Employing the modified tests of Harvey, Leybourne and Taylor [Harvey, D.I., Leybourne, S.J. and Taylor, A.M.R., 2006. Modified tests for a change in persistence. Journal of Econometrics 134, 441–469.] for a single change in persistence and repartitioning the sample when a break is found, this paper shows that US and UK inflation changes from I(0) to I(1) in the early 1970s, with a subsequent reversion to I(0) behaviour, compatible with modern macroeconomic theories, in the early 1980s.