Friday, February 12, 2016

The $10 Per Barrel Oil Tax Will Not Increase Gas Prices by 24 Cents a Gallon (Not That it Matters Anyways)


Roughly a week ago (2/4/2016), President Obama announced the details of his final presidential budget. It included measures to curb homelessness in veterans and in the general public, some money for NASA, but of all the stuff packed in, one proposal shone through as if it were a red dot and the Internet was filled with cats. (Which, to be fair, it basically is).



That's right: President Obama proposed a $10 per barrel tax on oil imported into and used in the United States. And judging by how people reacted, he presumably did this with malicious intent and baleful glee:


Want to know the surprising thing about the $0.24 figure, though? It's (probably) bogus. 

Admittedly that might not be the most surprising thing considering the title of this article, but, hey, sue me.1   

There are two convergent sources for the number. And since we always hear about how gas prices are affected by everything from the stock market to international relations, I'm sure that they are incredibly sophistica-


Oh...

That first equation I saw floating around on Twitter. Someone effectively said "hey! $10 a barrel, 42 gallons to a barrel, do some 'rithmetic and we get .24 cents." Which, yes, is exactly as correct as it seems on first blush. 1: If economics were that simple, then a monkey could literally do it. 2: Not all of a barrel of oil goes to the production of gasoline. In fact, industry estimates puts it at around 45-50%. It's still the biggest product but not the only product.

Image source: Investing Daily

That second equation is a bit more complicated and relies on what we egg-heads call Ordinary Least Squares (OLS) Regression. In laymen's terms, it allows us to parse through a bunch of data to come up with an estimate of how much one factor influences another. When you use available data from the federal government, this estimate too comes out to (roughly) a $0.24-0.30 increase.

There's a lot of hairy math and way more nuance involved (trust me, I'm taking a seminar in it this semester) but it helps us determine how significant an impact is. The problem in this case is subtle but really important. This model assumes that the price of oil in week 1 directly impacts the price of gas in the same week. Basically, there's no lag-- the effects are assumed to be simultaneous. Which, unless we're talking about quantum entanglement, is simply not the case.

This objection makes intuitive sense when you think about your job: How quickly are you really able to implement a change coming from the top into your day-to-day operations? It takes some time, right? Plus what happened in the previous days and weeks will affect what's happening now. Which is why the price of gas the previous week is actually a better estimate of price than the contemporaneous price of oil.

In order to really estimate what's going to happen, we need to employ what's called time series analysis. We're going to take a look at how the prices of oil and gas over time influence the price now.

*Full disclosure: I am still relatively new to doing this sort of statistical work, so input and constructive criticism from veteran social scientists and statisticians is definitely appreciated. But even if I'm still a bit green, it's still loads better than the bologna that certain media outlets have been pushing.*

I collected the weekly averages for the price of unleaded gasoline and Brent oil in the United States from November 1994 to the present2. I then tried to figure out how long of a lag to take into consideration and how far into the future I want to predict. I figured that any more than six weeks prior is really sort of stretching it (a lot can happen in six weeks and we'd get diminishing returns) and that predicting 4 weeks out is probably the furthest we could say for the same reason. But we could go further back, by the way. I decided to test how strong a predictor gas prices from half a year before were on prices today for kicks and giggles. I was expecting a null relationship but....

These numbers basically translate to me saying "You've got to be screwing with me."

I then decided to play with the hyperbolic scenario espoused by the punditry: An immediate $10 hike on oil. This, by the way, is incredibly unlikely since President Obama's (admittedly vague) plan said that it would be phased in over a matter of years. I took the average price of oil over the last six weeks and projected it over the next four (a huge no-no, by the way, but it turns out that predicting oil prices is harder than predicting gasoline. It's not a perfect proxy, but it will do considering how constrained our time-horizon is and how highly correlated the lagged price of oil is on its current price). I then went to Stata, ran the model, (full results in the appendix below), and then predicted what the price would be with a $10 hike and without a $10 hike.

(Note: Differences and weekly changes in price have been truncated and rounded via google sheets-- explaining why the numbers don't all gel perfectly).



The model is showing that-- even in the worst case scenario-- the price of gas would go up 21 cents after 4 weeks. This number is the most volatile, though; I'm much more comfortable asserting that the impact would be 11 cents the week immediately following the hike and 15 cents the subsequent one. After that, other market forces will decide whether that skyrockets, plummets, or stays relatively constant. Astute readers will notice, however, that none of these numbers are 24-30 cents per gallon.

A much more reasonable assumption is that the tax would come in waves. Maybe starting with an initial immediate increase of $3. Then, once manufacturers, consumers, and the market writ large manage to normalize and absorb the increase, tax again. This will reduce the overall burden on the consumers at the pump and at all the other places that we purchase oil-based products from (i.e., everywhere).



The model levies that the increase over four weeks would be 6 cents and over two it would be 5 (again, truncated and rounded via google sheets). What's really important is the changes from week to week between the tax and the no tax. Although you see an immediate increase,  the two are effectively indistinguishable afterwards. If done correctly, after an initial 3-6 cents, the prices of gasoline would not naturally3 waver any differently than the price of gas without the tax.

So what does this all mean? Bluntly, that predictive econometrics is black magic with a grimoire written in some indecipherable language.

Wait a minute...

But if we afford more than just a cursory glance at the book, we'll find that the proposed oil hike would probably not act as a $0.24 gas tax. It would undoubtedly cause an impact-- but it would be much milder.

What about the second part of the title?  The whole "not that it matters" bit? Well, it turns out that not only did Speaker of the House Paul Ryan declare the bill "Dead on Arrival," house Republicans have broken with decorum and are refusing to even hear the President's budget. Now, rejecting, ignoring, and effectively mocking a president's budget is a time-honored tradition sustained by both parties. This, however, is a brand new precedent.

"That was anticlimactic and mildly infuriating," you might be saying.

Yep.

Welcome to partisan politics.




Notes

1: Please don't.
2: Gasoline prices can be found here and Brent oil can be found here.
3: I say "not naturally" because these things are not on auto-pilot. Conscious decisions have to come into play. So if this tax were to happen and the price were to shoot up 24 cents, it was probably not due to the machinations of the market. Considering that the people pushing the 24 cent narrative have overwhelmingly been representatives of the oil and gas companies, a punitive "self-fulfilling prophecy" is possible.



Appendix

Each lag is a week so glag1 is price of gas lagged by one week, glag2 is two weeks, et cetera. Same deal with lags in the price of oil (olag)




The negative signs are an expression of multicollinearity-- a fancy word which basically means that the two factors are highly correlated with each other to the point where the computer has a hard time explaining how much is really caused by A or B. It's a problem in understanding the impact of the variables individually but not so much in estimating the price--which is what we're interested in here.  

Peter Licari Student in Political Behavior and Elections

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