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Heuristic Switching Model and Exploration-Exploitation Algorithm to Describe Long-Run Expectations in LtFEs: a Comparison

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Abstract

We elicit individual expectations in a series of Learning-to-Forecast Experiments (LtFEs) with different feedback mechanisms between expectations and market price: positive and negative feedback markets. We implement the EEA proposed by Colasante et al. (J Evol Econ 2018b. https://doi.org/10.1007/S00191-018-0585-1). We compare the performance of two learning algorithms in replicating individual short and long-run expectations: the Exploration-Exploitation Algorithm (EEA) and the Heuristic Switching Model (HSM). Moreover, we modify the existing version of the HSM in order to incorporate the long run predictions. Although the two algorithms provide a fairly good description of prices in the short run, the EEA outperforms the HSM in replicating the main characteristics of individual expectation in the long-run, both in terms of coordination of individual expectations and convergence of expectations to the fundamental value.

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Notes

  1. To avoid the effects of communication among subjects between sessions, two different values for \(p_f\) are implemented, so that there are some markets with a fundamental value equal to 65 and others with a fundamental value equal to 70. In the positive feedback treatment, the fundamental value is computed as \(p_f= \frac{d}{r}\), where the average dividend d is equal to 3.5 or 3.25, depending on the session.

  2. The parameters of the payoff functions are calibrated such that approximately \(\max \sum _{t=1}^{20} {}_i\pi ^{s}_{t} = \max \sum _{t=1}^{20} {}_i\pi ^{l}_{t}\), in order to give to subjects the same incentives to provide accurate predictions in the short as well as in the long run.

  3. For a detailed description of the rules, their meaning and performances, we refer the reader to the pertinent literature.

  4. Note that, if we exclude the peculiarity of the first period, the empirical data on long-run predictions always lie in that interval.

  5. Note that we eliminate the restriction on the parameter w in Eq. (8) so that it can take any real value. We obtain a parameter for each rule and each subject separately.

  6. We have eliminated the estimates of six subjects because the estimated values of \({}_i\phi _s\) are out of range due to an error in typing their predictions, two in the positive feedback and four in the negative treatment.

  7. In the EEA, homogeneous rational expectations are implemented by setting the mean of the probability distribution of each agent (i.e, \(\mu _i\)) equal to the fundamental value in the center of the range of actions. They then set \(\phi =0\) and replace \(p_{t-1}\) with the fundamental value.

  8. Note that we dot perform the same exercise for short-run predictions since the range of the distribution is given by the standard deviation of the market price, and we cannot compute a variable range if we include the fundamental value as an anchor.

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Acknowledgements

The authors are grateful for funding the Universitat Jaume I under the Project UJI-B2018-77, the Generalitat Valenciana for the financial support under the Project AICO/2018/036 and the Ministerio de Cienecias Inovación y Universidades under the Project RTI2018-096927-B-I00.

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Correspondence to Annarita Colasante.

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Appendix

See Fig. 20.

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Colasante, A., Alfarano, S. & Camacho-Cuena, E. Heuristic Switching Model and Exploration-Exploitation Algorithm to Describe Long-Run Expectations in LtFEs: a Comparison. Comput Econ 56, 623–658 (2020). https://doi.org/10.1007/s10614-019-09951-6

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