I am trying to estimate my model and there is one minor issue that I would like to have clarified. I am using gross interest rates in a log-linearized model. Therefore, it needs to be interpreted as a log deviation from its st.st value. I try to follow a guide prepared by prof. Pfeifer (Pfeifer 2017).
Since I use the st. st. value of the interest rate in a computation of the steady states of other variables of the model and it’s steady state value is used directly in some equations of the log-linearized model, do I need to treat the gross interest rate in the estimation procedure as a log deviation from the sample mean (that is non-zero) or as a log deviation from 0 (i.e. demeaned transformation).
In my model equations I use steady state value of the gross interest rate \bar{R}, which is a non-zero value (sample mean computed from 1 + nominal interest rate, i.e. 1 + R_data/100). Now I would like to use also the time series of the gross interest rate R to estimate the model parameters. So my question is, whether I should use demeaned time series (after log transformation, as you suggest in your guide), or should only take the log-transformation without the demeaning the series (and therfore retaining the non-zero mean).
In this case, I would recommend to not demean the interest rate in the data as you are clearly interested in the data mean, because it helps you pin down steady state of interest rate in the model.