Information Aggregation with Costly Information Acquisition

We study information aggregation in a dynamic trading model with partially informed traders. Ostrovsky [2012] showed that `separable' securities aggregate information in all equilibria, however, determining whether a security is separable requires knowing the exact information structure of agents. To remedy this problem, we allow traders to acquire signals with cost $\kappa$, in every period. We show that `$\kappa$ separable securities' characterize information aggregation and, as the cost decreases, almost all securities become $\kappa$ separable, irrespective of the traders' initial private information. Moreover, the switch to $\kappa$ separability happens not gradually but discontinuously, hence even a small decrease in costs can result in a security aggregating information. We provide a complete classification of securities in terms of how well they aggregate information, which surprisingly depends only on their payoff structure.