We document a new fact: in U.S., European and Japanese surveys, households do not expect deflation, even in environments where persistent deflation is a strong possibileity. This fact stands in contrast to the standard macroeconomic models with rational expectations. We extend a New Keynesian model with a zero-lower bound on inflation expectations. Unconventional monetary policies, such as forward guidance, are weaker. In liquidity traps, the government spending output multiplier is finite, and adverse aggregate supply shocks are not expansionary. A confidence-driven liquidity trap steady state with deflation does not exist.