A major criticism against staggered nominal contracts is that they give rise to the so called "persistency puzzle" – although they generate price inertia, they cannot account for the stylised fact of inflation persistence. It is thus commonly asserted that, in the context of the new Phillips curve (NPC), inflation is a jump variable. We argue that this "persistency puzzle" is highly misleading, relying on the exogeneity of the forcing variable (e.g. output gap, marginal costs, unemployment rate) and the assumption of a zero discount rate. We show that when the discount rate is positive in a general equilibrium setting (in which real variables not only affect inflation, but are also influenced by it), standard wage-price staggering models can generate both substantial inflation persistence and a nonzero inflation-unemployment tradeoff in the long-run. This is due to frictional growth, a phenomenon that captures the interplay of nominal staggering and permanent monetary changes. We also show that the cumulative amount of inflation undershooting is associated with a downward-sloping NPC in the long-run.