Persuading Large Investors

A regulator who designs a public stress test to elicit private investment in a distressed bank must account for large investors' private information on the bank's state. We provide conditions for crowding-in (crowding-out) so that the regulator offers more (less) information to better-informed investors. Crowding-in obtains if investors' private information is not too discriminating of the state. We show that the region of the common prior is consequential: if crowding-in occurs for ex-ante optimistic investors then crowding-out follows if they were instead pessimistic. Investors' value from more precise private signals may come from the effect on the public test's precision.