Decompose the overall difference

In the decomposition exercise of Equation1.1, the overall difference is attributed to two compo-nents. One component represents the effect of the external institution and the other represents the effect of intrinsic characteristics of decision makers. Recall the decomposed overall differ-ence as below,

If at least one decision maker decides not to volunteer, then P(V)6=1, and both the external institution and the selection of decision makers influence the overall difference in risk taking.

The institutional effect and the selection effect is discussed in the following subsections.¹⁰ 4.3.1 Institutional effect

Figure4shows the comparison between decisions inNon-voluntarytreatment and inVoluntary treatment. On average, decision makers in Voluntarytreatment invest more tokens than deci-sion makers inNon-voluntarytreatment on behalf of the recipients. The first column of Table4 shows that decision makers on average invest 7.09 more tokens (0.23 of standard deviation) for the recipients inVoluntarytreatment than in Non-voluntarytreatment. The second column of Table4shows that the difference in decisions between the two treatments is smaller but still sta-tistically significant when the background variables are controlled. The background variables have impacts on decisions on behalf of recipients. Risk taking on own behalf positively affects risk taking on behalf of others. The coefficient of the decision for self is statistically significant and less than one. This implies a link between attitude toward private risk and attitude toward others’ risk. Decision makers refer to private risk taking when deciding for others. I return to the other-self comparison in more detail in Section4.4. The negative effect of age on risk tak-ing means that older decision makers take less risk for others. This is consistent with previous results of increasing risk aversion with age (von Gaudecker et al., 2011;Dohmen et al.,2011;

Tymula et al.,2013). The pro-sociality in a favorable inequality (y-score) has negative effects on risk taking for others. The negative effect of the pro-sociality index (y-score) conforms to the findings that social preferences may influence the risk taking on behalf of others (Andersson

10In the pre-analysis plan (Xu,2017), I registered the method of propensity score matching to estimate the effects. A propensity score of each decision maker is computed from an estimated logistic model. Based on the score, each volunteer is matched with a decision maker inNon-voluntarytreatment so to identify the willingness to volunteer inNon-voluntarytreatment. If there is some unobserved variable that can explain the volunteering decision and is not included in computing the propensity score, then the matching quality deteriorates and the estimation can be biased. The results of propensity score matching are statistically significant and qualitatively similar to the results in this section but quantitatively smaller, see details in AppendixF.

et al.,2016b;Montinari and Rancan,2018).

The coefficients of dummy forVoluntarytreatment in the first two columns of Table4are both statistically significant. The difference in decisions for the recipients between the two treatments provides evidence for the institutional effect. The institutional effect is not equal to the conditional difference shown by the coefficient, unless the expected share of volunteering is equal to one. To estimate the institutional effect, we follow the expression of estimate in Equation3.3. The institutional effect is estimated by dividing the observed difference between the two treatments by the share of volunteering.

The estimate of the institutional effect is shown in Table 5. Decision makers who are willing to volunteer take more risk when they volunteer to provide assistance and decide for the recipients (Voluntarytreatment), than they do when they are asked to decide for the recipients (Non-voluntarytreatment). The difference is around 14.9 tokens with a standard error of 4.7.

The institutional effect is statistically different from zero (p<0.01). It is evident that the institution of decision making has impacts on the risk taking on behalf of the recipients, and the opportunity of volunteering leads to greater risk taking for the recipients.

Result 2.Volunteer decision makers take more risk on behalf of others in the institution where they have the opportunity to contribute to social assistance and decide than in the institution where they are asked to make decisions.

4.3.2 Selection effect

Figure5compares the decisions of the decision makers inNon-voluntarytreatment to the deci-sions of opt-out decision makers inVoluntarytreatment. The decision makers inNon-voluntary treatment invest less tokens on behalf of the recipients than the opt-out decision makers in Vol-untarytreatment. The opt-out decision makers in Voluntarytreatment on average invest 7.23 more tokens (0.23 of the standard deviation) for the recipients than decision makers in Non-voluntary treatment, as seen in the third column of Table 4. The fourth column of Table 4 shows that the difference of decisions between the non-volunteers inVoluntarytreatment and decision makers inNon-voluntarytreatment is slightly larger and statistically significant when the background variables are controlled. The effects of the background variables on risk taking for the recipients among the opt-out decision makers in Voluntarytreatment and the decision makers inNon-voluntary treatment are shown in the fourth column of Table4. These effects of the background variables are similar to the effects shown in the second column with all the decision makers included. The coefficient of decision for oneself is statistically significant. The coefficient of age is statistically significant and negative. One notable difference between the results in the fourth column and the second column is that the coefficient of y-score turns not statistically significant when the volunteer decision makers are not included.

