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Consumers shell-shocked by ever higher records for oil and gasoline prices may have been surprised by the mild Producer Price Index (PPI) update recently issued.

The Labor Department reported that from March to April, wholesale prices rose only 0.2 percent, half of what the markets had been expecting. The primary cause for this tame reading was that energy prices fell 0.2 percent, and in particular gasoline prices fell by 4.6 percent.

What, you think I misunderstood the news?

I'll reproduce the exact quote from the CNBC article linked above, just so you believe me:

The slower than expected overall inflation was due to falling energy prices and flat food prices, categories that boosted inflation in the previous month. Energy fell 0.2 pct, the largest drop since December, while food was unchanged in the month. Within the energy sector, gasoline fell 4.6 pct, the largest drop since December.

This struck me as odd. It reminds of a line from Chico Marx: "Who are you going to believe, me or your own eyes?"

I do a lot of work in energy economics, and so I follow oil and gas prices fairly closely. Despite the official figures, I was pretty sure gasoline prices went up from March to April; they certainly didn't fall 4.6 percent! I had to get to the bottom of this mystery.

First Stop, EIA

The first thing I did was check the price history at the Energy Information Administration. Yes, this is a government entity, but I've met some of their current analysts, and they are just the sort of retentive geeks you want crunching boring but important numbers. (If any are reading, I hope they realize that is a compliment.) Lo and behold, the EIA table shows that the lowest average weekly gasoline price in April was higher than all of the weekly averages in March. Clearly gasoline was more expensive in April than in March, just as I (and every motorist in the country) would have guessed. Hmm.

To Every Price, There Is a Season

After asking some colleagues and nosing around, I hit upon the answer. No, we weren't living in 1984, you see, it was that the Bureau of Labor Statistics (which calculates CPI and PPI) had made a seasonal adjustment to the raw gasoline prices that people actually paid and that the EIA recorded. As a different CNBC article explains:

Typically, gasoline prices rise sharply in April as the arrival of warmer weather encourages people to drive more. The government data is adjusted to reflect that pattern so that it can highlight variations from the trend. Because gas prices did not rise as much last month as they typically do in April, the seasonal adjustment showed that prices fell.

Now before we see whether this can explain the anomaly, a brief digression: The paragraph quoted above is a bit too simplistic. To correctly make a seasonal adjustment, one doesn't simply look at how much prices typically rise from the prior month to the month in question. This rule might make sense if annual prices were constant, but with a backdrop of ever higher prices year after year, the rule isn't quite right.

For example, suppose that, each and every month, the price of a widget always rises by 0.3 percent, year in and year out. According to the explanation given in the CNBC article, one might think then that if we look at widget prices last month and see that (as usual) they rose exactly 0.3 percent, then we would conclude, "Ah, that's normal; they always do that from March to April. So really widget prices were flat."

But to reason in this fashion would be wrong, of course, because we would reach the same conclusion for every month, and end up thinking widgets had stayed the same price throughout the year. (In other words, every month we would say, "Oh, that 0.3 percent rise is just due to the change in month; it did that this time last year, as well.") Yet in reality, widget prices would be about 3.7 percent higher after a twelve-month cycle, so clearly we wouldn't want to seasonally adjust all the price hikes away.

The correct way to do seasonal adjustments is actually rather complicated, and different econometricians could use different approaches. (For example, how far back do you go? Do you look at the change in gasoline prices from March to April 1924 to help interpret the monthly rise in 2008?) I'm not faulting the CNBC writer for the explanation given above — notice that I'm not trying to give a better description — but I still thought it worth mentioning that the analysis wasn't quite right.

So Is the Mystery Solved?

Now at this point, I put down my Guy Fawkes mask and bulletproof vest. My government hadn't lied to me after all. Phew!

But still something bothered me. That original article said gasoline prices had fallen by 4.6 percent, when in reality they went up by a decent amount. And we know that crude prices are surging up at record-breaking levels. Could seasonal adjustments really explain all that away?

To shed light on this question, I went back to the EIA data sets. Rather than weekly averages, this time I pulled up monthly averages, going back as far as they had them (August 1990). I constructed a new table (shown below), which lists April-over-March gas price increases from 1991 through 2008. I then added a column showing the average April-over-March increase for the entire time span from a given year up through 2007. Finally, I added a back-of-the-envelope "seasonally adjusted" column, which took the 2008 value for April over March — 6.6 percent — and then subtracted the relevant monthly average for the periods of different lengths.

