowledges funding from the Alfred P. Sloan Foundation (Grant G-2015-14131).

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Fahle, S., Sautua, S.I. How do risk attitudes affect pro-social behavior? Theory and experiment. Theory Decis 91, 101–122 (2021). https://doi.org/10.1007/s11238-020-09788-8

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