Hi!!
Hope all is well!
I’m going to estimate a model but two questions arose when I was transforming my data to the model equivalent. The model is an already loglinearized similar to the 3basic equations of Galí but adapted to a small open economy.

As of my knowledge, for the output gap, I need to filter (with a consistent filter such as the onesided HP filter) the log of real GDP per capita. However, I have seen many published papers using the log of real GDP. Am I missing something or I shall use it in per capita terms?

As this model is already loglinearized, the implied steady state is zero, so I need to demean all my observables such its mean is also zero. However, I’m struggling if I need to do this also for inflation and for interest rate. My concern is the following: in my country the inflation target is 3% on annual basis but the actual mean of inflation is closer to 4.5%. Initially, I would like the interest rate in the model to react to inflation above the 3% such as the Central Bank. However, doing this, my data is not consistent with the model because the implied mean in my data will be close to 1.5% (never hovering around the model’s steady state). Do you have some advice to tackle this issue?
As always, thanks in advance for your help!
Best,
Sebastian