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This paper studies the globalisation of CPI inflation by analysing core, energy and food components, testing for structural breaks in the relationships between domestic inflation and a corresponding country-specific foreign inflation series at the monthly frequency for OECD countries. The iterative methodology employed separates coefficient and variance breaks, while also taking account of outliers. We find that the overall pattern of globalisation in aggregate inflation is largely driven by convergence of the mean levels of the core component from the early 1990s, compatible with the introduction of inflation targeting in many countries of our sample. There is less evidence of increased synchronisation of shortrun movements in core than aggregate inflation, but an increased role for shortrun foreign energy inflation often contributes to the globalisation effect.