Experiment design and procedure

We conducted an online experiment where participants first answered a survey questionnaire and earned an endowment. The Appendix presents this survey questionnaire. Upon completing the survey, participants were presented with the opportunity to donate to a charity, Médecins Sans Frontières (Doctors Without Borders), using their earned endowment. We introduced the mission, general projects and recent COVID-19 activities of Médecins Sans Frontières. We selected this nonprofit organization given its global service and non-affiliation with any political or religious groups.

We randomly assigned participants to either a baseline group or a comparison group. In the baseline group, participants first decided whether they would donate to the charity and, if yes, how much to donate. We also asked participants how much they thought an average donor like them would contribute. We made this question incentive-compatible by offering an extra $0.5 if their guess was within $0.1 of the most frequent amount contributed. We solicited their initial donation and their first-order belief of an average donor's contribution simultaneously to study the correlation, rather than examining the causal relationship between the two. We offered participants the chance of public recognition after they made their donations. They had the choice to opt in to receive donor recognition in the form of a public announcement via social media, or they could remain anonymous.

Participants of the comparison group received similar treatment as those in the baseline group, except that they were given an opportunity to revise their donation decisions at the same time when they decided whether they would like to be recognized or not. In other words, participants who initially chose not to donate were provided a second chance to contribute with the option to be recognized. Those who initially chose to contribute also had the opportunity to revise their donations, including the option to increase or decrease their initial donations, or to change their minds and not give. The experiment procedure can be found in the Appendix.

We conducted this experiment using two subject samples: Amazon Mechanical Turk (MTurk) crowdsource workers and students from a public university in the United States. We recruited 239 participants from MTurk and obtained 203 valid observations after excluding incomplete answers, answers from repeated IP addresses, and those failing the attention check questions. On average, MTurk participants spent 11 min on the survey and earned $1 for their participation, plus a $2 bonus for completing the survey. This translates to an effective hourly wage of $16 per hour. We recruited 289 student participants and obtained 242 valid observations following the same data screening process. On average, student participants spent 14 min on the survey. We paid them $1 for participation plus a $4 bonus for completing the survey. This translates to an effective hourly wage of $21. We paid MTurk participants a lower bonus commensurate with the average MTurk compensation (Hara et al., Reference Hara, Adams, Milland, Savage, Callison-Burch and Bigham2018).

Participants kept their participation payment and made their contributions to Doctors Without Borders using their bonus only. Donations were completely voluntary. We recognized donors via social media and donated all the funds raised to Médecins Sans Frontières at the end of the experiment.

Data analysis and results

Table 1 presents the descriptive statistics by sample source and treatment. Participants from MTurk are mostly college-educated white males with an average age of 37 years old. The student participants are mainly female undergraduates with an average age of 27, with slightly more than half non-whites. We also report participants’ donation decisions in Table 1. We define donation as the average amount contributed by all participants in the final stage (i.e., after donation revision for those in the comparison group), including zero contributions. Belief is the perceived donation by an average participant. These three variables are reported both in dollar amounts and as percentages of the participant's total endowment. Participation is the percentage of donors who contributed out of all the participants. Recognition is the percentage of donors who choose to be recognized.

Table 1. Descriptive statistics

We observe that on average, students gave more than MTurk workers. An average MTurk worker gave $0.58, or 28.82% of his total $2 bonus, while an average student gave $1.26, or 31.40% of her $4 bonus. However, the difference between these percentages is statistically insignificant (p-value = 0.5137 for the unpaired two-tailed t-test).

The perceived average donation is higher among students compared to that of the MTurk workers. On average, the believed average donation of MTurk workers is $0.67, or 33.51% of the total endowment, while these numbers are $1.72, or 43.06% of the total endowment for students. The difference between these percentages of donation as a proportion of the total endowment is statistically significant at the 1% level (p-value < 0.01, unpaired t-test).

Regarding the donation participation rate, 51.72% of the MTurk workers contributed, compared to the value of 35.95% for students. The difference in participation between these two subject pools is statistically significant at the 1% level (p-value < 0.001, unpaired t-test). In addition, MTurk workers are more likely to opt in for recognition. 43.84% of the MTurk workers chose to be recognized, compared to 17.36% of the students who chose to be recognized. The difference between these two numbers is statistically significant at the 1% level as well (p-value < 0.001, unpaired t-test).

