Hi,

I do not understand the question. If you write your model with all the variables inside `exp`

functions, it means that all the variables are implicitly defined in logs. The moments reported by `stoch_simul`

are for the logarithm of the variables. Obviously the variance, for instance, of the logarithm of a variable is not the same as the variance of the same variable. More generally, \mathbb V[\varphi (X)] is not equal to the \mathbb V[X]. But you can approximate the second variance from the first one, with a first order Taylor approximation around a deterministic point x^{\ast} (*eg* the deterministic steady state):

\mathbb V[\varphi (X)] \approx \mathbb V [\varphi(x^{\ast}) + \varphi'(x^{\ast})(X-x^{\ast})]

since x^{\ast} is deterministic, we have equivalently:

\mathbb V[\varphi (X)] \approx \varphi'(x^{\ast})^2 \mathbb V [X]

Hence dividing the variance of \varphi(X) by the square of the derivative of \varphi evaluated at x^{\star} (usually the steady state) you obtain an approximation of the variance of X.

Best,

Stéphane

P.S. Needless to say we also have: \mathbb V[\varphi(X)] \neq \varphi\left(\mathbb V [X]\right) in general.