Year April/Mar Increase Over Prior x Years… …Period Average "Seasonally Adjusted" Chg 1991 3.5% 17 5.2% 1.4% 1992 3.8% 16 5.3% 1.3% 1993 2.5% 15 5.3% 1.2% 1994 1.9% 14 5.6% 1.0% 1995 3.6% 13 5.8% 0.8% 1996 8.3% 12 6.0% 0.6% 1997 -0.5% 11 5.8% 0.8% 1998 1.3% 10 6.4% 0.1% 1999 15.2% 9 7.0% -0.4% 2000 -3.4% 8 6.0% 0.6% 2001 10.1% 7 7.3% -0.7% 2002 11.8% 6 6.9% -0.3% 2003 -6.1% 5 5.9% 0.7% 2004 3.6% 4 8.9% -2.3% 2005 7.9% 3 10.7% -4.1% 2006 13.1% 2 12.0% -5.4% 2007 11.0% 1 11.0% -4.4% 2008 6.6%

Before proceeding, let's make sure we understand what the table is saying. In 1996, for example, gasoline prices in April were 8.3 percent higher than in March of that year. In contrast, in the year 2000, gasoline prices in April were actually 3.4 percent lower than the month before. (These numbers are shown in the second column.)

For another factoid, the table's middle columns show us that over the 17 years from 1991 through 2007, the (arithmetic) average price increase from March to April was 5.2 percent. However, in recent years the April-over-March increases have been much steeper, and that's why if we look back less distantly into the past, our average will go up. For example, if we only use a three-year average, we would say that from March to April, gasoline prices historically go up 10.7 percent.

Finally, the last column in the table simply takes the 2008 increase of 6.6 percent, and subtracts the period average for every year taken as the starting point of the period. For example, if we look back eleven years, we see that on average gas prices go up 5.8 percent from March to April. Since they went up 6.6 percent this year, we would say that — based on the previous eleven-year history — the crude seasonally adjusted price hike this year should have been +0.8 percent, because gas prices increased more this April than they usually do.

Now that we understand how the table works, we get to the fun part. Recall that the second CNBC article said that prices typically rise in April, and because this year's rise was below normal, the BLS reported a seasonally adjusted drop. Well, in the middle columns I have colored a year gray if the period average starting at that year is lower than the 2008 value. As you can see, if the BLS used a five-year window, the (crude) seasonally adjusted increase should have been positive, not negative. Indeed, only if the BLS used a window of the previous 1, 2, 3, 4, 6, 7, or 9 years, would the sign of its seasonal adjustment have been correct. For any other period length — including the nice round ones of five years and ten years — the 2008 increase is higher than the historical average.

Yet it gets worse. The BLS didn't simply report that gas prices fell, once adjusted. No, the BLS said they fell by 4.6 percent. So in the final column, I have colored green the one year for which the (makeshift) seasonally adjusted figure is lower than a 4.6 percent drop. In other words, if I adopt the crude technique suggested by the CNBC article, the only way I can generate a seasonally adjusted drop of at least 4.6 percent for 2008, is if I choose 2006 and 2007 as what happens in "typical" years. If I choose any other period length, then I will get a seasonally adjusted change that is greater than the BLS number.

What If We Don't Use a Crude Measure?

As I explained earlier, the proper way to perform seasonal adjustments really isn't what the CNBC article claimed, and yet that's the crude method I used for the table above. So it's possible that the BLS came up with its figure of minus 4.6 percent through a perfectly legitimate method. I tried to find a methodological essay on their site, but the best I came up with (due to a tip from a colleague) was a link to their latest model, which was far from edifying. I had an intuition that perhaps the increases earlier in 2008 were very large, so that the model expected 2008 on the whole to have a large increase, making the actual April increase comparatively modest. But that theory didn't work either, since the March-over-January increase in 2007 was far higher than in 2008. At this point I abandoned my quest to understand the official BLS number.

Conclusion

People have a right to be cynical about the government's official price inflation numbers. As others have downright mocked, it is crazy to report on "core" inflation, as if the impact of soaring food and energy prices can safely be neglected. In my experience, the government (at least the US government) doesn't actually lie in its periodic reports, because it doesn't need to: when it comes to models in the social sciences, there are all sorts of dials one can turn to get just about any result desired.

What really bothers me in this whole episode is that the press is so sloppy. I don't expect the average business reporter to pontificate on the evils of fiat money — of course not. But the CNBC story I cited originally reported things that were false. It was not true that "gasoline fell 4.6 percent" in April. No, the correct thing to say would have been, "After making a seasonal adjustment, the BLS reported that gasoline prices fell…"

The government wants to shape perceptions in order to minimize dissatisfaction with its irresponsible monetary and fiscal policies. When the financial press goes along and parrots statements that are obviously false, it fails in its duty to its readers.