If decision makers unwilling to volunteer take same risk on behalf the recipients as do the decision makers willing to volunteer, then there is no selection effect and the decisions of

015304560Decisions for others +/- 95%CI (tokens)

Non-voluntary treatment Voluntary treatment

Figure 4: DMs in Non-voluntary treatment vs. DMs in Voluntary treatment Notes: The left bar shows the average number of tokens invested by the decision makers in Non-voluntary treatment and the right bar shows the average number of tokens invested by the decision makers inVoluntarytreatment. The number of invested tokens ranges from 0 to 100. The error bars depict 95 percent confidence intervals of the mean decisions.

Table 4: Components of observed differences in Hypotheses 2-4

decision for self (tokens) 0.72^∗∗∗ 0.70^∗∗∗

(0.03) (0.03)

Notes: The dependent variable in the first four columns is the decision made on behalf of others. The decisions are in the number of invested tokens, ranging from 0 to 100. The dependent variable in the last two columns is the difference in deci-sions made on behalf of others and on behalf of oneself. The difference in decideci-sions ranges from -100 to 100. The independent variables are decision for oneself (excluded in the last two columns), x-score and y-score from the hypothetical dictator game (see AppendixA), age, dummy for female, dummy for high education, dummy for consistency in dictator game, dummy for preferring Republican party, and dummy for being in the pilot study. The x-score and y-score are computed only for the de-cision makers who were consistent in the hypothetical dictator game. For the inconsistent dede-cision makers, the two scores are set as the respective average values among the consistent decision makers. The first and second columns include the de-cisions for the recipients made by all the decision makers in both treatments. From the third column onward, each column includes the opt-out decision makers inVoluntarytreatment and the decision makers inNon-voluntarytreatment.^∗p<0.10,

∗∗p<0.05,^∗∗∗p<0.01. Standard errors are in parentheses.

Table 5: Estimates of the effects (Bootstrap s.e.) Estimates

Institutional effect 14.92^∗∗∗

(4.72)

Selection effect -15.23^∗∗∗

(5.51) Selection effect on other-self difference -19.63^∗∗∗

(4.25)

Notes: All the effects are measured as tokens. The positive in-stitutional effect means that the volunteers invest more for oth-ers inVoluntarytreatment than inNon-voluntarytreatment. The negative selection effect means that the decision makers who are willing to volunteer invest less for others than those unwilling to volunteer. The negative selection effect on other-self difference means that the other-self difference of the decision makers will-ing to volunteer is smaller than those unwillwill-ing to volunteer. The coefficients used to compute the estimates correspond to the co-efficients of the dummy forVoluntarytreatment in the first, third, and fifth columns in Table4. The estimate for the expected share of volunteering is the observed share of volunteering in Volun-tarytreatment. The estimates are computed by dividing the co-efficients with the share of volunteering. For the institutional ef-fect, all the decision makers are included in estimation. For the selection effect and selection effect on other-self difference, the non-volunteer inVoluntarytreatment and decision makers in Non-voluntary treatment are included. ^∗ p<0.10, ^∗∗ p<0.05, ^∗∗∗

p<0.01. Standard errors in parentheses are bootstrapped based on 800 replications with replacements.

opt-out decision makers should not be different from the decisions of the decision makers in Non-voluntary treatment. The observed difference instead shows evidence for the selection effect. Recall the estimate of the selection effect,

(E[Y^NV|V =1] − E[Y^NV|V =0])

| {z }

Selection effect

= Y_Non-vol −YNon-volunteers in Vol

V .

The selection effect is not equal to the coefficient of the dummy forVoluntarytreatment, unless the share of volunteering is equal to one. To estimate the selection effect, the average difference is divided by the mean share of volunteering. The selection effect is around 15.2 tokens with a standard error of 5.5. The selection effect is significantly different from zero (p<0.01).

Decision makers with different attitudes toward volunteering take different amounts of risk on behalf of the recipients, although the opportunity of volunteering is absent and they are asked to make the decisions. Decision makers unwilling to volunteer take more risk on behalf of the recipients than those willing to volunteer.

The selection effect shows that the non-volunteers take more risk on behalf of others than the volunteers do. In contrast, the finding in Section 4.1 shows that the non-volunteers take less risk on behalf of themselves than the volunteers do. This implies that volunteers and non-volunteers may exhibit different risk taking for others compared to risk taking for themselves.

The other-self difference in risk taking is discussed in Section4.4.

Result 3. When being asked to make decisions, decision makers who are willing to volunteer take less risk in decisions of social assistance than the decision makers who are unwilling to volunteer.