We perform regression analyses to complement the nonparametric analysis. We constructed the following probit regression model to analyze what factors influence subjects’ participation decisions:

(1)$$\begin{align}Probit\;( {participation} ) =& \beta 0 + \beta 1\ast Treatment + \beta 2\ast Belief \cr &+ \beta 3\ast Personal\;characteristics + \varepsilon\end{align} $$

The dependent variable, participation, indicates the participants’ decisions of whether to contribute to the charity or not. The value of this variable equals 1 if the participant gives any positive amount, and 0 otherwise. The independent variable, treatment, captures the treatment effect of allowing participants to revise their donations, which is the difference between the baseline group and the comparison group. This binary variable equals 0 for those in the baseline group and 1 for the comparison group. Belief is the perceived donation amount from an average person, measured as a percentage of the total endowment. We also control subjects’ personal characteristics, including age, gender and race. ɛ is the error term. We ran Model (1) using MTurk workers, students and the pooled sample, respectively, and henceforth.

Table 2 presents the probit regression results. We observe that participants’ perceived donation amount from an average person is positively correlated with their likelihood to donate. A 100% increase in the believed average donation is associated with 90.6–93.4% higher chances to give for MTurk workers in the model specifications with and without personal characteristics, respectively. Another way to interpret this result is that with each unit increase in the subject's first-order belief, the probability of the subject donating to the charity goes up by 0.906–0.034%. For students, a 100% increase in their believed average donation is correlated with a 76.9–97.1% higher likelihood to contribute to the model specifications with and without personal characteristics, respectively. In the pooled sample, a 100% increase in the believed average donation is correlated with 70.0–80.3% higher chances to donate in the model specifications with and without personal characteristics, respectively. All the above coefficients are significant at the 1% level.

Table 2. Probit regression results (Y = participation, marginal effects reported)

Standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

Allowing people to revise their donations also increases their likelihood to give. MTurk workers in the comparison group are 44.8–56.2% more likely to give compared to their counterparts in the baseline group in the model specifications without and with personal characteristics, holding everything else equal. These coefficients are significant at the 5% and 1% levels, respectively. For students, these coefficients are 31.6–33.6% in the model specifications with and without personal characteristics, respectively. These coefficients are significant at the 10% level. In the pooled sample, participants are 38.3–39.7% more likely to donate when they have the option to revise their donations. Both of these coefficients are significant at the 1% level.

We constructed the following OLS regression model to further analyze how first-order beliefs and the opportunity of donation revision influence participants’ actual donation. The dependent variable, donation, is the subject's actual donation as a percentage of the total endowment. The independent variables are defined the same as in Model (1). ɛ is the robust standard error.

(2)$$Donation = \beta 0 + \beta 1\ast Belief + \beta 2\ast Treatment + \beta 3\ast Personal\;characteristics + \varepsilon \;\;$$

Table 3 reports the regression results of Model (2). Our results show that first-order beliefs have a significant positive influence on participants’ donation in both model specifications with and without personal characteristics, and this is true across all samples. For MTurk workers, a 100% increase in their beliefs is associated with a 36.7–37.7% increase in the actual donation as a percentage of their endowment in the model specification with and without personal characteristics, respectively. For students, a 100% increase in their believed average donation is associated with a 32.4–39.0% increase in the actual donation in the model specification with and without personal characteristics, respectively. These numbers are 35.9–38.1 for the pooled sample, respectively. All the above coefficients are significant at the 1% level. We do not find revision has any significant impact on participants’ donations except in the model speciation controlling for personal characteristics with the pooled sample.

Table 3. OLS regression results (Y = donation)

Robust standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

These findings above support our Hypothesis 1. People's beliefs of an average person's donation correlate with their decision of whether to donate or not and their actual donation amount.

Next, we present the moderation models to further investigate how people's beliefs about an average person's donation and their initial donations influence their decisions on donation revision and public recognition. We first build a probit model, Model (3), to analyze the determinants of the subject's choice of donation revision. The dependent variable, revision, is the binary choice of whether participants utilized the opportunity of donation revision or not. It equals 1 if the subject revised his or her donation and 0 otherwise. The independent variable, initial donation, is one's donation amount as a percentage of the total endowment before revision. The other independent variables are the same as defined in previous models. We added the interaction term between one's first-order belief and initial donation to test the moderating effect of beliefs.

