Indexation in Calvo pricing and steady states of nominal price variables in DSGE model with nonzero inflation target

Dear Johannes,
First thank you very much for your previous guidance, I am grateful.
I have 3 questions regarding trend inflation (gross inflation target 1.02) in DSGE model.

Q1. I plan to use indexation to past inflation rate in Calvo pricing,
Define P(t) as current price, P(t-1) as past price,PAI(t-1) as past inflation, Po as optimal price, w as weight of past price P(t-1), 1-w as weight of optimal price Po
Calvo pricing equation:
In DSGE model with inflation target 1.02 in monetary policy rule, when I define calvo pricing, can i use full indexation to past inflation: P(T-1)*PAI(t-1)?

Q2. when inflation target is 1.02, P(t) has many steady states, P(t) is final good price in my model, I also have nominal intermediate good price which is related to final good price, does it mean nominal intermediate good price also have many steady states? I mean does nominal variables whose steady state depends on P(t) also have many steady states?

Q3. will this lead to indeterminancy problem in estimation?

Thank you very much!
Best wishes,

  1. Yes, full indexing to past inflation should be possible
  2. With inflation targeting, all nominal variables have infinitely many steady states
  3. The determinacy regions may be affected, but there is no reason to assume that you will have indeterminacy for sensible parameter values
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