The Jacobian of the static model is singular in NK SOE

Hello everyone,
I am trying to build a standard NK SOE model with fiscal policy. The model shows no residuals and the steady state seems to be fine, however I’m having some troubles with collinearity between equations and additionally the TFP process also seems to have problems too.
I would be very grateful if someone could help me to identify the error.

NK_SOE_FS.mod (11.6 KB)

The collinearity comes from a unit root in the model. The bigger problem is the instability. See