(3)$$\begin{align}Probit\;( {Revision} ) =& \beta 0 + \beta 1\ast Belief + \beta 2\;\ast \;Initial\;Donation \cr & + \beta 3\ast Belief\ast \;Initial\;Donation + \beta 4\ast Personal\;characteristics \cr &+ \varepsilon \end{align}$$

Table 4 presents the regression results for Model (3). We used the pooled sample only because there was a limited number of participants who revised their donations in the comparison group (n = 48), including 36 participants of MTurk workers and 12 participants of students. We run the model specifications without and with personal characteristics, respectively. Our results show that first-order beliefs have a positive effect on one's choice of donation revision. The higher the believed donation is, the more likely the individual is to revise his donation. In addition, the interaction term between the believed donation and one's initial donation is negative and statistically significant at the 10% level. We use Figure 1 to visualize the interaction effect of belief and initial donation on one's revision decision and explain the moderating effect of first-order beliefs on people's choice of donation revision as their initial donation increases.

Table 4. Probit regression results (Y = revision, marginal effects reported)

Standard errors in parentheses. ***p < 0.01, *p < 0.1.

Figure 1. The influence of belief and initial donation on donation revision.

Figure 1 presents the probabilities of participants revising their donations using their first-order beliefs as the moderator. It shows that there is a significant difference in the likelihood of donation revision between those with a higher belief (represented by the red line), which is one standard deviation above the mean, and those with a lower belief (represented by the blue line), which is one standard deviation below the mean (μ = 0.349, σ = 0.338).

We observe a significant negative relationship between participants’ initial donation and their likelihood of revision for those with a higher first-order belief (p < 0.001). The more they gave in the initial stage, the less likely they chose to revise their donations in the later stage. For those with a lower belief, there is a slight positive relationship between the initial donation and their choice of revision. Yet, this positive relationship is small in magnitude and statistically insignificant. In general, participants having higher beliefs were more likely to revise their donations compared to their counterparts with a lower believed average. Those who initially gave a lower amount but had a high level of beliefs were mostly likely to revise their donations in the presence of public recognition. On the contrary, donation revision was least effective for those with lower first-order beliefs.

Moreover, we build the following probit model, Model (5), to analyze subjects’ choice of public recognition. The dependent variable, recognition, is the binary choice of whether participants opt in for public recognition or not. It equals 1 if the subject chose to be recognized and 0 otherwise. All the independent variables are defined the same as in Model (4).

(4)$$\begin{align}Probit\;( {Recognition} ) =& \beta 0 + \beta 1\ast Belief + \beta 2\;\ast \;Initial\;Donation \cr & + \beta 3\ast Belief\ast Initial\;Donation + \beta 4\ast Personal\;characteristics \cr & + \varepsilon \end{align}$$

Table 5 reports the regression results for Model (4). Our results show that beliefs have a positive effect on one's choice of recognition. The higher the belief is, the more likely the individual prefers to be recognized. These coefficients are statistically significant at the 1% level. People's initial donation also has a positive impact on the choice of recognition. These coefficients are all significant at the 1% level in both model specifications without and with personal characteristics. Additionally, the interaction term between one's first-order belief and initial donation is negative and statistically significant at the 5% level. We use Figure 2 to illustrate the moderating effect of first-order beliefs on people's choice of public recognition as their initial donation increases.

Table 5. Probit regression results (Y = recognition, marginal effects reported)

Standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

Figure 2. The influence of belief and initial donation on public recognition.

Figure 2 illustrates the probability of participants choosing public recognition in the same fashion as Figure 1, using first-order beliefs as the moderator. There is a significant difference in people's preference for public recognition between those with a higher belief (represented by the red line), which is one standard deviation above the mean, and those with a lower belief (represented by the blue line), which is one standard deviation below the mean. Although there is a positive relationship between one's initial donation and the likelihood of choosing to be recognized for both types of participants with various levels of beliefs, the marginal effect of their initial donation on the choice of recognition is larger for the group with a lower belief compared to their counterparts with a higher belief. Additionally, these two lines cross at the point where participants gave 60% of their endowment as an initial gift. To the left of this 60% threshold, participants with a higher belief were more likely to opt in for public recognition compared to those with a lower belief, holding other things equal. On the right of this 60% threshold, participants with a lower believed average donation were more likely to opt in for public recognition compared to those with a higher belief. This implies that for those with a relatively small initial donation (less than 60% of their endowment), the higher their first-order beliefs were, the more likely they would choose to be recognized. However, the influence of beliefs on the choice of recognition decreases as a person's initial donation reaches 60% or more of his or her endowment. These findings imply that public recognition is most effective for generous donors who think others would give less.

Based on the results above, we draw the following conclusions:

Result 1. First-order beliefs are positively correlated with people's tendency to give and their contributions.

Result 2. People with higher first-order beliefs and low initial donations are more likely to revise their contributions.

Result 3. Individuals with higher initial donations and lower first-order beliefs are most likely to choose to be recognized. This indicates that people tend to seek greater reputational returns by standing out.