Information Aggregation with Costly Information Acquisition

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