This paper analyses the implications of monetary policy for the dynamic behaviour of inflation, in a ‘natural’ rate model characterized by endogenous unemployment persistence. We present evidence for the main industrial economies that suggests that inflation displays persistence which is of the same order of magnitude as the persistence of deviations of unemployment from its ‘natural’ rate. We provide a theoretical explanation of this fact based on a model of the dynamic interactions between central bankers and labour market insiders. The clash in the objectives of central bankers and labour market insiders is what causes both inflation and unemployment to display the same persistence in this model. The analysis suggests that inflation persistence could be addressed in a welfare‐improving way, if central banks adopted monetary policy rules that targeted unanticipated changes in unemployment rates instead of deviations of unemployment from its ‘natural’ rate.