Hi, everyone.
I am estimating nonlinear model parameter values using the SMM estimation method in Dynare 5.2.
(1) When I directly estimate parameter values using nonlinear equations and data, the data moment and moments have got quite different moments data.
(2) When I log the variables to estimate, the moment estimates obtained are very similar to the model,
So I would like to ask, I use the same data,
what is the reason for this phenomenon?
How do you map the model to the data in the first version? The logged one is in percentages, so the units of measurement do not matter. That is almost impossible to do for the level version. You would need to correctly scale A.
Thanks for your reply, Prof, Pfeifer. For the first version:

Use HP filter to trend out of Y,C
. get the cycle series Y_c, C_c

Ues the Y_c, C_c
as data to match model.
so get the matched moments:
About SMM in Dynare, which can find the confidence bands of the model moment
?
That does not make sense. Your data will grow exponentially, while the HP filter in the limit will remove linear trends. You need to log the data before the filtering and then use logs in the model as well.
@wmutschl Do you know whether there is a way to get the standard errors of the model moments?