Complexity and Under-vs. Overreaction in Expectation Formation

In a between-subjects design, subjects are randomly assigned to either a simple or complex information treatment. In the simple treatment, subjects observe past values of variable A, and are asked to predict future values of A. In the complex treatment, subjects observe past values of A and an additional variable B, and are asked to predict future values of A.

In our secondary intervention, we vary the persistence of A (as well as B in the complex treatment), and the informativeness of B in predicting A (in the complex for treatment).

2019-05-22

2019-08-31

Subjects’ one-step-ahead forecasts of the future realizations of variable A.

By using the forecasts made by subjects, we will construct the following variables:
• Forecast accuracy (captured by the scores earned in the experiment);
• Over- and underreaction to (i) variable A; (ii) variable B; and (iii) overall reaction level to both variables;
• Perceived persistence and correlation levels of subjects.

Subjects’ response times for each forecast

Response time can be used as a proxy for cognitive effort as well as complexity.

In the experiment, subjects observe the past realizations of a time-series variable (named “A”) and predict its future values. There are two types of informational treatments. In the simple treatment, A follows an AR (1), and subjects observe past values of A. In the complex treatment, subjects additionally observe a leading indicator, named “B,” with A and B jointly generated by a bivariate VAR (1). The VAR (1) process is parametrized so that the predictability and persistence of A both remain fixed across the two treatments.

A key feature of the experimental design is that we keep the predictability of A constant across all treatments. In other words, by incorporating all the available information, a rational agent would make equally accurate predictions in both simple and complex treatments.

Besides the complexity of information, we also vary the persistence of A (and B, they are always equal in our design) and the correlation between A and B. This allows us to study how the effect of information complexity depends on the informativeness of each variable.

In total there are six treatments, two simple treatments and four complex. In the two simple treatments, the persistence of A is either low or high. In the four complex treatments, the persistence of A, and the correlation between A and B, is either low or high.

In the experiment, subjects first observe the initial 40 realizations of A (and B if applicable). They are asked to forecast the next realization of variable A for 40 rounds. They make one prediction at a time. After they make one prediction, they are shown the actual realization of A (as well as B in complex treatments) for that round. After they make all 40 predictions, they finish the experiment by completing a questionnaire.

We incentivize the subjects with a base payment $1.00 and a bonus payment. The bonus payment depends on the subject’s prediction accuracy. The exact formula for the accuracy score is 100*max {0, 1 - |D|/10}, where D is the difference between the actual value and the prediction. In each round, subjects earn a score according to this formula. In the end, subjects are paid with bonus $1.00 plus (total earned points of 40 rounds)/500. A subject can only receive this payment after completing the entire experiment.

Block randomization with a pseudo-random random number generator. As we have six treatment arms in total, we randomize in blocks of six.

Individual-level randomization

No

We aim to collect about 150-170 subjects in each of the 6 treatment arms.

About 1000 subjects, recruited via Amazon Mechanical Turk.

150-170 subjects per treatment arm.

Analysis Plan for “Complexity and Under- vs. Overreaction in Expectation Formation”