'Modern' theories of the Phillips curve inadvertently imply that inflation is an integrated or near-integrated process, but this implication is strongly rejected using US data. Alternatively, if we assume that inflation is a stationary process around a shifting mean (due to changes in monetary policy), then any estimate of long-run relationships in the data will suffer from a 'small-sample' problem as there are too few stationary inflation 'regimes'. Using the extensive literature on identification of structural breaks, we identify inflation regimes which are used in turn to estimate with panel data techniques the US long-run Phillips curve.