Linearized vs nonlinear

Hi all,
I have a simple question.

I have a the nonlinear NK model and the linearized one.
The question is: are the second moments ( obtained from the stochastic simulation of both models the same?

I get some small difference (+/- 5 %) in the linearized NK model. Are they supposed to be 100 % the same ?


That depends on what you compare. If you compare theoretical moments at order 1 from the logarithm of the levels in the nonlinear model to the percentage deviations in the linearized one, they should be exactly the same.

Many thanks for the feedback,

Yes I am comparing

in the nonlinear model with

in the linear one.
They are both percentage deviations so I expected the same second moments at order =1.

Then there must be a mistake somewhere.