This paper studies the design of optimal time-consistent monetary policy in an economy where the planner trusts its own model, while a representative household uses a set of alternative probability distributions governing the evolution of the exogenous state of the economy. In such environments, unlike in the original studies of time-consistent monetary policy, managing households' expectations becomes an active channel of optimal policymaking per se, a feature that the paternalistic government seeks to exploit.

We adapt recursive methods in the spirit of Abreu, Pearce, and Stacchetti (1990) as well as computational algorithms based on Judd, Yeltekin, and Conklin to fully characterize the equilibrium outcomes for a class of policy games between the government and a representative household that distrusts the model used by the government.