Effort and Risk Taking under Performance Thresholds

2021-04-13

2021-06-13

The change in effort and risk taking behaviour after the introduction of the threshold.

N/A

We will test our hypotheses using an online experiment:

There are 20 rounds in the experiment. In each round, participants make a choice on how many matrix tasks (between 0 and 100) to solve at the end of the experiment (“Effort Choice”). The matrix task consists in counting the numbers of zeroes in 10*10 binary matrices. At the end of the experiment one round is randomly selected and participants have to solve and are paid for the number of matrices chosen in that round.

- In Round 1, participants make one effort choice. They are paid 0.1 GBP per correctly solved matrix.
- In Rounds 2-5, participants again make an effort choice in each round, but now a threshold is introduced. Participants’ payments are increased by a fixed amount once they exceed a threshold level. The threshold varies in each round.
- In Rounds 6-8, participants again make an effort choice in each round. There is no threshold, but participants can choose whether to be paid a fixed amount (“No Risk”) or be paid according to a binary lottery (“Risk”). Payoff parameters vary creating three different risk decisions.
- Rounds 9-20 feature a threshold and risk combining the four different thresholds with the three different risk decisions across the 12 rounds.
- Afterwards we elicit some demographics from participants (age, gender, social class, education, ethnicity, self-reported math-skill, ambition and willingness to take risks).
- At the end of the experiment participants solve the number of tasks and are paid only if all tasks are solved according to the randomly selected round.

The design is within subjects. The order of tasks is randomized by the software (Qualtrics).

Subjects

No

Subjects

At least 500 subjects and up to the number that ensures 200 Round 1 choices between 40 and 80 (see below).

500+ subjects, within subject treatment variation. Each subject answers 6 questions with high thresholds and 6 with low thresholds, implying 3000+ (non-independent) observations of high thresholds and 3000+ (non-independent) observations of low thresholds.

Main test: We are interested in testing whether different thresholds trigger different effort provision and risk taking. To do so, for the main test we define two kinds of threshold for each participant, based on the participant’s baseline effort provision: low thresholds and high thresholds. We will restrict the analysis to people who in Round 1 provided effort between 40 and 80. For this subsample, we will define: - Low threshold: The thresholds of 20 and 40 tasks. - High threshold: The thresholds of 80 and 100 tasks. Test 1: We regress \Delta Effort, defined as the difference between effort choices in Rounds 9-20 and corresponding choices in Rounds 6-8, on dummy variables indicating whether the threshold is low or high. Controls will be gender, age, social class, ethnicity, and education. Standard errors will be clustered at the participant level. Test 2: We regress \Delta Risk, defined as the difference between risk choices in Rounds 9-20 and corresponding choices in Rounds 6-8, on dummy variables indicating whether the threshold is low or high. Controls will be gender, age, social class, ethnicity, and education. Standard errors will be clustered at the participant level. We performed a power analysis using a pilot with 34 participants. To do so, we performed simulations in which we bootstrapped the sample and assigned treatments (thresholds) randomly (code available upon request). We conclude that with a sample of 500 participants, we expect around 200 participants with Round 1 choices between 40 and 80 and in this case we have 80% power to detect at the 5% level an effect of high thresholds on effort of 2.5 tasks and on risk of 7 percentage points. Secondary tests: To more closely test the model, we will define four types of thresholds: - the low threshold to be the highest threshold weakly below the participant’s effort choice in the corresponding Round 6-8, - the high threshold to be the lowest threshold strictly above the participant’s effort choice in the corresponding Round 6-8, - the very high threshold to be any threshold at least 21 units but less than 40 units above the participant’s effort choice in the corresponding Round 6-8 and - the extremely high threshold to be any threshold at least 41 units above the participant’s effort choice in the corresponding Round 6-8. Note that any of these might be missing for some participants. Note also that we do not define very low and extremely low thresholds as we do not expect behavioural differences between those types of thresholds. We will run the same regressions as defined above using these four thresholds and study to what extent they are in line with the model. Tertiary tests: - We are interested in exploring heterogeneity by other background variables, and in particular gender. - We are interested in comparing effort choices in R2-5 with R1 depending on the difficulty of the threshold.