## Thursday, December 4, 2014

### Gasoline and Brent

Over two years ago Jim Hamilton posted that the relationship between the retail price of U.S. gasoline and the price of Brent, empirically, is given by

$$g_t = 0.839 + 0.02499 b_t + e_t,$$

an equation that comes from an OLS regression of weekly prices of gasoline on prices of Brent oil, from 2000 through June 2012. $$R^2=0.962$$ and the standard errors of the constant and the slope coefficients are $$s_\alpha=0.013$$ and $$s_\beta=0.00019$$. (Gasoline and Brent, by the way, are cointegrated.)

Jim explains why the numbers are what one would expect, given that one barrel of oil holds 42 gallons, and average taxes on gasoline, refining costs, and markups.

Given the recent slump in oil prices, I was curious to see what would be the predicted and actual prices of gasoline for this week.

First, I update the data through the week of November 24* (the most recent for which FRED has data for both gasoline and Brent) and run the regression. The estimated coefficients are now

$$g_t = 0.8429 + 0.0249 b_t + e_t$$

with $$R^2=0.9646$$ and standard errors $$s_\alpha=0.0129$$ and $$s_\beta=0.00017$$.

Here I show you the actual (red) and predicted prices (blue) of gasoline:

The most recent data point for Brent, for the week that ended on December 1, 2014, is $74.44, which produces a predicted gasoline price of$2.69 per gallon, down from the previous week's $2.82. The average price of Brent Tuesday, Wednesday and so far today has been about$70. If the average weekly price were to stay at $70 through next Monday, the predicted price of gasoline this week would be$2.59, marginally lower than last week's.

How about the year ahead? With the caveat that predicting oil prices is in that grey area between the brave and the foolish, the November panel of forecasters polled by Consensus Forecasts produced an average forecast for Brent of $91 for the end of November 2015. That's a whopping$17 increase from last week's price, and would put gasoline prices back above $3/gallon ($3.11, to be more precise).

*Note: the EIA's website provides slightly more up-to-date gasoline prices, but the series is not identical to the one on FRED--the two differ by about \$0.085 lately.