I work with a 2-country NK DSGE model. I work with the non-linear form. According to Sims’ Notes, I express all prices in terms of inflation rates (because stationarity). In the system of optimality conditions, the nominal exchange rate does not disappear (for example, it is not possible to express the nominal exchange rate in terms of the change of the nominal exchange rate).
Im my model, there is only a 1% technology shock. Can I assume that the nominal exchange rate is equal to 1 in steady state? I mean, when there are no differences between the 2 countries in the deterministic steady-state, it is reasonable to assume a nominal exchange rate = 1?