Suppose U = f( K, L, RER) where K= capital, L= labor, RER = real exchange rate.
Then can I add oil price in this function? My question was, there is a relationship between RER and oil price if the country is a net oil importing country.
If the country is a net importer, why not imagine that it is a buyer on the international oil market. In this case, if the oil price of the rest of the world is exogenous, the national import price of this good depend directly on the RER.
First of all you have to run a regression or correlation test between oil price and unemployment. if there is any significant relation then you can add them.
Think again of U=f(K,L). Usually, output Y is determined by a production function. And then, U might be related to Y, at least in terms of the transitory to components, i.e. the unemployment gap to the output gap, according to Okun's law.
Usually, there should be a relationship between the nominal exchange rate and the oil price. Oil prices are denominated in US-Dollar, and if the dollar depreciates, oil prices will increase, in order to keep oil income at a constant. This relationship should be also visible in terms of the RER, since price levels do not adjust instanteneously. In the RER case, it might be also better to include the real oil price. You can account for supply side shocks if you add the oil price in the unemployment equation.
I followed " Unemployment and the Real Exchange Rate in Latin America" of World Development, Elsevier. From that theory, I asked the question. Hope, you can help me.