Hi everyone,
I wonder how one can take the disinflation process into account while estimating a small open economy model? I mean in the disinflation period, inflation clearly has a downard trend therefore one cannot use demanded inflation in estimation. Currently, I am using hp filtered inflation however I want to estimate the model with raw data, not hp filtered data. I wonder your opinions about what is the best practice for constructing and estimating a model under disinflation.

where pi_obs is quarter on quarter price index (P(t)/P(t-1)) and pi_ss is price index at steady state and pi_hat is log liniarized price… every where here inflation is a price index like pi=1+inflation.

Thank you very much for your answer,
However, I could not get it. What is the reason of multiplying pi_hat with s.s. value of inflation? Could you please explain this?
Thank you.

The reason is that observed inflation rates can be written as steady state value times one plus the percentage deviation:
pi_obs=pi_ss(1+pi_hat)=pi_ss*pi_hat+pi_ss
For example, if pi_SS is 1 and pi_obs=1.1, inflation is ten percent above its steady state and hence pi_hat is 0.1.This is just an example of an observation equation (see the lower part of [Simple model. Unkown error!))

But more importantly, what are you trying to do exactly? What do you mean with disinflation process? Do you simply mean a period where inflation is below its steady state value due to a series of shocks? Or do you mean a structurally different phase where the inflation target was lower than before?

I think he means that “inflation” has a downward path, a downward trend… there is no problem with this… in my model there is a clear disinflation process and nothing happened… actualy I think he considers since inflation has a downward path it may have a unit root… try modeling Quarter/Quarter inflation not Year/Year. ON Q/Q basis you shouldn’t have any problems.

What i mean by “disinflation” is that inflation and inflation target has a downward trend through time. That is to say, inflation itself is non stationary. Therefore, I guess, I need to introduce a unit root process for inflation target. My question is how should i transform my observable consistent with my model? For example should I use change in inflation as an observable or inflation itself?