Nº 20-17: Policy Announcement Design

We study the general problem of information design for a policymaker - a central bank - that communicates its private information (the "state") to the public. We show that it is optimal for the policymaker to partition the state space into a finite number of "clusters” and to communicate to the public to which cluster the state belongs. Optimal communication is more precise when the policymaker's beliefs conform with prior public expectations, but is more vague in case of divergence. We characterize the policymaker's trade-offs via a novel object - the information relevance matrix - and label its eigenvectors as principal information components (PICs). PICs with the highest eigenvalues determine the dimensions of information with the highest welfare sensitivity and, hence, are the ones that the policymaker should be most precise about.