Experimental Design Details
We use an online, real-effort experiment to answer our research questions and test our hypotheses. We use the same task as the experiment run by Bushong, Rabin, and Schwartzstein (2021), which involves counting the number appearances of a specific character in a matrix of size 10x15.
We define a contract in the experiment as the combination of two attributes, the payment and a schedule to perform blocks of tasks at specific times of the day. Each block of ten tasks must be done at a specific time of the day. For example, a contract can specify a payment of $10 to do a total of 30 tasks tomorrow in three blocks of 10 tasks to be done at 10:30, 13:00 and 14:30, respectively. A higher number of tasks leads to a less flexible contract by involving a higher number of times at which the participant must perform the tasks. The design includes 7 different numbers of tasks, from 10 to 70 tasks.
We set up two stages in this experiment. The first stage of the experiment is to get participants’ reservation wages for different numbers of tasks/schedules. Before eliciting their responses, to allow participants to form a better understanding of the difficulty of the task, we offer participants a couple of trial tasks before they write down their reservation wages.
To ensure that participants give their truthful reservation wages, we implement the Becker–DeGroot–Marschak method (Becker, DeGroot, and Marshak; 1964). First, we ask participants to give their reservation wage for different numbers of matrices with their associated schedules. After that, a random number generator will generate a number of matrices M and an actual pay P. Their reservation wage R for M matrices will be compared to the actual pay. If P ≥ R , they will count M matrices at the specified schedule and receive P as their compensation. Par- ticipants must finish counting the matrices to receive any payment. If P < R, the participant will not perform any task and finish the experiment with only her participation fee.
The second stage of the experiment is to ask subjects to choose their favorite contract from various menus. We use the data on reservation wages from the first stage to construct contracts and menus. The second stage will be conducted within two weeks after the completion of the first stage experiment. We will randomly resample a smaller group of participants from the pool of participants in the first stage. Before randomly resampling, we may exclude some participants whose answers strongly suggest lack of comprehension, non-truthful responses or unwillingness to perform the tasks. Specifically, we may exclude participants that consistently report higher reservation wages for lower number of tasks or that report unusually high reservation wages relative to the distribution of reservation wages in the sample. Participants will not know about the possibility of being selected to the second stage unless they receive an invitation after the first stage is completed. The reason for doing so is to ensure that the incentive-compatible Becker–DeGroot–Marschak method works correctly and that participants report their truthful reservation wages in the first stage.
In the second stage, participants will start choosing contracts from menus after reading instructions. They will choose from around 30 to 40 menus. After choosing from all menus, one of the participant’s contract choices might be chosen at random and executed. Doing so ensures their decisions are all incentivized. Participants must finish the number of tasks dictated by the realized contract to receive any payment in the second stage.
To measure menu effects, each menu will contain 2 or 3 contracts, one of them (the optimal contract) with a wage higher than the reported reservation wage in stage one. Another contract (the suboptimal contract) will have a payment equal to its reservation wage. If there is a third contract it will either have also a payment equal to its reservation wage or lower. If a participant does not choose the optimal contract, we increase the markup on its payment above its reservation wage and continue to do so until the participant finally chooses the optimal contract. We then measure the size of the particular menu effect by the largest markup before the switch to the optimal contract happens.
The experiment involves three types of menu effects that introduce an inferior contract to an existing 2-contract menu: the attraction effect (adding a contract close to the suboptimal one); the compromise effect (adding a contract with the attributes in between the optimal and suboptimal contracts) and the similarity effect (adding a contract close to the optimal one).
We vary the application of markups so that sometimes the optimal contract involves lower wages and higher flexibility than the suboptimal ones and vice versa. This way we will identify potential asymmetries in menu effects within and across participants.
The order of presentation of menus will be random for each participant.
Becker, Gordon M, Morris H DeGroot, and Jacob Marschak (1964). “Measuring utility by a single-response sequential method”. In: Behavioral science 9.3, pp. 226–232.
Bushong, Benjamin, Matthew Rabin, and Joshua Schwartzstein (2021). “A model of relative thinking”. In: The Review of Economic Studies 88.1, pp. 162–191.