Costly Persuasion by a Partially Informed Sender

I study a model of costly Bayesian persuasion by a privately and partially informed sender who conducts a public experiment. The cost of running an experiment is the expected reduction of a weighted log-likelihood ratio function of the sender's belief. This is microfounded by a Wald sequential sampling problem where good news and bad news cost differently. I focus on equilibria that satisfy the D1 criterion. The equilibrium outcome depends crucially on the relative costs of drawing good and bad news in the experiment. If bad news is more costly, there exists a unique separating equilibrium, and the receiver unambiguously benefits from the sender's private information. If good news is more costly, the single-crossing property fails. There may exist pooling and partial pooling equilibria, and in some equilibria, the receiver strictly suffers from sender private information.