Exchange rates in DSGE

Good afternoon,

How do you deal with exchange rates when having intermediate goods that are also exchanged on global markets?

Usually, the exchange rate will make the trade balance of final goods equal to zero. But what happens if this trade balance incorporates, on top of final goods exports and imports, intermediate goods exports and imports (incorporated into the production of the final good) ?

I find this to be tricky as the exchange rate now ends up in more FOCs than just the trade balance of final good, and the import and exports of final goods equations. This exchange rate ends up in the marginal cost function of firms too (but also in households’ decisions as a commodity such as energy can be exchanged on international markets and be consumed by households and firms as intermediate input). Finding the SS value for the exchange rate becomes then tricky.

Thank you

I doubt there is a trick here. You seem to simply end up with a more complicated equation system that needs to be solved.