Should real exogenous observable variables be converted to per capita terms? For example, given the state space representation:

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!!