I am wondering when we should add hp_filter option in stoch_simul.
All the examples given by J. Fernandez-Villaverde used the option hp_filter=1600. If I delete this option, the results of moments change a lot. It seems that all the variables are stationary in those rbc models, then why they should be hp-filtered before calculating the moments?
As you observed, the HP filtering has important effect for the theoretical moments of a model. That means that the model generates some low frequency components that are removed by HP_filtering.
If you do calibration and compare the theoretical moments of your model with HP filtered data, it seems more consistent to compare the HP_filtered theoretical moments and the HP_filtered data