We study the properties of the optimal interest rate rule under different sources of inflation persistence. In our model, the optimal policy minimizes price dispersion, which depends on the degree of price indexation. When indexation is zero, inflation persistence depends only on the level of trend inflation, the inflation gap is purely forward-looking and the optimal policy targets inflation stability. Full indexation makes the inflation gap persistent, eliminates the effects of trend inflation and makes the optimal policy target the real interest rate. We compare our results with empirical estimates of the FED's policy in the post-WWII era
