The Lucas imperfect information model with imperfect common knowledge

Abstract

In the Lucas imperfect information model, output responds to unanticipated monetary shocks. We incorporate more general information structures into the Lucas model and demonstrate that output also responds to (dispersedly) anticipated monetary shocks if the information is imperfect common knowledge. Thus, the real effects of money consist of the unanticipated part and the anticipated part, and we decompose the latter into two effects, an imperfect common knowledge effect and a private information effect. We then consider an information structure composed of public and private signals. The real effects disappear when either signal reveals monetary shocks as common knowledge. However, when the precision of private information is fixed, the real effects are small not only when a public signal is very precise, but also when it is very imprecise. This implies that a more precise public signal can amplify the real effects and make the economy more volatile.