Central bank communication design in a Lucas-Phelps economy

In a Lucas-Phelps island economy, an island has access to many informative signals about demand conditions. Each signal incorporates both public and private information: the correlation of a signal[U+05F3]s realizations across the economy determines its publicity. If information sources differ in their publicity then price-formation and expectations-formation processes separate, causing output gaps to open. An output-stabilizing central bank prefers "averagely public" information, and sometimes limits the clarity of its policy announcements to achieve this. The bank's incentive to engage privately in costly information acquisition and transmission is strongest not for the most influential signals, but instead for those which drive the largest wedge between prices and expectations: signals that are far from averagely public.