This is an experiment about how people aggregate forecasts from multiple stock analysts to estimate the average return from a stock. First, there will be 10 practice periods. These 10 periods will not be used in calculating your income from this experiment, and you can use them to understand the experimental setup better. They will be followed by 10 paid periods, which will be used in calculating your income.
In each period, you will receive earning forecasts from two stock analysts regarding the earning per share (EPS) for the stocks of a company. In every period, the information will be provided for a new company. Thus, the EPS in each period is independent of each other. In each period, your goal is to predict the true value of the EPS for that period’s stock based on the information you receive.
For each stock, the true EPS, \(T\), is drawn from a normal distribution with mean 1,000 and variance 10,000. We refer to this as the prior distribution of \(T\). You will also observe forecasts from two stock analysts. Forecast of analyst 1, \(X_1\), equals \(T\) plus an error term \(\varepsilon_1\). That is, \(X_1=T+\varepsilon_1\) where \(\varepsilon_1\) is drawn from a normal distribution with mean 0 and variance \(\sigma_1^2\). Forecast of analyst 2, \(X_2\), equals \(\alpha X_1 + (1 - \alpha) T\) plus an error term \(\varepsilon_2\). That is, \(X_2=\alpha X_1 + (1 - \alpha) T + \varepsilon_2\) where \(\varepsilon_2\) is drawn from a normal distribution with mean 0 and variance \(\sigma_2^2\). Moreover, \(\varepsilon_1\) and \(\varepsilon_2\) are drawn independently of each other. Values of \(\alpha\), \(\sigma_1^2\) and \(\sigma_2^2\) may be different across periods, and you will be informed of those values in each period.
In every period, first you will be informed of the exact way forecasts \(X_1\) and \(X_2\) are generated in that period. Then, you will receive the two forecasts and will be asked to enter your prediction for the true EPS. In each of the paid period, you will earn a reward of $3 with a probability that will depend on your prediction \((P)\) and the true EPS \((T)\). Moreover, the closer your prediction is to the true EPS, the greater would be the probability of earning the $3 reward. This scheme is designed in a way such that the probability of earning the $3 reward is maximized if you report what you believe the true EPS is, on average, based on the two forecasts you receive and the prior distribution of \(T\), as your prediction.
After each of the 10 practice periods, you will be informed of the true EPS for the stock and the probability that you would have earned $3 based on your prediction if it were a paid round. For the 10 paid periods, you will be informed of the true EPS from each period and whether you had won the $3 reward in that period at the end of all the paid periods.
If you complete the experiment, your income will be the sum of your earnings from the 10 paid periods plus the participation fee of $5. You will be paid by bank transfer within 3 business days of your participation.