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Hi, professor Pfeifer

I construct a two-sector and two-country model. The two sectors are tradable and non-tradable sector. Assuming the production functions of both sectors are cobb-douglas functions , the technologies of both sectors are labour-augmented and non-stationary. I want to study the impact of non-tradable productivity slowdown on macroeconomic variables , while assuming that productivity in other country remains at its steady state level throughout the period considered. My question is how to detrend this kind of model ?

You detrend it as always: every variable with its own trend. The problem is figuring out what the trend growth in this setup is. Usually, it should be a composite of the growth rates in the different countries. However, there might be restrictions on e.g. preferences and aggregation technology necessary to guarantee the existence of a well-defined balanced growth path.