Unit roots in the small open economy DSGE

The unit roots could come from equations like

PiH=e-e(-1)+PiHF; QC=QC(-1)+PiT-PiN;
They basically look like unit root processes and I wonder if that is desired.

If the unit roots are desired, they pose no problem unless you want to estimate or simulate the model. For IRFs at order=1, this is no problem. See also:
[Exchange rate peg and level irfs)