Inflation persistence, Price Indexation and Optimal Simple Interest Rate Rules

We study the properties of the optimal nominal interest rate policy under different levels of price indexation. In our model indexation regulates the sources of inflation persistence. When indexation is zero, the inflation gap is purely forward- looking and inflation persistence depends only on the level of trend inflation, while full indexation makes the inflation gap persistent and it eliminates the effects of trend inflation. We show that in the former case the optimal policy is inertial and targets inflation stability while in the latter the optimal policy has no inertia and targets the real interest rate. We compare our results with empirical estimates of the FED's policy in the post-WWII era.