Level specification of exogenous shock

Hi everyone.

I have a simple question on how to set up a model with a level specification of exogenous shock.
As usual, a log-level specification of exogenous shock is widely used.
However, in my project, I try to use not the log-level specification but the level specification shock for some reasons.

For instance, in a case to use a log-level specification of an exogenous shock, we use

exp(y) = exp(z)exp(k(-1))^alphaexp(n)^(1-alpha)exp(h(-1))^(1-alpha);
z = (1-rho) + rho
z(-1) + e;
with initial value z=1;

Thus, my main question is as follows:

To adopt the level specification of an exogenous shock, Is it right to set up a model like this?

exp(y) = exp(z)exp(k(-1))^alphaexp(n)^(1-alpha)exp(h(-1))^(1-alpha);
exp(z) = (1-rho) + rho
exp(z(-1)) + e;
with initial value z=log(1);


What do you mean with “level specification”? Something like https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Basu_Bundick_2017/Basu_Bundick_2017.mod ?

I guess you are right. I mean that, as in Heiberger and MauBner (2020) 11-12p, the exogenous process for Zt is specified in levels, not log-levels.

Ok, but then I gave you an example code.