A number of previous studies suggest that inflation expectations are important in considering the effectiveness of monetary policy in a liquidity trap. However, the role of inflation expectations can be very different, depending on the type of monetary policy that a central bank implements. This paper reveals how a private agent forms inflation expectation affects the effectiveness of monetary policy under the optimal commitment policy, the Taylor rule, and a simple rule with price-level targeting. We examine two expectation formations: (i) different degrees of anchoring, and (ii) different degrees of forward-lookingness. We show that how to form inflation expectations is less relevant when a central bank implements the optimal commitment policy, while it is critical when the central bank adopts the Taylor rule or a simple rule with price-level targeting. Even for the Japanese economy, the effects of monetary policy on economic dynamics significantly change according to expectation formations under rules other than the optimal commitment policy.