I searched various questions in this forum but I still can’t find answers to my question. So forgive me to bother you guys.

My question is this:

In order to confront the model with real data, we need to keep them the same form. In the model part, dynare does taylor expansion to linearize the model. So we express the equations in exp(x) form and then the variables are actually x= log(X). For example, if the equation is theta=u/v, I express this equation as exp(theta)=exp(u)/exp(v). Then all the variables are log level rather than [log level - log(steady state) ].

But in the real data part, we hp filter the log series to get the cyclical part of all the series. That’s percentage deviation from the log trend.

So You can see that the model part includes a steady state but the data part doesn’t.

My question is if I use this data to estimate the model as specified, it is correct? If it is wrong, how should I correct this, model or data?

Thank you very much!