Transforming variables in linear model

[francescosat]

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...

ex:

model (linear)

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

[jpfeifer]

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).

[francescosat]

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

0 = (y-C/Y*c-I/Y*i-g)+Yf/Y*(yf-Cf/Yf*cf-If/Yf*if-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/Y*c-I/Y*i-g*G/Y)+Yf/Y*(yf-Cf/Yf*cf-If/Yf*if-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?

[jpfeifer]

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.