I am estimating a nonlinear DSGE model. When I take the variables to the data, I match the detrended model variables to detrended data (not demeaned). However, the steady state values of the observables implied by the model are not consistent with the corresponding sample means.
I read the paper “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” by Johannes Pfeifer, especially on Section 1.4, where the author provides two ways of taking models to data. The first way is to write down a stationary model and enter data made stationary. This is exactly what I am doing. Following this way, am I supposed to obtain a steady state value for any observable that is consistent with the sample mean?
Thanks a lot in advance.