Model (linear) and Moments

[petros_varth]

Hi all,

When you introduce a model in log-linear form, the theoretical moments are for the log of the endogenous variables??
And if this is the case,how you can take from these theoretical moments the moments of the levels??

Thanks

[StephaneAdjemian]

Hi,

When you introduce a model in log-linear form, the theoretical moments are for the log of the endogenous variables??

Yes.

And if this is the case,how you can take from these theoretical moments the moments of the levels??

No, because of the Jensen inequality. Note that you don't have to linearize the model yourself. You can write the non linear
equations of the model in the model block and Dynare will linearize the model for you.

Best,
Stéphane.

[petros_varth]

Thanks a lot Stephane.

[lor_men]

Hi, I am having a related problem. I need to pass from the expectation of the logs to the expectations in levels. I need this because I am solving my model analytically and want to check the correctness of the results I get comparing them with dynare and I solve the model analytically in logs. I wrote my model in levels and in logs (using exp() on each variables) and took a second order approximation.
I thought to recover the levels from the logs by using the properties of the lognormal distribution. For instance, the theoretical mean in levels should equal the exp of the theoretical mean in logs + one half of the theoretical variance in logs. I compared the two but the values are different for most variables. Could it be because in a second order approximation the variables in logs are not normal, since there is a quadratic term of the shock in the policy function? Notice that my model is very simple and there is no state variable apart from a non-autocorrelated productivity shock. Anyway I tried using a first order approximation of the model in logs and the same problem arises.
Lorenzo