On exogeneous observable variables

Should real exogenous observable variables be converted to per capita terms? For example, given the state space representation:
Screenshot from 2020-08-26 13-10-35
where x_t = [x_t^{exo}, x_t^{endo}]'. I understand that endogeneous observable variables (x_t^{endo}) like output, consumption and investment should be in real per capital terms.

How about real exogeneous observable variables (x_t^{exo}) like crude oil which are measured in barrels? In my model, x_t^{exo} follows an exogenous process, and I feel that I should not convert the crude oil data to per capital terms to make it consistent with the model assumption that it is an exogenous variable. All thoughts are welcomed. Gracias!!

That depends on your model. The reason we transform real variables to per capita terms is to deal with population growth that is often absent in the model. Most models are written down in stationary form with a fixed number of people producing output. To make the actual data consistent with this assumption, you need to transform everything to per capita terms. With oil in your model it may be similar. Oil demand can go up because more people consume oil or because every person consumes more oil.


Thanks Prof. Pfeifier for the insights. The model is actually a SOE model, so crude oil is mainly exported and not directly consumed by agents in the model. This is also kinda true in the data as the model is being built for a resource-dependent African economy that mainly export crude oil. So there is kinda almost close to zero demand for crude oil locally. Local demand is for refined oil which is imported.

So my take is that if the commodity good is consumed locally, then we should put it into per capita terms. If it is mainly exported, then probably it should not be in per capita terms. Would love your comment on this statement…thanks!

In that case, I agree that is should not be per capita