Inference from Selectively Disclosed Data

Abstract: We consider the disclosure problem of a sender with a large data set of hard evidence who wants to persuade a receiver to take higher actions. Because the receiver will make inferences based on the distribution of the data they see, the sender has an incentive to drop observations to mimic the distributions that would be observed under better states. We predict which observations the sender discloses using a model that approximates large datasets with a continuum of data. It is optimal for the sender to play an imitation strategy, under which they submit evidence that imitates the natural distribution under some more desirable target state. We characterize the partial-pooling outcomes under these imitation strategies, and show that they are supported by data on the outcomes that maximally distinguish higher states. Relative to full information, the equilibrium with voluntary disclosure reduces the welfare of senders with little data or a favorable state, who fully disclose their data but suffer the receiver's skepticism, and benefits senders with access to large datasets, who can profitably drop observations under low states.