Information Aggregation with Costly Information Acquisition

TL;DR

This paper examines how costly information acquisition influences the aggregation of information in dynamic trading, revealing that lower costs lead to widespread information aggregation across securities.

Contribution

It introduces the concept of `κ separable securities' to characterize information aggregation and shows the discontinuous transition as acquisition costs decrease.

Findings

Almost all securities become κ separable as costs decrease.

The transition to κ separability is discontinuous, not gradual.

Security classification depends solely on payoff structure.

Abstract

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.