A central bank and the public are engaged in an infinitely repeated monetary policy game with cheap talk. The central bank's type is private information. First, when the central bank is sufficiently impatient, there is only uninformative babbling equilibrium. Second, if the central bank is sufficiently patient, there exists another equilibrium in which the central bank fully reveals its private information. Third, if the central bank is sufficiently patient then the fully revealing equilibrium is Pareto superior to the babbling equilibrium.