There are several ways to model an import sector or import goods as shown in M. Uribe and S. Schmitt-Groh´e (2017) and Gali(2015). However, they do not mention why they model import goods a particular way? I am sure it will affect shocks such as TOT shocks. Any references on this will be much appreciated. Thanks!!
It always depends on what you are trying to do, e.g. whether there is pricing power in these markets, whether there is more than one import good etc.