We present a unified duality approach to Bayesian persuasion. The optimal dual variable, interpreted as a price function on the state space, is shown to be a supergradient of the concave closure of the objective function at the prior belief. Strong duality holds when the objective function is...

Labor economists increasingly work in empirical contexts with large numbers of unit-specific parameters. These settings include a growing number of value-added studies measuring causal effects of individual units like firms, managers, neighborhoods, teachers, schools, doctors, hospitals, police...

Determining a plausible number of components in a factor model is a nontrivial issue in case of weak data, sparse model restrictions and diffuse prior information. We discuss the issue of structural parametric identification in a static factor model and introduce orthogonal restrictions which...