Cognitive Noise in Belief Formation

I conduct a laboratory experiment using the subject pool of the BonnEconLab at the University of Bonn. Due to the COVID-19 crisis, the experiment will be conducted online.

See the experimental design for details.

2021-05-17

2021-06-30

Noise in decision-making

Noise is measured by the distance between the Bayesian forecast and the subject’s stated forecast.

For each subject, the computerized experiment consists of two blocks, each containing eight subsequent trials. The computer presents the blocks to the subject in random order. On each trial, a value of x is chosen from a known prior distribution. This prior distribution is the same across the 16 trials (and is the same across blocks). The computer then draws a random observation y1 from a normal distribution with mean x and variance s^2. The variance s^2 is the same for all eight trials in a block but different across blocks. The subject is shown the value of y1 and has to forecast what the NEXT independent draw y2 from that same distribution (with mean x) will be. They make their forecast, then the second draw occurs. The subject receives a score, which depends on the squared distance between a subject’s forecast and the outcome of the second independent draw. The closer the subject’s forecast is to the actual outcome y2, the higher the score. Then, for the subsequent trial, a new value of x is drawn from the same prior distribution, and the whole procedure is repeated.

I adopt a within-subject design with two blocks that are presented to the subject in random order:

a) Block "Low Variance":

The variance of the random variables y1 and y2 is set to s^2=40,000, implying a standard deviation of s=200.

b) Block "High Variance":

The variance of the random variables y1 and y2 is set to s^2=360,000, implying a standard deviation of s=600.

The computer randomly determines a) the order in which the two blocks appear; and b) which series of stochastic realizations subjects face. Half of the subjects face the same series of stochastic realizations since this allows cross-sectional comparison. The other half faces different, randomly selected series of stochastic realizations.

Order of the blocks within subjects
Series of stochastic outcomes that subjects will face

No

N/A

140 subjects completing the experiment; 16 observations per subject

70 out of 140 subjects face the low variance block first, while the other 70 subjects first face the high variance block.
70 out of 140 subjects face the same series of stochastic realizations for the purpose of comparability (so 35 of these subjects face the low variance block first; the other 35 subjects face the high variance block first). The other 70 subjects face different series of stochastic realizations (again, 35 of these subjects face the low variance block first; the other 35 subjects face the high variance block first).

The sample size allows detecting medium-sized effects (Cohen’s d = 0.5) at a power of 80%.