Our design encompasses two treatments (HardEasy and EasyHard). In both treatments, subjects work on Raven's Progressive Matrices which are commonly used to measure fluid intelligence. We split the matrices in two parts such that one part is easier (Easy) and another one is harder (Hard). Matrices in part Easy and part Hard do not repeat or overlap. All participants receive a show-up fee, but no additional payment for correct answers on the matrices.
Subjects are randomly assigned to one of the two treatments or the role of being Observer (2 subjects per session, one female and one male). In treatment HardEasy, subjects work on the Hard part in Stage 1 and the Easy part in Stage 2. In treatment EasyHard, subjects complete the two parts in the reverse order, i.e. they first work on the Easy part and then the Hard one. Stage 1 establishes a within-subject reference point with respect to performance on the matrices. Since subjects know that their answers on the matrices reflect a measure of their IQ, their performance feedback (rank) is expected to be image relevant. We calculate a subject's rank as a percentile compared to a predetermined reference group (university students who answered the same matrices in a previous experiment). In both treatments, subjects solve Part 1, observe their Rank 1 and report it privately to the two observers (who can verify the report). In Stage 2, participants do Part 2 of the quiz. For subjects in treatment EasyHard, Part 2 is more complicated than Part 1. Thus, we expect them to perform worse on average than in Part 1, such that on average their rank decreases. For subjects in treatment HardEasy, on the contrary, the average rank increases compared to Rank 1. Construction of Rank 2 is based on exactly the same matrices (part Hard and Easy) for all subjects, so we do not expect any absolute difference between Ranks 2 in treatments HardEasy and EasyHard. After Part 2 is completed, the own Ranks 1 and 2 are displayed privately to each subject, so that subjects see whether they performed better or worse than in Part 1. The only expected difference is their reference points, i.e. Rank 1. Then we suggest subjects to throw a dice twice privately and report the numbers they got. The first reported number is added to the number of correctly solved matrices of each person in the reference group, the second reported number to their own number of correctly solved matrices (a scope for lying). Observers know about the existence of a further task in Stage 2, but not the exact nature of the dice rolls. Once the reported dice rolls are added and the Overall Rank is updated, participants go to Observers again and report their final ranks privately.
We test the following hypothesis: subjects in treatment EasyHard (who on average experience a loss in social image due to a worse Rank 2 than Rank 1) lie more than subjects in treatment HardEasy (who on average experience a gain in social image). The two treatments (HardEasy and EasyHard) differ only in the average reference points (Rank 1). Key outcomes are whether the individuals lie and to which extent, i.e. the average reported dice rolls for the reference group and oneself by treatment (HardEasy versus EasyHard). We investigate whether HardEasy and EasyHard subjects differ in the reported dice roll difference, conditional and unconditional on their individual reference points. In particular, we compare the average reported difference in dice roll reports (average reported number to be added to own performance minus average reported number to be added to reference group's performance) from treatments HardEasy and EasyHard. If this difference is significantly higher in treatment EasyHard than in treatment HardEasy, this provides evidence for loss aversion in social image concerns because it implies that subjects who risk losing social image are ready to lie more than those with social image gains. In several specifications, we additionally control for measures of subjects' risk aversion, loss aversion, social image concerns as well as various sociodemographic characteristics and their interactions with the main treatment variables.