Two sector dsge

Most probably not. Rather some more fundamental error.

I would be worried about this. Why is there a unit root involving real variables. You need to understand this.

You are the model builder. You need to figure out what is going on in your own model. As the problem seems to be present in the closed economy version already, it seems rather fundamental.

Maybe there is a problem with closing the model so you get a non-stationary net foreign asset position. See the SGU paper on closing small open economy models at