This paper uses the European Monetary Union (EMU) as a natural experiment to investigate whether more effective monetary policy reduces the persistence of inflation. Taking into account the fractional integration of inflation, we confirm that inflation dynamics differed considerably across Euro area countries before the start of EMU. Since 1999, however, results obtained from panel estimation indicate that the degree of long run inflation persistence has converged. In line with theoretical predictions, we find that the persistence of inflation has significantly decreased in the Euro area probably as a result of the more effective monetary policy of the ECB.