Price normalization in flexible vs. sticky price economies

Steady state
1

Hi all,

I am working on a two-country DSGE model with both flexible-price and sticky-price versions.

I noticed that:

  • In the flexible-price economy, I usually need to normalize prices to close the model (e.g., set PH​=0, PF=0 in log-deviations or normalize the consumption basket index).
  • But in the sticky-price economy (with Calvo pricing), the model seems to run without explicitly normalizing the price level.

My questions are:

  1. Why is the price normalization necessary for the flexible version but not for the sticky version?
  2. Is it because in the sticky model, the Phillips curve (or Calvo equation) already pins down the price level dynamics, while in the flexible model the absolute price level is indeterminate without a normalization?

Thanks in advance for any clarification!
Best,
Jiacheng

2

In most sticky price models, the price level is also indeterminate. The price level has a unit root and only inflation is uniquely determined. That is only different if you have an nominal anchor like a price level target.