So this is similar to the point Scott Sumner made in Oil and Money don’t mix but cast through my frame of looking at the world. This result may be well known but I have not heard it stated before.
My simple conjecture is this: A rise in the price of oil in the face of a constant interest rate represents a tightening of monetary policy.
Because so much oil is imported from overseas and because oil profits are deposited into US T-Bills.
So, what happens when the price of oil goes up. US consumers ship lots of money to Oil Producing Countries.
Those oil producing countries then buy US T-Bills. This would tend to drive down the US T-Bill rate. However, the T-Bill rate must wash with the Fed Funds rate.
So money goes out of T-Bills and into overnight reserve market. This tends to push down the Fed Funds rate. The Open Market Operations Desk responds by selling T-Bills (or buying fewer) and destroying (or creating fewer) reserves.
This tightens monetary policy in the United States.
Another way to think about it would be this.
Higher oil prices transfer money from consumers with a high propensity to spend on consumer goods to oil producing countries with a high propensity to save.
The natural response of this change would be to drive down interest rates thereby encouraging businesses to invest more and soak up the savings.
However, the interest rate cannot fall because it is targeted by the Central Bank. Thus savings rise but investment does not. The net effect is contraction in Aggregate Demand.
This is only worsened by the fact that a central bank may respond to higher oil prices by actually raising the nominal interest rate.