Experimental Design
I analyze whether individuals react differently to gains and losses of their self-image: Are they more willing to avoid self-image-relevant information if they expect positive or negative updates about their self-image? I analyze whether subjects who expect positive feedback are more likely to acquire information than those who expect negative feedback.
My experimental setup includes three stages. In Stage 1, I elicit subjects’ prior beliefs about their performance in the upcoming intelligence test. I treat prior beliefs as a within-subject reference point in intelligence, a self-image-relevant domain. In Stage 2, I induce an exogenous shift in self-image. I put subjects’ self-image at either loss or gain by varying the task complexity. The second belief elicitation is necessary to see whether the treatment variation worked, i.e. whether subjects indeed expect losses and gains when I assume they do. I then ask subjects whether they are willing to acquire feedback about their performance and elicit willingness-to-pay/willingness-to-accept (WTP/WTA) to do so, as well as their beliefs about their performance. In Stage 3, I let subjects work on the remaining tasks and elicit their beliefs once again upon completion. First, I analyze whether belief updating is symmetric for those with gains and losses in self-image.
Additionally, I perform analyses both unconditionally and conditionally on belief updating. I test whether subjects who care about their self-image avoid ego-relevant feedback. Then, I analyze whether those who experience a loss in self-image are more willing to acquire feedback than those who experience gain. I also test whether subjects with marginal self-image losses have a disproportionately stronger willingness to acquire feedback than those with marginal gains in self-image.
IQ test
In this experiment, subjects work on Raven’s Progressive Matrices (RPMs), which are commonly used in experiments to measure fluid intelligence. They are picture puzzles with a missing piece. Among the available answers, subjects should choose the best logical fit to fill in the blank space. RPM tests commonly consist of five sets of matrices (A to E), with 12 matrices in each set. These sets progress in difficulty. Set A includes the easiest matrices; Set B is slightly harder, and so on. Set E contains the 12 hardest matrices. Based on the reference sample, which includes 413 observations (students) from a previous experiment (the same lab in 2014) who worked on a full set of the same RPM matrices, I expect student subjects would solve all the matrices in set A correctly. Hence, I will not use the 12 easiest matrices in this experiment. I will use 48 matrices from sets B to E.
Those 48 matrices are split into two parts: EASY and HARD. Matrices from sets B and C belong to the EASY part. Matrices from sets D and E form the HARD part. Both parts are progressive, i.e. they start with easy tasks and get more complicated over time. Matrices in the EASY and the HARD parts do not repeat or overlap. Subjects get one point if they solve a matrix correctly, and get zero points otherwise. Subjects have a time limit of 30 seconds per matrix, which ensures that their performance is comparable within the experiment as well as to the references sample where the same time limit was imposed.
Stage 1
After reading the instructions and answering control questions, subjects proceed to the first belief elicitation. I elicit their prior beliefs about their overall performance, i.e. a number of correctly solved matrices in both parts. By indicating the number of matrices they think they will solve correctly, they see the following phrase being autocompleted: “I think I will solve X out of 48 picture puzzles correctly. This means that I think I will perform better than Y% of previous participants”. I inform subjects that their performance is compared to the reference sample, which includes 413 observations (students) from a previous experiment (the same lab in 2014) who worked on a full set of the same RPM matrices. I incentivize the decision using the binarized scoring rule. Participants can earn one euro in each belief elicitation task. Importantly, with the binarized scoring rule, subjects still have a small probability to get paid for the belief elicitation task even if their guess and their actual performance differ a lot. Hence, their payoffs are not (directly) indicative of their performance.
I treat subjects’ prior beliefs about their performance in the IQ test as a within-subject reference point in intelligence. The procedure of belief elicitations is always the same. I always ask subjects about their beliefs about their overall performance. Payoffs of multiple belief elicitations are independent.
Stage 2
Subjects work on part 1 of the test. In treatment GAIN, part 1 is EASY, such that subjects, on average, solve more matrices than they expected and hence can expect positive feedback about their performance. In treatment LOSS, on the contrary, subjects work on HARD tasks, so they on average perform worse than expected. After participants complete 24 tasks in part 1, I elicit their beliefs again. Then, I elicit their willingness to pay to get feedback (which might be negative) using the Becker-DeGroot-Marschak mechanism.
Stage 3
Subjects work on the remaining 24 RPM tasks. It means that subjects from treatment GAIN work now on the HARD part, while those from treatment LOSS work on the EASY part. All participants in the experiment work on exactly the same 48 picture puzzles described above. Once subjects complete the task, I elicit beliefs about their performance again before they proceed to get (or not) their feedback. I display their feedback in the same format as belief elicitation, i.e. it says “You solved X out of 48 picture puzzles correctly. This means that you performed better than Y% of previous participants”.
Technical details
This experiment will be conducted online with subjects from the DICE Lab, University of Düsseldorf. Subjects receive a show-up fee of 3 Euro as well as a 5 Euro endowment at the beginning of the experiment which might be used for the feedback WTP/WTA. 5 Euro endowment assures that (a) in order to ensure (not) getting feedback, the stakes are rather high, but (b) subjects cannot make an absolute loss after their decision is realized. Additionally, subjects face three rounds of belief elicitations (in Stages 1, 2, and 3) which pay at most 1 Euro each. On top of that, some parts of the post-experimental questionnaire (namely, overconfidence and loss aversion elicitations) are also incentivized. Total earnings are only paid out upon completion of the experiment to prevent subjects from potentially dropping out.
Hypotheses
This experimental setup allows me to formally test the following hypotheses:
Hypothesis 1. (Willful ignorance) Individuals who care about their self-image may avoid feedback relevant to their self-image.
I analyze the share of subjects with negative willingness to pay to acquire feedback. I hypothesize that this share will be non-negligible.
Hypothesis 2. (Asymmetric belief updating) Individuals who care about their self-image may update their beliefs stronger if they experience an actual gain in a self-image relevant domain compared to an actual loss in a self-image relevant domain.
In line with motivated beliefs literature, I hypothesize that the absolute difference between prior beliefs and 1st posterior beliefs will be larger for subjects in GAIN than in LOSS.
Hypothesis 3. (Reference-dependence) Individuals who care about their self-image and on average expect the loss in their self-image are more willing to acquire information than those who on average expect the gain in their self-image of the same size.
Hypothesis 4. (Loss aversion) Individuals who care about their self-image and expect a marginal loss in their self-image are more willing to acquire information than those who expect a marginal gain in their self-image.
I will rely on Mann-Whitney U tests and regression analyses to test the hypotheses described above.