This paper explores the ability of the New-Keynesian (NK) model to explain the recent periods of quiet and stable inflation at near-zero nominal interest rates. We show how (conventional and unconventional) monetary policy shocks enlarge the ability to explain the facts, such that the theory supports both a negative and a positive response of inflation. Central to our finding is that monetary policy shocks may have temporary and/or permanent components. We find that the NK model can explain the recent episodes, even if one considers an active role of monetary policy and restrict ourselves to the regions of (local) determinacy. We also show that a new global solution, capturing highly nonlinear dynamics, is necessary to generate a prolonged period of near-zero interest rates as a policy choice.