UPDATE: 29 Feb 2016
Due to some font and formatting problems (pointed out by a reader), I had to update this blog post to fix the OLS regression output tables below. I am going to see if I can "pinch and tweak" some of the formatting to see if that will help with future posts of this kind. -Rich
A quick note before I continue on with, and conclude, my blog series on gasoline and oil prices: I know that the spacing of my blog looks off in some spots. Despite my efforts to make spacing uniform, things do not come out quite correctly. I apologize. To help get my R output spacing to be more uniform, I installed the stargazer package developed by Marek Hlavac.
I am concluding this topic with this post. Here are links to my previous three posts in case you need/want to go back to them: [1], [2], and [3].
Modeling The Data
With much of the exploratory analysis complete, I will continue my analysis by performing several ordinary least-squares (OLS) regressions on the data. The results are below:
1. OLS Regression of the non-differenced price data
=============================================================================================
Dependent variable:
-------------------------------------------------------------------------
avgConvGas
(1) (2) (3)
---------------------------------------------------------------------------------------------
wti 0.052 1.108***
(0.085) (0.050)
brent 0.928*** 0.968***
(0.070) (0.024)
Constant 0.244*** 0.109 0.263***
(0.062) (0.103) (0.054)
---------------------------------------------------------------------------------------------
Observations 96 96 96
R2 0.945 0.841 0.944
Adjusted R2 0.943 0.840 0.944
Residual Std. Error 0.131 (df = 93) 0.221 (df = 94) 0.131 (df = 94)
F Statistic 793.560*** (df = 2; 93) 498.330*** (df = 1; 94) 1,597.500*** (df = 1; 94)
=============================================================================================
Note: *p<0.1; **p<0.05; ***p<0.01
Looking at the univariate regression output above, we see that the WTI crude spot price and the Brent crude spot price are statistically significant in the models where they are the sole independent variables -- see the output in the table columns (2) and (3). In the multivariate model regression output in which they are both independent variables -- table column (1) -- the WTI crude spot price is no longer statistically significant. Even though the coefficient for the WTI crude spot price is greater than zero in that model, at the 95% confidence level it could be zero in the model because zero falls within that range of values.
2. OLS Regression of the differenced price data
===========================================================================================
Dependent variable:
-----------------------------------------------------------------------
diffGas
(1) (2) (3)
-------------------------------------------------------------------------------------------
diffWTI 0.394** 1.043***
(0.181) (0.077)
diffBrent 0.706*** 1.067***
(0.181) (0.073)
Constant -0.003 -0.002 -0.004
(0.012) (0.013) (0.012)
-------------------------------------------------------------------------------------------
Observations 95 95 95
R2 0.710 0.661 0.695
Adjusted R2 0.703 0.658 0.691
Residual Std. Error 0.116 (df = 92) 0.125 (df = 93) 0.119 (df = 93)
F Statistic 112.357*** (df = 2; 92) 181.580*** (df = 1; 93) 211.444*** (df = 1; 93)
===========================================================================================
Note: *p<0.1; **p<0.05; ***p<0.01
In the regression output from the differenced values of the WTI and Brent crude spot price, the univariate models are both statistically significant, similar results to the non-differenced variable regression output. However, in the multivariate model of the differenced values, WTI crude spot price is statistically significant.
The conclusion I would draw from this is that WTI crude oil spot price is less significant than Brent crude oil spot price in regards to the U.S. gasoline spot price, but that it does have a share of the significant effect on the change in U.S. gasoline spot price.
Causal Analysis
Finally, I used the grangertest() function in R in order to perform a causal analysis on both the non-differenced and the differenced variables. This test looks for the causal relationship between the variables, like the age old question of which came first: the chicken or the egg. In the output below, I am including the results that were found to be statistically significant. (For the full run of Granger causality tests, please see my R script.)
