Price level in Gali ch.3/7

Hello everyone,

I was looking at Johannes Pfeifer’s mod file for the NK model (particular ch.3 and 7 but maybe also in other chapters) and I noticed that in the model block with the first order conditions, we define one time the phillips curve pi=bettapi(+1)+kappay_gap;
and a few lines further down we define again the price level with exact the same definition pi=p-p(-1);

Hence, we have in the model block one variable but two definitions, I just wondered why we do this and how is this possible that the model still works (side note: the code runs, there are no errors).

Thanks for any clarification.

The NK-PC determines the dynamics of inflation.
The second equation you have mentioned, the definition of the price level, determines the dynamics of the log price level.
Therefore the number of equations equals the number of variables.

Thanks a lot for your reply.
So, I think I see what you mean. In the end we could also write the second equation the following way p = pi+p(-1) and then it does not look like there are two defintions for pi but only one (for a beginner perhaps from didactic perspective better).

Would you agree?

Correct. It does not matter how you specify your equations as long as they are mathematically the same.
\pi_t+p_{t-1} =p_t
\pi_t+p_{t-1} -p_t=0
p_t-\pi_t-p_{t-1} =0
Given a process for \pi_t, each equation above will determine p_t the same way.

Alright, thanks a lot Max.