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))^alpha*exp(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))^alpha*exp(n)^(1-alpha)*exp(h(-1))^(1-alpha);
exp(z) = (1-rho) + rho*exp(z(-1)) + e;

with initial value z=log(1);

Sincerely.