Oil and the Dollar

There are a variety of reasons why oil prices and the exchange rate might move together. A drop in U.S. interest rates relative to Europe was likely one factor that contributed to both the increase in the price of oil and the increase in the value of the euro earlier this year. Over the last few weeks, expectations of weaker European output helped the dollar to gain against the euro and also brought oil prices down. Yet another example, and the one people often think of first, would be if there is a higher inflation rate in the U.S. than Europe. In that case we might expect to see an increase in the price of oil that exactly equals (in percentage terms) the decrease in the value of the dollar.

In all of the above examples, depreciation of the dollar is associated with an increase in the dollar price of oil. But it is also possible for the relation to go in the opposite direction. For example, strong economic growth in the U.S. would cause the dollar to appreciate as the price of oil increased.

The graph below plots the cumulative logarithmic change since 1999 in the dollar price of one euro along with the dollar price of one barrel of oil. If the inflation effect were all that was going on these data, we would expect to see the two series track each other closely. The dollar has depreciated by 30% over this period while the price of oil today is 10 times what it was in 1999. Obviously something other than the pure inflation effect has been involved.

Cumulative change since January 1999 in (1) natural log of spot price of West Texas Intermediate in dollars per barrel (from EIA) and (2) natural log of exchange rate in dollars per euro (from FRED).

Because the nature of the news impacting both exchange rates and the price of oil has been different at different points in time, I was curious to explore the correlation between oil prices and exchange rates using a rolling regression. For any day t, I calculated the change in the natural logarithm of the price of oil over the last 5 business days, and regressed it on a constant and the change in the natural log of the dollar/euro exchange rate over same 5 days. To get a sense of how the relation has changed over time, on any day t I estimated this relation using only the most recent 200 business days, so that for each day between October 1999 and August 2008 I obtained a different coefficient estimate relating the price of oil to the value of the dollar. The graph below plots those estimated regression coefficients for each day, along with 95% confidence intervals. [Note for the wonks: the latter were based on Newey-West standard errors with lag length 10, made necessary because the overlapping nature of 5-day intervals introduces serial correlation in the regression residuals].

Coefficient and 95% confidence interval relating percent change in oil price to percent change in dollar based on 200-day rolling window.

In the early part of the sample, the correlation was actually negative– days when the dollar appreciated tended to be days when the price of oil rose. As Menzie has noted, for the sample as a whole the correlation between the two variables is not statistically significant. Since 2003, however, the correlation has almost always been positive (the dollar depreciating on days when oil prices went up) and often suggests a coefficient near 1.0, consistent with the inflation story. As of the most recent 200 days, the estimated coefficient had risen all the way to 1.76– a 1% decline in the dollar is associated with almost a 2% increase in the price of oil– and that coefficient is statistically significantly greater than one. To explain a coefficient bigger than one, something more than the simple inflation effect would have to be at work.

Another way to gauge how important this relation might be is to look at its out-of-sample forecasting performance. Here I calculated the answer to the following question. Suppose you could know today what the actual change in the exchange rate over the next 5 days was going to be, and you used the regression coefficients estimated over the previous 200 days to predict what the change in the oil price over the next 5 days would be, given the future exchange rate. How big an error would you make in trying to "predict" the price of oil if you already knew what the exchange rate would be? I looked at the average squared value of a forecast error constructed in this way over the most recent 200 days (each forecast using different regression coefficients as estimated from a different previous sample), and divided it by the average squared change in realized oil prices over the last 200 days. One minus this magnitude corresponds to an out-of-sample uncentered R-squared, which again can be calculated for each day between August 2000 and August 2008. This number measures the fraction of the variance of oil price changes that could be explained by the exchange rate according to the most recently estimated regression, and is plotted below.

Out-of-sample R-squared.

Over much of the sample, this R-squared is actually negative, meaning one would have had a better forecast if one had simply predicted that the price of oil would not change next week as opposed to predicting that it would move in the direction and by the magnitude implied by the most recent regression of the oil price on the exchange rate. On the other hand, in the most recent data the relation appears to be statistically useful. Recently, 20% of the variance of oil prices could be accounted for by news that also mattered for the dollar/euro exchange rate.

Between January 1, 2007 and July 14, 2008, the dollar depreciated by 18%. If we take that most recent coefficient estimate of 1.76, the regression above would have predicted a logarithmic increase in the price of oil of 31%, or a move from $61/barrel in January 2007 to $83 in July. In fact, oil peaked at $145 on July 14. Since, then, the dollar has appreciated by 5.9%, while the price of oil has fallen by 23%.

The exchange rate is unquestionably one variable that influences the dollar price of oil. In recent data, as much as 20% of oil price movements could be attributed to changes in the exchange rate, or at least to news developments that matter for both exchange rates and oil prices. But that also means that 80% of what we see happening to the price of oil is completely uncorrelated with whatever might be influencing the exchange rate.