NK Model w/ non-linear FOC -- trend inflation and price level

Hi everyone,

I was looking at Johannes Pfeifer’s mod file for the baseline NK model with non-linear first order conditions (github link posted below).

The model has zero steady state inflation and I want to modify it to incorporate trend inflation. I know that this requires modifying some of the FOCs and several equations in the steady state block. My question is in regard to the price level equation


With no zero steady inflation the static equation will not have a residual equal to zero. I have modified this equation to


where now the static equation has a zero residual. My question is whether this is correct or there is another way to write this equation when inflation does not equal zero in the steady state?

Any comments or examples of a small nk model with trend inflation would be much appreciated!


You need to be careful here. With trend inflation, the price level P will have a unit root with drift so that no steady state exists. For that reason you should only have inflation rates in your model.