Experimental Design
We are conducting our study using Prolific (www.prolific.co), a web-based platform for recruiting participants. It consists of two stages: a baseline solicitation and an experiment. The baseline solicitation, now completed, provided the information necessary to design the experiment pre-registered here. In both, subjects completed an unrelated survey for another study, then had the opportunity to donate some of a $3 bonus to one of a list of charities, and then were asked questions eliciting beliefs about donations. We asked subjects about the average donation of others (“belief1_i”), the share making a non-zero donation (“belief2_i”), and the share donating $1 or more (“belief3_i”). We also asked subjects how much they would donate if they knew that others had donated an average of $0.50 and if others had donated $1.
We designed the experiment to answer the following research questions:
R1. Do reported hypothetical conditional donations predict the effect of information about the average donation of others?
R2. Do reported beliefs about the donations of others predict the effect of information about:
R2a) the share of individuals donating?
R2b) the share of individuals donating $1 or more?
R2c) the average donation?
Our design randomizes information between subjects. In the control group (denoted by CG) subjects will make their donation decisions without being provided any information about giving behavior in the baseline solicitation. In our treatments, we accompany the solicitation with information about past donations from the first wave. The “Average Donation” treatment (T1) states that “Participants in our last Prolific survey donated an average of $.64.” The “Share Donating” treatment (T2) states that “43% of participants in our last Prolific survey made a donation.” The “Share Donating $1+” treatment (T3) states that “35% of participants in our last Prolific survey donated $1 or more.”
Our analysis will test whether effects of each treatment are heterogeneous in the relevant subject beliefs. Research question R1 relates to heterogeneity in reported hypothetical conditional donations. We use the elicited hypotheticals to define D-hypo_i as the predicted treatment effect of learning the average of others' donations, which we calculate using a linear combination of the hypothetical donations conditional on others’ donations of $0.50 and $1. Only 87 subjects believe that their donation would change, i.e. that D-hypo_i ≠ 0 . We therefore split all of these subjects between C and T1, with the remaining subjects distributed evenly across all four arms according to stratified randomization described next.
To promote balance across treatment arms and enhance precision for our heterogeneity analyses, we utilized stratification in our randomization. We stratified based on the sign of four variables: D-hypo_i, belief1_i, belief2_i , and belief3_i . Because only 13 subjects have D-hypo_i <0 , we did not further subdivide them using the other variables. Because subjects with D-hypo_i >0 are assigned to either C or T1, we did not subdivide them based on belief2_i or belief3_i. We created a separate category for subjects with belief1_i =0 , many of whom report the logically inconsistent belief that belief2_i >0 , i.e. that some subjects donate but that the average donation is zero. Then, to the extent that we could do so without reducing the count within strata to single digits, we further subdivided strata into “high” and “low” groups based on whether their belief1_i (which was the most accurate belief on average) was above or below the median for their stratum. We assigned subjects in each stratum as evenly as possible across treatment arms and then as needed assigned any additional subject to arms in the following order: Control, then “Average Donation,” and then “Share Donating $1+.”
December 20, 2020 update: Because information about moments of the donation distribution had limited effects on subjects’ beliefs about these moments, we decided to run a small follow-up to test whether increasing the salience of the information would have more effect. In this follow-up experiment, the single treatment group sees the “Share Donating” treatment (T2) stating that “43% of participants in our last Prolific survey made a donation,” while the control group does not see this sentence. In this version, the treatment information appears on the second line of text, rather than following the table of donation options, and it appears in bold. We focus on subjects who did not complete the main experiment or were in the control group to avoid multiple treatments. We focus on subjects whose baseline belief about the share making a non-zero donation (“belief2_i”) was not too close to the true value of 43% so that the expected direction of response in beliefs would be clear.