Experimental Design Details
I. Workers' experimental design
In the first stage, the worker starts by performing a knowledge test for which she is incentivized to answer correctly as many questions as possible; she then is incentivized to report beliefs about her absolute and relative performance. In the second stage, the worker is only informed about whether she fails or succeeds at the test, i.e., whether her final output in the previous task is ranked or not in a specific percentile. The novel aspect of our design is that the worker is truthfully informed that her final output depends on two elements: an internal one, which is the actual own ability to answer the knowledge test (i.e., the number of correct answers), and an external one, which is a component of luck (i.e., the performance of another player that previously performed the same knowledge task or a random number added by the computer). The worker knows that her final output is the average between her own true performance and the performance of another participant who previously performed the knowledge quiz (or the random number). A failure or success depends on whether this average is ranked or not in a specific percentile that is revealed to them. Our definition of success (failure) is based on a comparison to a group of selected participants who have already completed the knowledge quiz, with success defined as being ranked in the top 50% and failure as being ranked in the bottom 50%. However, we acknowledge that we may define a different cutoff value for defining success and failure to explore the effects of using different cutoff values on behavior.
For the worker, we use a 2x2 treatment between-subjects design. The first treatment variation consists of varying the source of the noise (i.e., the performance of the other matched player or the random number chosen by the computer). The second treatment variation consists in whether the distribution of responsibility points is displayed or not to the Employer and has payoff consequences. We will ensure there is no possibility for hedging by randomizing the payment across different parts of the experiment.
A. Treatment Baseline -Private
In this treatment, the worker's final output in the knowledge quiz is obtained as the average between her own true performance and the performance of another participant who previously performed the knowledge quiz. Furthermore, the message generated by the worker's distribution of responsibility points for her failure or success will not be displayed to the Employer or any other player.
B. Treatment Strategic - Other player
In this treatment, the worker's final output in the knowledge quiz is obtained as the average between her own true performance and the performance of another participant who previously performed the knowledge quiz. In contrast to the baseline treatment, the message generated by the distribution of responsibility points of failure or success is a signal that will be sent to another player who is randomly matched with her, the Employer. The worker is aware of this before providing distributing responsibility points between herself and the other player. Based on the generated message, the Employer decides whether to hire or not the worker. The worker receives a high bonus if the Employer hires her, and a low bonus otherwise. The Employer obtains a medium bonus if he does not hire the worker. If the Employer hires the worker, he receives a low bonus if the worker's true performance is not ranked in the top 50% and a high bonus if her true performance is ranked in the top 50%.
C. Treatment Strategic - Computer
This treatment is identical to the Treatment strategic - Other player, but the only difference is that the worker's final output in the knowledge quiz is obtained as the average between her own true performance and a random number generated by the computer.
The introduction of this noise on true performance allows for motivated beliefs to emerge (e.g., falsely attributing failure to bad luck/success to own or others’ ability). In the third stage, we aim to capture these beliefs in the form of taking or not taking “responsibility” for failure or success. That is, the worker is asked to justify why she thinks she failed or succeeded at the test. For doing so, the worker has to distribute responsibility points for her failure or success to her own ability and/or to the performance of the other matched player (or to the random number chosen by the computer). The chosen distribution of responsibility points will generate a justification message that will be displayed to the Employer.
II. Employer experimental design
The employer will make a series of hiring decisions and a final follow-up questionnaire. First, he is familiarized with the general knowledge quiz the workers performed. Afterward, the employer makes a series of hiring decisions after observing whether the worker's outcome is ranked or not in the top 50% and the message generated by the distribution of responsibility points of failure or success that the worker made. The payoffs are identical to the ones described in Treatment Strategic -Other player.
In each of the hiring decisions, the Employer must decide whether to hire a worker or not. After the Employer makes all hiring decisions, one decision is selected at random as the decision that counts for his payoffs.