Perhaps a really stupid question. In New Keynesian models, we are familiar with the unit root in prices, which is typically fine, as long as the inflation rate in the model is well-behaved.
If we are using a recursive formulation for optimal Calvo pricing (i.e., a non-linear model with price stickiness), does this imply we can set our initial value for the price level P equal to anything?
I am thinking of initializing the simulation with P = 1.00; however I’m all ears if people have done something else with more success.
Thank you in advance for any knowledge.