Unconditional Cooperation (Part 2)

Figure 4-3: Contributions and expected contributions (creation vs. prevention)

Both under outcome risk and under no outcome risk average contributions (depicted by solid lines) are higher in the prevention frame than in the creation frame in every round. Moreover, both under creation- and prevention-framing average contributions are higher in treatments with outcome risk than in treatments without outcome risk in every round.46 Figures 4-11 and 4-12 in appendix A6 show average contributions

0 1 2 3 4 5 EU R 0 2 4 6 8 10 Period Risk 0 1 2 3 4 5 EU R 0 2 4 6 8 10 Period NoRisk

Average over all subjects

Contributions and Expected Contributions

Contribution_Creation Expectation_Creation

Outcome Risk and Prevention Framing in Social Dilemmas

separately for each of our 16 independent observation. Expectations about contributions made by group members (depicted by dashed lines) are found to be higher under prevention framing as well as under outcome risk already in the first round. In order to validate the significance of these observations, we run several non- parametric tests. P-values reported below show test-statistics of two sided Mann- Whitney tests.

PR vs. CR: When comparing average amounts contributed in all ten rounds (further

denoted as average contributions) for each independent observation (matching pool of 12 subjects), contributions are significantly higher in the PR-treatment compared to the CR-treatment (p=0.043, n=447). This holds also true when comparing contributions collected in the first round (p=0.021, n=48). Likewise, expectations about average contributions of group members48, which subjects revealed in the first round, are significantly higher in the PR- than in the CR-treatment (p=0.022, n=48).

PnR vs. CnR: Neither average contributions (p=0.149, n=4) nor first round

contributions (p=0.119, n=48) are significantly higher in the PnR- than in the CnR- treatment. However, the difference in first round expectations about others´ contributions is found to be highly significant (p=0.004, n=48).

PR vs. PnR: Average contributions are significantly higher in the PR- than in the

PnR-treatment (p=0.021, n=4) as are first round contributions (p=0.070, n=48). In contrast, the difference in first round expectations is not found to be significant (p=0.194, n=48).

CR vs. CnR: The contributions observed in the CR-treatment are higher than in the

CnR-treatment, a difference which is weakly significant both for average contributions (p=0.100, n=4) and for first round contributions only (p=0.083, n=48). In the same line, first round expectations are significantly higher in the CR-treatment (p=0.025, n=48).

Figure 4-4: Treatment differences with Wilcoxon rank sum tests

Table 4-2 presents different specifications of a tobit model regressing average contributions on a variety of explanatory variables.

Dep. Var.: Average

contr. I II III prevention 0.609† (0.328) 0.609 † (0.334) 0.610 † (0.333) risk 1.013* (0.414) (0.416) 1.023* (0.354) 0.759* prevention  risk 0.598 (0.502) (0.508) 0.589 (0.507) 0.588 risk aversiona _0.002 (0.028) (0.017) -0.019

risk aversion  risk 0.041

(0.055) constant 1.041*** (0.256) 1.018*** (0.297) 1.152*** (0.225) # observations 192 17949 ₁₇₉ (# groups) (16) (16) (16) Pseudo R2 _{0.49 0.48 0.48} Log Pseudolikelihood -135.58 -127.62 -127.33

Tobit regressions with errors clustered for independent observations (groups);

standard errors in parenthesis; : interaction; *** represents significance at p=0.001, ** at p=0.01, * at p=0.05, and † at p=0.10.

a _{Discrete variable ranging from 0 (extremely risk seeking) to 10 (extremely risk}

averse).

Table 4-2: Sum of contributions over ten rounds

Outcome Risk and Prevention Framing in Social Dilemmas

Errors are clustered for our 16 independent observations (matching pools of 12 subjects each). Regressions confirm the previous finding that both prevention framing and outcome risk have a significant impact on total contributions (outcome risk at a 5% level, prevention framing at a 10% level). The interaction effect of both, however, is not found to be significant. The level of risk aversion elicited in part 350 is found to have a non-significant impact on contributions – neither in the outcome risk treatments nor in the treatments without outcome risk. 51

This appears surprising as we have shown in section 4.2.2 that risk aversion resulting from utility curvature should have an impact on contributions in the treatments exhibiting outcome risk. It is, however, important to note that Holt and Laury’s (2002) mechanism cannot distinguish between risk aversion arising from concavity of the utility function and risk aversion resulting from probability weighting. In fact, for the payoffs involved in laboratory experiments subjects are often assumed not to exhibit a concave but a linear utility function, implying observed risk aversion to stem from probability weighting (Abdellaoui, 2011; Wakker 2010).

As shown in Figure 4-3, average contributions lie consistently below average expectations about others´ contributions in the CnR-, PnR-, and CR-treatment. Only in the PR-treatment average contributions match or even exceed average expectations. This finding is confirmed by a random effects tobit model regressing contributions to the public account on expectations, which is presented in Table 4-3. Each matching pool (containing 12 subjects) is treated as an independent observation, resulting in 16 independent observations in total. In all treatments participants’ contributions are significantly affected by their expectations on others’ contributions indicating that subjects are on average conditional co-operators. However, in the CnR-treatment, participants contribute only €0.87 on average for

each euro they expect others to contribute.52 This relation is not significantly different for the CR- and PnR-treatments. Solely in the PR-treatment participants are on average willing to contribute an amount at least as high as the average they expect others to contribute.53

Dep. Var.: contribution

expectation 0.865*** (0.059) expectation  CR 0.065 (0.065) expectation  PR 0.181** (0.064) expectation  PnR -0.112 (0.090) constant no # observations 1920 (# groups) (16) # rounds 10 Wald chi2 1993.31 Log Likelihood -3276.69

Random effects tobit regressions: standard errors in

parenthesis; : interaction; *** represents significance at p=0.001, ** at p=0.01, * at p=0.05, and † at p=0.10.

Table 4-3: Contributions as a function of expectations

Looking at single observations, in the PR-treatment subjects chose a contribution lower than their average expectation (on others’ contributions) only in 34.6 % of all contribution decisions, compared to 52.0 % in the CR-treatment, 66.9 % in the CnR- treatment, and 59.0 % in the PnR-treatment. This self-serving bias ( Fischbacher et al., 2001) is confirmed when looking at conditional contribution patterns further below. Fischbacher and Gächter (2010) argue that the self-serving bias in conditional contributions itself leads to a decay in contributions even if an entire group of participants consists solely of conditional cooperators. Indeed, while contributions decrease over time in all other treatments they remain fairly constant in the PR- treatment – the treatment with no self-serving bias on average.

52 _{Applying a chi}2_{-test we can reject the null hypothesis that this coefficient is not different from one}

Outcome Risk and Prevention Framing in Social Dilemmas