I am formulating a flexible price section of a model just like Smets and wouter 2007 has done for the output gap expression.
This is relatively straightforward for closed economy model. But when I include risk premium, foreign bonds, imports, net capital inflow, real exchange rate and other things, I don’t know how to model real exchange and other related variables in flexible price scenario?
For example, real exchange rate is defined in terms of domestic and foreign inflation. But how should one get the domestic inflation when prices are fully flexible?
The real exchange rate is a relative price. Conceptually, it has nothing to do with inflation. That is just the way you compute it from the nominal exchange rate. But that nominal exchange rate is also ill-defined in a flex-price model.
In flex-price models of NK framework, all relative prices are equal to one(or constant) as I know . So, I mean how to find or define RER in flex-price model by another way.
Again, that depends on the model. If your model is a flex-price model with one good and the law of one price holds, then obviously the real exchange rate will be identical to 1. In contrast, if your model includes non-tradables, then you will a price index in each country and their ratio will be the real exchange rate.