Persuading large investors

A regulator who designs a public stress test to avert default of a distressed bank via private investment 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 an endogenous more (less) informative signal to better-informed investors. We show that crowding-in occurs as long as investors remain responsive to public news and they are sufficiently well informed: the regulator's test perfectly reveals the state as investors' become privately perfectly informed. Investors' value from more precise private signals may come from their effect on the public test's precision.