Thursday, February 12, 2009

Retail Sales Gain Could Be Seasonal Adjustment Error

When comparing changes in monthly activities, it is often misleading to compare raw data when trying to estimate trend changes. The reason for this is that some activities tend to change on a seasonal basis. Retail sales for example tend to be extra large before Christmas. Similarly, some data could change because of calendar factors, because different months different number of working days. That is why much data is adjusted for calendar and seasonal factors.

There's nothing improper about that principle, but the problem is that these adjustments aren't as easy to do in practice as one might think, because like other phenomena’s, the effects of these seasonal factors tend to vary. For example, while it is to be expected that January retail sales will be lower than December retail sales because of the seasonal factor of Christmas, just how much should you seasonally adjust? Given the fact that the relative preference for Christmas purchases over regular purchases fluctuate, it is not as easy simply running some kind of statistical regression over historical data fluctuations. Indeed, it is arguably impossible to correctly estimate each year that fluctuating preference and separate it from trend movements.

Because it is impossible, statisticians have little choice but to use historical data to estimate it, so you could hardly blame them. But what this means is that we should take monthly changes with a grain of salt and not pretend that they really exactly estimate trend movements.

It is in this light we should see the surprising increase in U.S. retail sales for January that were announced today, and that followed several months of steep declines. Some economists have argued that this was probably due to seasonal adjustment problems, and I agree. The unadjusted number actually fell 19.7% compared to December 2008, while the adjusted number rose 1%. In other words, there was an enormous seasonal factor imputed.

A too great seasonal upward adjustment of the monthly change from December to January could reflect that the seasonal downward adjustment for December was too great. A too big seasonal downward adjustment would in turn reflect that they overestimate how great the preference for Christmas purchases was. Is there any reason to believe that the preference for Christmas purchases over regular purchases could be lower this year than usual? Yes, I would argue that there is one good reason, namely the recession. In hard times, people would presumably make everyday purchases of food and other necessities a higher priority than expensive Christmas gifts than usual, and so the relative preference for Christmas purchases was lower than before.

This means that while the seasonally adjusted decline in December wasn't as large as reported, retail sales probably didn't really rise in January.


Blogger Ron McK said...

December 2008 had only three weekends before Christmas, whereas the previous two Decembers had four weekends prior to Christmas. This may have pushed some weekend Christmas shopping pushed back into November in 2008.

Trading day changes are even harder to adust for than other seasonal patterns, so this may have caused December 2008 to be adjusted futher down than it should have been, producing the greater increase to January.

1:05 AM  

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