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We revisit time-variation in the Phillips curve, applying new Bayesian panel methods with breakpoints to US and European Union disaggregate data. Our approach allows us to accurately estimate both the number and timing of breaks in the Phillips curve. It further allows us to determine the existence of clusters of industries, cities, or countries whose Phillips curves display similar patterns of instability and to examine lead-lag patterns in how individual inflation series change. We find evidence of a marked flattening in the Phillips curves for US sectoral data and among EU countries, particularly poorer ones. Conversely, evidence of a flattening is weaker for MSA-level data and for the wage Phillips curve. US regional data and EU data point to a kink in the price Phillips curve which remains relatively steep when the economy is running hot