Identifying Wisdom (of the Crowd): A Regression Approach

Experts in a population hold (a) beliefs over a state and (b) beliefs over the population’s belief distribution. If these are generated via Bayesian updating from a common prior using signal observations from a fixed information structure, a linear regression using the experts’ beliefs identifies the information structure, provided there are no more states than signals. Furthermore, an eigenvector equation derived from the experts’ beliefs identifies the prior. Thus, the ex ante informational environment (i.e., how signals are generated) can be determined using ex post data (i.e., the experts’ beliefs). I interpret these findings and also discuss identification when states outnumber signals.