Projection Bias in Effort Choices

The main intervention consists in randomizing subjects in sessions 1 and 2 in such a way that they have a light workload in session 1 and a hard workload in session 2 (treatment 1) or a hard workload in session 1 and a light workload in session 2 (treatment 2).

2019-04-01

2020-02-29

The main outcome variable is the amount of tasks that subjects sign up for in session 3, as well as how much of this is predicted by the WTW at the end of session 2 based on the treatment they are in.

The main part of the design is a between-subjects design. Every participant who signs up will be asked to do tasks in 3 sessions. In all sessions, subjects have to do a given amount of required tasks. I randomize at the individual level whether subjects exert low effort in the first session and high effort in the second; or high effort in the first session and low in the second. Since the total amount of work is kept the same for all, this rules out the possibility that different choices over future work are driven by learning. However, if subjects who worked more in session 2 are more tired, then projection bias predicts that they will be less willing to accept to do extra work at the end of session 3. Therefore, at the end of session 2 I will elicit the willingness to work (WTW) more right away (at the end of session 2), as well as the WTW more in session 3. The degree to which the session 2 WTW predicts session 3 WTW gives a *direct* measure of the population-average projection bias.

I am planning on pooling the answers from the end of session 2 from the within-subjects design with the between-subjects design for purposes of statistical power. I will *not* however use the data from the end of session 1 in the between subjects analysis. This pooled dataset is my main data for the between subject design.

Secondary outcomes are the difference between WTW at the end of session 1 and 2 *withing* subjects. At the end of each of session 1 and 2, I elicit the WTW right now, as well as WTW in session 3.

Moreover, I ask questions to measure whether subjects project their own transient willingness onto others, and whether they project it onto their own past choices.

The secondary design adds to this baseline by asking subjects also at the end of session 1 for their WTW right away, and for their WTW in session 3. Together with the same answers at the end of session 2, this can be used to estimate the degree of projection bias at the individual-level. By asking these subjects to participate in the same experiment several months later, I will measure how stable projection bias is for a given individual.

In addition to these primary goals focused on simple projection bias, I will ask several questions at the end of session 2 and session 3 to test whether subjects mispredict others' preferences; and whether they make mistakes in remembering their own choices based on how they currently feel about such past choices.

The real effort task I refer to in the description below is a task that consists in counting how often a given character appears in a matrix that contains different characters.

The baseline design consists of a sign-up session, three main sessions, and a final debriefing survey. In the sign-up session I get subjects’ consent to participate; I describe the study, the type of task they will be asked to complete, and the choices they will be asked to make; and I test their comprehension. Those subjects that pass the comprehension test can enroll in the study, the others are excluded.

Moving on to the experiment, the main part of the design is a between-subjects design. Every participant who signs up will be asked to do tasks in 3 sessions. They will do additional tasks in session 1 and 2, as well as choose how much extra work to do in those sessions as well as in the final session.

In session 3, subjects complete the work they signed up for and then complete the debrief survey.

The real effort task I refer to in the description below is a task that consists in counting how often a given character appears in a matrix that contains different characters. The tasks are chosen such that subjects in the pilot take roughly 45-70 seconds to complete one task.

The baseline design consists of a sign-up session, three main sessions, and a final debriefing survey. In the sign-up session I get subjects’ consent to participate; I describe the study, the type of task they will be asked to complete, and the choices they will be asked to make; and I test their comprehension. Those subjects that pass the comprehension test can enroll in the study, the others are excluded.

Moving on to the experiment, the main part of the design is a between-subjects design. Every participant who signs up will be asked to do tasks in 3 sessions. In all sessions, subjects have to do a given amount of required tasks. I randomize at the individual level whether subjects exert low effort in the first session and high effort in the second; or high effort in the first session and low in the second. Since the total amount of work is kept the same for all, this rules out the possibility that different choices over future work are driven by learning. However, if subjects who worked more in session 2 are more tired, then projection bias predicts that they will be less willing to accept to do extra work at the end of session 3. Therefore, at the end of session 2 I will elicit the willingness to work (WTW) more right away (at the end of session 2), as well as the WTW more in session 3. The degree to which the session 2 WTW predicts session 3 WTW gives a *direct* measure of the population-average projection bias.

In session 3, subjects complete the work they signed up for and then complete the debrief survey.

I will run the following:

1. Pilot:
- I elicit the WTW after subjects have done 10, 40, and 70 tasks
- I test the following 3 methods of eliciting WTW, see below.


Elicitation methods that I test in the Pilot:

1. Price list where the number of tasks are fixed and the payments varied
2. Multiple piece-rates for the task, and subjects state the number of tasks they are willing to do (Augenblick and Rabin (2018))
3. Subjects report directly the smallest payment for which they are willing to do a fixed amount of work

Based on the pilot, I will choose the most precise elicitation method and choose the effort level in order to maximize the power of test. One of the identifying assumptions is that people's WTW fluctuates as they do more work. If this is not the case, then projection bias predicts the same as no projection bias. I randomize subjects in a 3 x 3 design, so that 15 subjects belong to each of the 9 possible subgroups.

Randomization by computer, at the time subjects enroll for the main study.

Individual-level randomization

No

One for the pilot (one batch)

The remaining will be done in batches of 9, given how Amazon MTurk charges for larger batches (unless policies change).

200 individuals recruited on MTurk

Pilot: 145 subjects, randomizing 3x3, i.e. 15 in each subgroup

The following are estimates, since I will base the number of tasks on the results of the pilot, which will give an idea over the statistical power I will have and (given my fixed budget) allow me to compute the sample size.

Between subjects design: 100 in total, 50 in each subgroup (high effort first vs low effort first)
Within subjects design: 200 in total, 100 per subgroup (high effort first vs low effort first)

Repetition a few months later: Randomly chosen half from the 'within-subjects' group - that is, another 100

I will defer this computation until after having run the pilot, as there is no point in guessing the population standard deviation for this task, nor of the change in WTW that is directly proportional to the treatment size (not to the effect size - which is about the size of projection bias itself).