Experimental Design Details
See also the attachment.
The experiment consists of two parts that are one day apart in a stylized setting. Participants are required to complete ten unpleasant effort tasks in each session as mandatory work and to make a few valuation choices of these tasks on top. The particular effort task is to count the numbers of “0”s in a matrix that contains different numbers of “0”s and “1”s (e.g. Abeler et al., 2011). The decision state in each of the two parts is varied by the accumulated fatigue/tiredness from the tasks at different stages of mandatory work in that part, either at the beginning (good state, not tired) or at the end (bad state, tired).
The main choice variables of interest are participants' predicted tiredness (on a scale of 7) and willingness-to-accept (WTA) for one additional task either at the end of Part 1 or Part 2. These WTA choices for different time horizons, i.e. immediate choices or advance choices, will be elicited within-subject in one of the two states in each session:
• Choice 1 (immediate): WTA in Part 1 for an additional task in Part 1
• Choice 2 (advance): WTA in Part 1 for an additional task in Part 2
• Choice 3 (immediate): WTA in Part 2 for an additional task in Part 2
Each of these choices is described at the beginning of the corresponding session. To ensure incentive compatibility, these choices are implemented as bonuses in different sessions through a BDM mechanism, and the bonus will be paid out right after each session. Manipulation checks on perceived tiredness will be included before each choice.
At the end of Part 2, I will measure a few additional variables of interests, including actually perceived tiredness, beliefs about own task performance (average task completion time in seconds), memory (a binary indicator of whether one can correctly recall own advance choice two days ago), and the preferred decision state. Participants also fill in a short questionnaire that collects self-reported measures of time preferences, sophistication, daily behaviors related to time preferences, and other control variables (a self-reported measure of projection bias as the extent to which adaptation is underestimated, frequency of regret, risky attitude, general confidence level, and interpersonal empathy).
Depending on the treatment, each of the above WTA choices will be elicited in one of the two states (good state: after the first out of ten tasks; or bad state: after the ninth out of ten tasks). To ensure statistical power, the variation in Part 2 only happens at the beginning of Part 2, ensuring a balanced number of participants conditional on the decision state in Part 1.
• Treatment Good-Good: both Part 1 and Part 2 choices are elicited in a good state
• Treatment Good-Bad: Part 1 choices are elicited in a good state and Part 2 choices are elicited in a bad state
• Treatment Bad-Good: Part 1 choices are elicited in a bad state and Part 2 choices are elicited in a good state
• Treatment Bad-Bad: both Part 1 and Part 2 choices are elicited in a bad state
Note that the main outcomes of interests are Choice 1 and Choice 2 elicited in Part 1, where the variation in decision states is between-subject (Good vs. Bad) and the statistical power is the biggest. Choice 3, another immediate choice, will be elicited in Part 2, where half of the subjects in Good state treatment in Part 1 will be randomized into Bad state and the other half remains in Good state. The same procedure applies to those who are in Bad state treatment in Part 1.
Although this design effectively generates four treatment conditions ad hoc, the main comparison focuses on choices in good and bad states within each of the two parts for sake of statistical power. That is, when investigating state dependence in Part 1 (or in Part 2), observations will be pooled only based on the decision state in Part 1 (or in Part 2). More fine-grained comparisons conditional on the decision state in the other part will only be conducted if power permits.
Primary hypothesis: state dependence
Restrict attention to Part 1 choices. The main hypothesis about state-dependent preference misperceptions is that participants will predict themselves to be less tired and are thus willing to accept lower compensations for additional work in a good state than in a bad state. This concerns the comparison of both immediate choice and advance choice across decision states in Part 1.
Primary hypothesis: identification of time preferences
Restrict attention to Part 1 choices. As a result of state dependence, time preferences identified using advance choices made in different states will differ systematically. The ratio/difference of the advance choice (Choice 2) in good state and the immediate choice (Choice 1) in bad state will thus be smaller than the ratio/difference of the advance choice (Choice 2) in bad state and the immediate choice (Choice 1) in bad state.