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We show that with a unit root in inflation, the new Keynesian Phillips curve (NKPC) implies an unobserved components model with a stochastic trend component and an inflation gap. Our empirical results suggest that with an increase in trend inflation during the Great Inflation, the response of inflation to real economic activity decreases and the persistence of the inflation gap increases due to an increase in the persistence of the unobserved stationary component. These results are in line with the predictions of Cogley and Sbordone (), who show that the coefficients of the NKPC are functions of time‐varying trend inflation.