Submitted by Econbrowser

The latest CPI release provided some much needed relief on the inflation front. What caught my eye was some of the discussion regarding the seasonal adjustment. This inspired me to wonder what seasonal adjustment was doing.

From Reuters, by Emily Kaiser:

WASHINGTON (Reuters) - High gasoline prices got you down? Come to the land of seasonal adjustment, where the sun is always shining and gas prices fell 2 percent last month.

What? You paid more? Well, in the real world, gasoline prices did rise by a sharp 5.6 percent in April from a month earlier, but the way that the Bureau of Labor Statistics adjusts the figures to smooth out seasonal oddities, it appeared to be down in the consumer price index released on Wednesday.

“The drop makes absolutely no sense. Where does the BLS buy their gas?” asked Mark Vitner, senior economist at Wachovia.

No, there is not a magical government gas station where pump prices remain below $3 per gallon while the national average stands at $3.72.

Another branch of the very same U.S. government, the Department of Energy’s Energy Information Administration, said average retail gas prices actually shot up 9.5 percent in April from March.

So who’s right?

It has to do with how the Bureau of Labor Statistics compares current price trends with the norm.

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.

So, while it makes sense to do seasonal adjustment in the fashion that it is done, this article makes it clear that sometimes it can be useful to examine both the seasonally adjusted and unadjusted series.

Figure 1: CPI-All Urban, not seasonally adjusted (blue) and seasonally adjusted (red), 1982-84=100. Source: BLS via FREDII, accessed 14 May 2008.

Figure 2: Month on month inflation annualized for CPI-All Urban, not seasonally adjusted (blue) and seasonally adjusted (red), 1982-84=100. Source: BLS via FREDII, accessed 14 May 2008.Seasonally unadjusted inflation is higher seasonally adjusted last month, exactly for the reasons cited in the article. One interesting aspect, highlighted in this BLS fact sheet, is that the seasonally adjusted series is the weighted sum of the seasonally adjusted component series. This means seasonally adjusting the aggregate not-seasonally-adjusted series using the X-12 seasonal adjustment routine does not yield the official seasonally adjusted series.

While this approach makes perfect sense, one could argue another plausible approach would be to see if the seasonality in the aggregate series could be modeled. Working on the levels of the aggregate CPI does not allow for much identification of seasonal terms; but modeling the seasonal term in inflation leads to the following picture.

Figure 3: CPI-All Urban, not seasonally adjusted (teal), adjusted using X-12 with arithmetic adjustment factors, and CPI All Urban official seasonally adjusted (red), 1982-84=100. Source: BLS via FREDII, accessed 14 May 2008, and author’s calculations.I am not arguing that this is a better measure of seasonally adjusted inflation. All I want to highlight is the interesting finding that this approach leads to a higher read on CPI-All Urban inflation in 2008M04, that is 4.8% vs. 2.5% month/month, annualized. To the extent that it is harder to identify seasonal patterns in the aggregate series than in individual series, this approach is inferior.
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