Theory of Mind in Learning to Forecast Experiments

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2021-09-10

2021-09-24

The independent variable ToM has levels 1) individual ToM score, 2) average ToM group score, and 3) categorization in top (=1), middle upper (=2), middle lower (=3), and bottom (=4). The main learning to forecast measurement (dependent variable) contains the deviation of prices from the rational expectation equilibrium measured by the relative absolute deviation (RAD) and the scale of price fluctuation, i.e. the amplitude of price. Further measures from the learning to forecast experiment literature will apply.

The dependent variables are taken from Hommes, C., Sonnemans, J., Tuinstra, J., & Velden, H. van de. (2005). Coordination of expectations in asset pricing experiments. Review of Financial Studies, 18(3), 955–980.

We test whether groups with higher ToM scores reduce price deviation from fundamental value, price amplitude, and standard deviations of price expectations.

In addition, we consider subjects characteristics as controls.

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We use a standard laboratory experiment.

Stage 1：We perform the ToM test (eye gaze test) on all subjects and divide them into top, middle upper, middle lower and bottom quartiles (for 24 people sessions) based on the ToM scores. Hence, each session has four groups.

Stage 2：We apply a learning-to-forecast experiment with six subjects in each group. The price determination functions are defined as follows p(t)=1/(1+r) (F(t) + d) + e(t), where p(t) is the realized period priced, d is the dividend of the asset, r is the risk-free interest rate, F(t) is the average price forecast for period t, and e(t)~N(0,1) is a small iid shock to the price. The rational expectations equilibrium (REE) of the economy is, therefore, p(t)=d/r. Find more information in Bao, T., Hommes, C., & Makarewicz, T. (2017). Bubble Formation and (In) Efficient Markets in Learning‐to‐forecast and optimise Experiments. The Economic Journal, 127(605), F581-F609.

Stage 3: We will collect background information about subjects. In addition, we perform numeracy and a CRT test to measure their cognitive ability used as controls.

Programming will take place in zTree.

Students are invited from a subject pool and randomly register for a session.

With the student group, we apply the ToM test to every person. We rank the 24 student subjects by their ToM score and cluster them in for cohorts. We then compare the forecasting behaviour of such groups (see analysis plan) as a standard approach considered in other experimental studies on the LtF environment. Hence, we consider a so-called quasi-experiment.

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In total, we consider six sessions with 24 subjects, i.e. six times four groups.

four group level observation for each session

6*24=144 student subjects

Considering a Wilcoxon signed-rank test with six observations (Diff=Top - Bottom=0) the minimum detectable effect size is 1.22 (assuming a power of 80% and significance levels of 5%. However, even doubling the sample size would yield 0.79.