Using the statistical technique of fuzzy clustering, regimes of inflation and unemployment are explored for the United States, the United Kingdom and Germany between 1871 and 2009. We identify for each country three distinct regimes in inflation/unemployment space. Similarities exist across countries in both the regimes and the timings of the transitions between regimes. However, the typical rates of inflation and unemployment experienced in the regimes are substantially different. Further, even within a given regime, the results from the cluster analysis reveal persistent fluctuations in the degree of attachment to that regime of inflation/unemployment observations over time. The economic implications of this are that, first, the inflation/unemployment relationship or Phillips curve experiences from time to time major shifts. Second, that it is also inherently unstable even in the short run. It is likely that the factors which govern the inflation/unemployment trade-off are so multi-dimensional that it is hard to identify periods of short-run Phillips curves which can be assigned to particular historical periods with any degree of accuracy or predictability. The analysis shows that reliance on a trade-off between inflation and unemployment for policy purposes is misplaced even in the short run.