# Observable Equations Non-Linear Model Linear Equations

Hi all,

I just have a quick question regarding the observable equations in non-linear models.
I treated all the data with logs and one-sided hp-filters to make them stationary. Interest rates are treated as log(1+r/400) - mean(log(1+r/400)) and inflation rate as the log first differences of the GDP deflator.

Now to my question. I have a non-linear model for which I use the exp() transformation for the endogenous variables. There are, however, some equations already log-linearized in the model. (I take this model from a published but not estimated paper and want to check it with estimation).
I know that for the exp() variables I have to declare the observable equation as: obs_x = x - steady_state(x) in order to match them to the data.
But for instance my interest rate and output variables are always used in log-linearized equations. Should I now declare the measurement equations in the same fashion or just match them one-to-one as in a log-linearized model?

One log-linearized equation, for example, is the Taylor rule:

r-r_star = rho_r *(r(-1)-r_star) + (1-rho_r)*(phi_pi*pi+phi_Y*(y-steady_state(y))) + eps_r;


I want to apologize if this question has been answered before, I could not find it though.

Thank you very much and have a wonderful weekend.

I am not sure I understand the problem. In a model with a mixture of loglinearized and nonlinear equations, you have the definition
\hat x_t=\log x_t -\log \bar x
linking the loglinearized variable \hat x_t to the level variable x_t. You can then specify the observation equation in terms of either of the two.