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This paper investigates the nature of inflation dynamics with a special focus on inflation persistence. Using data from euro area member-states we estimate dynamic non-linear panel models addressing in detail econometric issues concerning unobserved heterogeneity, genuine state dependence, and the initial conditions problem. After controlling for observed and unobserved heterogeneity, our results suggest that the degree of inflation persistence is genuine and varies depending on whether the inflation rate is too high, within the range of ECB's target of price stability, too low or negative. This implies that policies to stabilize inflation in the short run will have longer-run effects.