I think that the problem comes from capital or the timing of capital or investment-related variables. When I eliminate wages and labor hours, this has no effect on the determinacy of the model. A model without capital works even in the context of an open economy. The problem introduced by capital disappears once variable capital utilization is considered, so there must be some countervailing effect of ks or u. Nevertheless, I do not want unit root behavior in my model, which might not come from the real exchange rate (because there is no unit root in open economy models without capital), but from the circularity mentioned above (ks depends on both k and u, but u depends on ks). The question is how to re-introduce capital or investment-related variables.