Wednesday, April 26, 2006

More on gas prices, Iraq and Bush's Ratings

The Professor Pollkatz graph I linked to last week generated a bit of a stir, it was even mentioned on the Rush Limbaugh show, was picked up by a number of blogs that I enjoy (including the J-Walk blog). Many comments on other blogs admitted to a correlation between gas prices and Presidential ratings but disputed that there was a direct causation. In other words, the relationship was mainly spurious in nature. I doubt this, for any number of reasons, but it is possible that time series can seem highly correlated when there is, in actuality, no true relationship.

In this evolving entry, I will investigate in more detail the relationship between Iraq death count, gasoline prices, and President Bush's rating. I have monthly data from February 2001 through February 2006. I have monthly reported U.S. deaths in Operation Iraqi Freedom, the U.S. average price for a gallon of regular unleaded gasoline, and the Presidential Approval Rating from Gallup. I have also gathered and created other variables that might be useful in explaining Presidential approval ratings, including monthly national unemployment, the number of heating days in the month (as reported by the U.S. Energy Information Agency), the capacity and utilization of domestic oil refineries (as reported by the U.S. EIA), whether the month corresponded to the two months before and the month of a national election, whether the month corresponded to a major event, including 9/11, the invasion of Afghanistan, the invasion of Iraq, hurricanes Katrina and Rita, the first and second elections in Iraq. I also created a dummy variable that takes a value of one for the month of what I term a gasoline related event, including the two hurricanes.

I first attempted to recreated the picture by PollKatz, which I was able to do fairly accurately.



I also plotted the monthly presidential ratings against the monthly death count from Operation Iraqi Freedom (OIF), the relationship seems to suggest an inverse relationship between the number of deaths in a given month and the President's approval rating:



As I mentioned, there are a number of techniques that statisticians and econometricians have developed to help determine the difference between causation and correlation. One "easy" way is to test so-called Granger Causality GC, which essentially asks whether there is a causative relationship between two variables X and Y. The causative relationship can go from X to Y only, Y to X only, or Y to X and X to Y.

Granger causation is tested by regressing Y on an arbitrary number of its own lagged values and the same number of lagged values of X. If the hypothesis that the parameters on the lagged values of X are jointly equal to zero is rejected, it is claimed that X GC Y. To test the reverse, we flip the dependent variable to be X rather than Y.

I did this for the relationship between Presidential Ratings and Gas Prices and Presidential Ratings and Monthly OIF Deaths using three lags (one quarter):

H₀: Gas price does not Granger-cause Rating: chi2(3) = 7.95 p = 0.04.

H₀: OIF Deaths do not Granger-cause Rating: chi2(3) = 6.90 p=0.07

chi2(3) indicates a Chi-squared test statistic with three degrees of freedom. The standard of 5% significance level is good enough for me. Therefore we can reject the first null at the 5 percent level and conclude that gas prices do GC presidential ratings. At the 7 percent level we can conclude that Iraqi deaths do GC presidential ratings.

Therefore one answer to the question asked in the title of my original post "Gas Prices, Iraq, or Both?" is: BOTH.

I flipped the relationship around to test for mutual causation (it might be expected with gas prices but would not be expected with Iraqi deaths)

H₀: Ratings does not Granger-cause Gas Price: chi2(3)=11.32 p=0.01

H₀: Ratings does not Granger-cause OIF Deaths: chi2(3)=5.59 p=.13

Here, we find that Presidential Ratings ratings seem to GC gas prices but Presidential Ratings have no causal relationship with OIF Deaths, which should make the troops in Iraq feel better.

Does it make sense that ratings could GC gas prices? If Presidential Ratings are reflective of an overall mood of lowered or negative expectations about the immediate present and the near future, then gas prices might change with Presidential Ratings. However, is this truly causation or reflective of a different variable (call it general social mood) that drives both Presidential Ratings and gasoline prices? This is one of the obvious limitations with the Granger Causality approach. Nevertheless, it is a cheap and dirty way to try to extricate whether there is an inter-temporal relationship between two variables.

Finally, it is necessary to investigate Granger causality between gasoline prices and OIF deaths. This is the crux of the problem, as it is likely that events in Iraq and the greater Middle East are contributing to changes in gasoline prices. If this is the case, a structural model might be necessary to fully identify the separate contributions of gasoline prices and OIF deaths on presidential approval ratings.

The results follow intuition:

H₀: OIF deaths Granger-cause Gas Price: chi2(3)= 9.70 p=0.02

H₀: Gas price Granger-cause OIF deaths: chi2(3) = 6.29 p=.09

The Granger causation tests suggest that OIF deaths cause gas prices at the 2% confidence level but at conventional levels OIF deaths are not caused by gasoline prices (although if one was happy with the 10% significance level, there is limited evidence of some causation).

Therefore, there seems to be a more complicated relationship between OIF deaths, gasoline prices, and presidential approval rating than the initial Prof. Pollkatz (and my graph above) seem to suggest. It is therefore necessary to move beyond the bivariate Granger causation tests to a more sophisticated analysis. The next step will be to look at Vector Autoregression (VAR) models and impulse response functions. Eventually, it is likely that a structural model will have to be developed with which it is possible to estimate exactly how much OIF deaths and gasoline prices separately contribute to presidential ratings.

posted at 4/26/2006 10:23:00 PM (2) comments

Comments:

If you want to see if there is a causal relation there, you really need to pull the bumps out that are obviously caused by third variables (9-11, Iraq war onset, Saddam captured), and if you probably should linearly detrend both as well.

# posted by  Anonymous : 7:26 PM

 

Do you have updated graphs? Do the curves of inverted gas prices over administratino ratings still appear to be closely tied?

# posted by  Anonymous : 11:29 AM

 

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