'Irrational Inattention'
(AsPredicted #154,320)
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1) Have any data been collected for this study already?
No, no data have been collected for this study yet.

2) What's the main question being asked or hypothesis being tested in this study?
Do individuals fail to incorporate information due to overprecision and/or rational inattention? Do rational inattention and overprecision reinforce each other when forming posterior beliefs?

3) Describe the key dependent variable(s) specifying how they will be measured.
The key dependent variables of this experiment are the prior and posterior beliefs of respondent i. These variables are the estimates of the average age of a group of people in a picture provided before and after receiving information. From those two variables, we then can construct the change in belief of respondent i after receiving information.

There are 10 predetermined pictures (k∈[1,10]) in two sets with five pictures each. For the first set, we only measure prior beliefs, while for the second set, we measure both prior and posterior beliefs. Both variables are elicited using point estimates provided by the respondents. The pictures within each set are shown in a random order.

4) How many and which conditions will participants be assigned to?
Our design has four experimental conditions (2x2 design). There will be an information treatment and an overprecision treatment. In the overprecision treatment, respondents receive feedback on their performance in terms of how well their beliefs are calibrated after the first set of five pictures. We expect this treatment to exogenously vary overprecision for the next set of five pictures. Since this treatment will result in two different feedback messages (positive/negative message), depending on the respondents' calibration in the first five pictures, this treatment will result in a categorical treatment indicator (treatment_op) capturing the three treatment conditions ((a) no, (b) negative, and (c) positive feedback). In the information treatment, the groups differ in the form of information they receive in the second set of five pictures. Both groups are shown a word cloud containing a random draw of ages in the picture (informative bits) along with unrelated information (words; non-informative bits). One group receives a larger number of non-informative bits while keeping the informativeness of the signal constant. This results in a second binary treatment indicator (treatment_info).

Participants are randomly assigned to one of the two conditions with 2/3 chance to end up in the overprecision treatment condition (i.e., performance feedback) and a 1/2 chance to end up in the information treatment condition. We have a between-subject design.

5) Specify exactly which analyses you will conduct to examine the main question/hypothesis.
To assess the effects of overprecision and information processing costs (=rational inattention) on how subjects update their beliefs in the pictures k∈{6,7,8,9,10}, we will empirically estimate the effects of the two distinct treatments as well as their interaction in a belief updating framework following Coibion et al. (2018) or Fuster et al. (2019).

The dependent variable is either the posterior belief of respondent i for picture k (〖posterior〗_(i,k)) and the change in beliefs (i.e. 〖posterior〗_(i,k)-〖prior〗_(i,k)). On the right-hand side, I{i∈treatment_info} is an indicator variable that is one if the participant is in the higher processing cost treatment group, I{i∈treatment_op} is an indicator variable that captures the overprecision treatment (0 if no feedback, 1 if negative feedback, 2 if positive feedback). All of these are interacted with either (〖prior〗_(i,k)), which denotes the prior of respondent i for picture k, or the difference between the prior belief of respondent i in round k and the signal (〖signal〗_(i,k)-〖prior〗_(i,k)).

We estimate the model both excluding and including a vector of controls composed of age, gender, highest attained degree, income, nationality, regional fixed effects, screen size, and an indicator variable that asks for the difficulty of the pictures.

We will estimate the effects in each of the k pictures separately and in a pooled version including picture fixed effects. Given that our main hypotheses are directional, we will base the analysis on one-tailed t-tests.

6) Describe exactly how outliers will be defined and handled, and your precise rule(s) for excluding observations.
Among all respondents who completed the survey, we exclude observations in which a respondent gave a subjective error larger than the distance between the prior and either 0 or 100 (pre-specified bounds of the answers), whichever is larger, in at least one of the 10 rounds. We will drop the respondent completely if we observe this behavior more than once.

We will also drop any observation in which a respondent gives at least one answer that is above 80 years or below 20 years. We will drop the respondent completely if we observe this behavior more than once.

We will further drop responders whom we identify as speeders. We define speeders as respondents who are faster than 25% of the respective median time consistently across more than 50% of the prior estimates if this time is less than 10 seconds.

As a robustness test, we trim respondents' answers to both posterior and prior according to i) the minimum and maximum age in a picture, ii) the distance from the median response (>/< three standard deviations), and iii) the 1st and 99th percentile.

7) How many observations will be collected or what will determine sample size?
No need to justify decision, but be precise about exactly how the number will be determined.
This experiment is administered by Bilendi to a representative population of the German population. We require 1.200 respondents with complete answers.

8) Anything else you would like to pre-register?
(e.g., secondary analyses, variables collected for exploratory purposes, unusual analyses planned?)
We will test whether the overprecision treatment increases (decreases) overprecision, depending on whether the feedback is positive (negative), using a measure of overprecision before and after the overprecision treatment in a Diff-in-Diff style analysis. We measure overprecision using the Subjective Error Method (Bosch-Rosa et al., 2021). We will perform this analysis independently in the two feedback groups (positive/negative) using a one-tailed t-test.

Furthermore, we will explore the time spent on information as one channel for the observed effects in the main analysis.

Additionally, we elicit further self-reported variables on the answering behavior and general feedback of respondents at the end of the survey to get a better idea of the data.