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 possibil- ity. This fact stands in contrast to the standard macroeconomic models with rational expectations. We extend a standard New Keynesian model with a zero-lower bound on inflation expectations. Unconventional monetary policies, such as forward guid- ance, are weaker. In liquidity traps, the government spending output multiplier is finite, and adverse aggregate supply shocks are not expansionary. The possibility of confidence-driven liquidity traps is attenuated.