Are long-term inflation expectations important determinants of actual long-term inflation and monetary policy?

Standard analysis of monetary policy is that economic agents’ long-term inflation expectations must be “anchored” to prevent the return of excessive (or, conversely, insufficient) inflation. This assumes that expected long-term inflation is an important determinant of actual long-term inflation, which implies that central banks must react to changes in long-term inflation expectations. But are long-term inflation expectations really a determinant of actual inflation in the long run? Looking at the situations of the United States and the euro zone, we see no significant link between expected long-term inflation, regardless of how it is measured, and actual inflation in the medium term. Anchoring inflation expectations therefore has no effect on inflation in the long run.