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 that temporary and permanent shocks to the natural rate (and inflation) are sufficient for the ability of the simple NK model to explain the recent facts. Based on the identified shocks from a novel approach, we show that the model can replicate key macroeconomic variables in accordance with the term structure of interest rates. We find that the term structure helps to identify permanent shocks. Our analysis is restricted to an active role of monetary policy and the traditional regions of (local) determinacy. We also show that capturing highly nonlinear dynamics can be useful to generate a prolonged period of near-zero interest rates as a policy choice.