## 1 Introduction

^{1}

## 2 Experimental setting

^{2}The market price depends exclusively and explicitly on the one-step-ahead predictions of the subjects and it is independent of the longer horizon predictions. Based on that difference, we decide to label the one-step-ahead predictions as short-run predictions, and for all the other predictions we employ the label “long-run” predictions.

### 2.1 Treatments

^{3}: periods 1-10 and 11-20 with a turning point at period 10. In the P(T) treatment the fundamental value linearly increases (decreases) until period 10, while it linearly decreases (increases) afterward. For each different pattern of the fundamental value, we consider both positive and negative feedback treatments to evaluate the effect of the feedback system on expectation formation. The feedback system is labeled by the subscript \({}_P\) for the positive and \({}_N\) for the negative system. We end up with the following eight treatments: \(B_P\) (\(B_N\)) baseline with positive (negative) feedback, \(I_P\) (\(I_N\)) increasing with positive (negative) feedback, \(P_P\) (\(P_N\)) peak with positive (negative) feedback, \(T_P\) (\(T_N\)) trough with positive (negative) feedback.

### 2.2 Information

### 2.3 Procedures

### 2.4 Expectations feedback and the fundamental value

^{4}the market price in period t depends negatively on the average short-run price predictions so that, the higher the predictions, the lower the market price:

^{5}

### 2.5 Earnings

^{6}Note that, while subjects receive immediate feedback on the forecasting errors of their short-run predictions, they experience some delay in evaluating the accuracy of their long-run predictions. Thus, we provide them with the Earnings Table to facilitate the evaluation of their long-run forecasting accuracy (see Table 3 in the Appendix). The individual earnings per period are \(\pi _{it}=\pi ^s_{it}+\pi ^l_{it}\). A subject’s total earnings are the sum of earnings across all periods, i.e., \(\Pi _{i}=\sum _{t=1}^{20}\pi _{it}\).

## 3 Conjectures

### 3.1 Coordination and convergence of predictions

^{7}Whereas subjects quickly coordinate their short-run predictions on the market price, they strongly disagree on their predictions on the future price trajectory. This result suggests that subjects’ disagreement markedly increases with the horizon. Conversely, in the negative feedback system, they report a strong connection between coordination and convergence: once the market price converges to the fundamental value, there is simultaneous coordination of short- and long-run predictions. In this case, the subjects’ disagreement mildly depends on the horizon.

### 3.2 The term structure of cross-sectional dispersion of predictions

^{8}As typically detected in the literature, subjects are backward-looking in forming their expectations. Therefore, let us introduce the idea that the longer the forecasting horizon, the longer the past price history included in the formation of subjects’ expectations. In particular, we consider the linear extrapolation forecasting rule, where the extrapolation coefficient is the average of the past h price increments, where h stands for the price “history”. The parameter h depends on the subject, i.e., \({}_ih\). Formally, the expectations formation rule is given by:

B | I | P | T | |||
---|---|---|---|---|---|---|

Positive feedback | \(\alpha >1\) | \(\alpha >1\) | \(\underline{\alpha }>1\) | \(\overline{\alpha }\approx \underline{\alpha }>1\) | \(\underline{\alpha }>1\) | \(\overline{\alpha }\approx \underline{\alpha }>1\) |

Negative feedback | \(0<\alpha <1\) | \(0<\alpha <1\) | \(0<\underline{\alpha }<1\) | \(0<\underline{\alpha }<1<\overline{\alpha }<2\) | \(0<\underline{\alpha }<1\) | \(0<\underline{\alpha }<1<\overline{\alpha }<2\) |

## 4 Results

### 4.1 Coordination and convergence of short-run predictions and prices

^{9}

^{10}In the positive feedback markets, Fig. 4 shows that individual predictions coordinate around the last realized price after a few periods in all treatments. On the contrary, in negative feedback markets, short-run predictions need approximately 10 periods to coordinate, as shown in Fig. 5. Even though we consider a time-varying fundamental value, results in terms of coordination of short-run predictions are in line with the existing literature (see Heemeijer et al. 2009; Colasante et al. 2018). Conjecture 1 and Conjecture 2 find support in the experimental evidence.

### 4.2 The term structure of the cross-sectional dispersion of subjects’ predictions

B | I | P [3-10] | P [11-116] | T [3-10] | T [11-16] | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Positive | 1.42 | (0.08) | 1.79 | (0.10) | 1.14 | (0.08) | 1.54 | (0.16) | 1.20 | (0.19) | 0.92 | (0.11) |

Obs. | 75 | 75 | 40 | 30 | 40 | 30 | ||||||

\(R^{2}\) | 0.79 | 0.83 | 0.86 | 0.74 | 0.54 | 0.95 | ||||||

Negative | 0.62 | (0.07) | 0.17 | (0.10) | 0.65 | (0.06) | 1.48 | (0.19) | 0.92 | (0.06) | 1.61 | (0.11) |

Obs. | 75 | 75 | 40 | 30 | 40 | 30 | ||||||

\(R^{2}\) | 0.52 | 0.04 | 0.76 | 0.72 | 0.87 | 0.90 |

^{11}in \({}_ih\). Therefore, the term structure significantly changes its shape, reflecting the variability of \({}_ih\) and the corresponding variability of the estimated trend across subjects.