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We study the effects of positive steady-state inflation in New Keynesian models subject to the zero bound on interest rates. We derive the utility-based welfare loss function taking into account the effects of positive steady-state inflation and solve for the optimal level of inflation in the model. For plausible calibrations with costly but infrequent episodes at the zero lower bound, the optimal inflation rate is low, typically <2% even after considering a variety of extensions, including optimal stabilization policy, price indexation, endogenous and state-dependent price stickiness, capital formation, model uncertainty, and downward nominal wage rigidities. On the normative side, price-level targeting delivers large welfare gains and a very low optimal inflation rate consistent with price stability. These results suggest that raising the inflation target is too blunt an instrument to efficiently reduce the severe costs of zero bound episodes. Copyright , Oxford University Press.