Baseline DSGE + government

I am not sure I understand @punnoosejacob’s answer. Conceptually, an model economy does not need to be saddle path stable or have a non-stationarity. So even a small open economy does not have to be closed.

That being said, we usually think that saddle path stable equilibria are the ones that interest us. In that case, there is a transversality+No-Ponzi condition that rules out explosive paths for debt. From that point of view, the models needs to include a condition that assures that debt does not explode.