Transforming variables in linear model

Hi again. I am trying to replicate a model. I do have log-linearized focs. My problem is that some of the variables are not expressed in log deviations but in a different way.

For example i need to put in the model the variable x as (xt-X/Y) instead of (xt-X/X) using capital letters for steady state.

As far I understood, if i write x on Dynare, he treats the variable as (xt-X/X) but I need (xt-X/Y).

What I am doing is to transform the variable in x*X/Y in this way i should obtain what I need but is not working…


model (linear)

x*X/Y+… //this should be the transformed variable, in order to obtain (xt-X/X)*X/Y = xt-X/Y

I don’t get it. Please provide an explicit example. Be particularly precise what the variable is you are interested in and what parameters are (or functions thereof like steady state values).

ok, for example I have this log linearized foc (it’s a 2 country model, variables f are foreign variables)

0 = (y-C/Yc-I/Yi-g)+Yf/Y*(yf-Cf/Yfcf-If/Yfif-gf); //capital letters are steady states

The paper I am studying says that all variables are expressed in percentage deviation from steady state but some are not. For example g=(Gt-G)/Y. For this reason I transformed the variable g in g*G/Y in dynare in this way:

0 = (y-C/Yc-I/Yi-gG/Y)+Yf/Y(yf-Cf/Yfcf-If/Yfif-gf*Gf/Yf);

In this way I should obtain the transformation I need but I am not sure Dynare accepts this.

More generally, there is a way to write a variable in the form: x=xt-X/Y (still using capital letter for steady state) in a linear model in dynare?

For Dynare, a variable is a variable, no matter how you define it. You can enter the first equation you wrote down with g defined as g=(Gt-G)/Y. Dynare only knows g and does not care what it means. It will solve the model for exactly this variable. If you want a different interpretation, you must redefine the variable accordingly.