Implementation and Orderings of Public Information

We explore the relationship between public information and implementable outcomes in an environment characterized by random endowments and private information. We show that if public signals carry no information about private types, then an exact relationship holds: a more informative public signal structure, in the sense of Blackwell, induces a smaller set of ex-ante implementable social choice functions. This holds for a large set of implementation standards, including Nash implementation, and Bayesian incentive compatibility. The result extends the notion, dating to Hirshleifer (1971), that public information can have negative value to an endowment economy under uncertainty.