I have written my own piece on How Oil Prices Impact the U.S. Dollar but Jens Nordvig of Nomura has an equally thorough take that is worth reading:
What does the spike in oil prices mean for the dollar?
Recent memories suggest that higher oil prices are bad news for the dollar. First, we have been used to a generally negative correlation between oil prices and the dollar since around 2004. This was especially the case in the first part of 2008, when the correlation between EUR/USD and Brent reached very high levels. Second, past episodes of tension in the Middle East suggest that the dollar tends to weaken when there are oil supply shocks. This was the case during the first Iraq war in 1991 and in the run-up to the second Iraq war in 2003.
Beyond the observed correlations, there are also fundamental reasons to explain why the dollar should be negatively correlated with oil prices. We can think of three:
1. High US energy intensity: the US economy is more energy intensive than most other developed market economies. Linked to this, the US is a bigger oil importer than the eurozone. This again means that the US’s terms of trade deteriorate more than other economies when oil prices go higher.
2. Petrodollar flows: When oil prices rise, oil-exporting countries generate more revenue. If a significant proportion of additional revenue is allocated into non-dollar currencies, the net impact can be USD selling. In 2008, when oil prices rose above $100/barrel for the first time, we saw a strong correlation between EUR/USD and oil prices (Figure 2). This correlation is consistent with an increasing share of euro in the reserves of oil-exporting countries, such as Russia and the Middle East.
3. Asymmetry in inflation targets: Oil price shocks affect monetary policy differently in different countries. The Fed tends to focus on core inflation (Greenspan used to focus on the core PCE deflator for example). This means that higher oil prices are not a primary concern in relation to monetary policy. The ECB by contrast focuses on headline inflation, and we have observed in the past that upward pressure on headline inflation from global energy prices (such as in mid-2008) has the potential to trigger rate increases. This asymmetry in inflation targets creates a weak USD bias in the face of oil prices shocks, at least in relation to EUR/USD.