1. Granger Causality Tests on the non-differenced price data
The two statistically significant results were that both WTI and Brent crude spot prices Granger cause the U.S. gasoline spot price:
Granger causality test
Model 1: avgConvGas ~ Lags(avgConvGas, 1:1) + Lags(c(wti + brent), 1:1)
Model 2: avgConvGas ~ Lags(avgConvGas, 1:1)
Res.Df Df F Pr(>F)
1 92
2 93 -1 3.9445 0.05 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
... and that the Brent crude spot price Granger causes U.S. gasoline spot prices:
Granger causality test
Model 1: avgConvGas ~ Lags(avgConvGas, 1:1) + Lags(brent, 1:1)
Model 2: avgConvGas ~ Lags(avgConvGas, 1:1)
Res.Df Df F Pr(>F)
1 92
2 93 -1 10.184 0.001938 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Based on the p-values of the probability values (Pr(> F)) of the F tests in the output above shows us that the Brent crude oil spot price does Granger cause U.S. gasoline spot prices -- with a significance well within the 95% confidence level. In the multivariate model, both WTI and Brent crude spot prices can be said to Granger cause U.S. gasoline spot prices. However, when I combine these results with the linear regression results above, I would say that the WTI spot price is not significant in the multivariate Granger test results and that it weighs down the effects of the Brent spot price.
2. Granger Causality Tests on the differenced price data
The statistically significant results for the differenced data was slightly different. The multivariate model results were not significant within the 5% confidence level (but were significant within the 10% confidence level.)
The model that was statistically significant again showed that Brent crude oil spot prices Granger cause U.S. gasoline spot prices:
Granger causality test
Model 1: diffGas ~ Lags(diffGas, 1:1) + Lags(diffBrent, 1:1)
Model 2: diffGas ~ Lags(diffGas, 1:1)
Res.Df Df F Pr(>F)
1 91
2 92 -1 4.0147 0.04808 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Conclusion
To bring this blog series to a close, the simple conclusion that I draw from my research and analysis is that U.S. gasoline spot prices are more influenced by the Brent crude spot price than by the WTI crude spot price. During my thesis research, the work of Dr. Phillip K. Verleger, Jr. that is listed below in the references played a large role. In the article "The Margin, Currency, and the Price of Oil", Dr. Verleger explores the hypothesis that the Brent crude oil price represents the marginal market for oil. I believe that my research and analysis replicates his work and results.
The interesting thing to watch in the coming months is whether or not the marginal market will move now that the U.S. has lifted its ban on the export of crude oil.
References:
- "U.S. gasoline prices move with Brent rather than WTI crude oil," U.S. Energy Information Agency, November 3, 2014. http://www.eia.gov/todayinenergy/detail.cfm?id=18651.
- Nathan S. Balke, Stephen P. A. Brown, Mine K. Yucel, "Crude Oil and Gasoline Prices: An Assymetric Relationship?" Federal Reserve Bank of Dallas. Economic Review, First Quarter 1998. https://www.dallasfed.org/assets/documents/research/er/1998/er9801a.pdf.
- Clive W. J. Granger, "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, vol. 37, no. 3, Aug 1969, pp. 424-38. http://www.jstor.org/stable/1912791
- James H. Stock and Mark W. Watson, Introduction to Econometrics, 2nd ed. Boston: Pearson, 2007.Introduction to Econometrics
- Philip K. Verleger, Jr., "The Determinants of Official OPEC Crude Prices," The Review of Economics and Statistics, vol. LXIV, no. 2, May 1982. Retrieved December 6, 2014. http://www.jstor.org/.
- Philip K.Verleger, Jr., "The Margin, Currency, and the Price of Oil," NABE Business Economics, vol. 46, no. 2, 2011. http://www.nabe.com/pubs.
- Philip K. Verleger, Jr., "How Wall Street Controls Oil," The International Economy, Winter 2007. http://www.international-economy.com/TIE_W07_Verleger.pdf.
