Exogenous variable as observable variable in estimation

I had a follow-up question to my earlier one regarding mixed frequency, but I thought this would be better as a separate question/thread.

Background: One of the shock processes in the model represents the price of oil. It is exogenous to my model (the price of oil is not determined by the model).

I have monthly data on the price of oil.

Question: Is it advisable, in general, to avoid specifying one of your varobs that is also specified by an exogenous process in your model? Would this deteriorate the estimation results? I have a fairly good mix of endogenous variables as varobs, but I was wondering about including variables determined by an AR process such as government spending shocks and oil price shocks (which I happen to have relevant data for).

Again, any help is appreciated.

Chris

Generally, you want to use all relevant information that you have. If you can perfectly observe a relevant variable, you may want to use it. That should improve your model estimates, not deteriorate them. If you were to not observe that variable, the model would need to infer its putative dynamics from the other observed data, which should only happen with errors.
The only case where that may not be advisable is if there is a gap between the actual object in the data and the concept measured. For example, there is not just one oil price, but there are prices for a variety of sorts (e.g. Brent vs. WTI). But even in that case, you may simply add measurement error.

Thank you for your reply, Johannes. As always, it is appreciated.