On the equivalence of information design by uninformed and informed principals

We compare information design, or Bayesian persuasion, by an uninformed principal (who has no information about the state of the world when making her choice) and by an informed principal (who has private information and can condition her choice on that information). We show that, under the assumptions of monotone preferences of the principal and nondegenerate information structures, a Pareto undominated outcome is implementable by the uninformed principal if and only if it is implementable by the informed principal.