  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, separability is not robust to small
changes in the traders' private information. To remedy this problem, we enhance
the model by allowing traders to acquire signals with cost $\kappa$, in every
period. We show that '$\kappa$ separable securities' aggregate information and,
as the cost decreases, nearly 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.
Finally, even with myopic traders, cheaper information may accelerate or
decelerate information aggregation for all but Arrow-Debreu securities.
