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2019-04-04Macro `n Cheese

Hassling Hassett

A short and snappy read from Roger this week, on the topic of residual seasonality

Over the past few years, we have held a lot of discussions on the prevalence of “residual seasonality” in US data. In particular, the BEA seems to have had problems with first quarter data. However, the BEA’s comprehensive update of 2018 included a revision of the methodology, which is why this problem was supposed to have been addressed. Thus, it was with no small degree of irony that econ twitter responded to CEA chair Kevin Hassett’s claim from a couple of weeks ago that residual seasonality is to blame for the weak start to Q1:

 

Imagine, however, if there is something to that notion. Imagine if the current FED and market anxiety about soft US data is just a fad. It would be a twist of irony if we are again being fooled by statistical quirks into thinking that the US is heading for a slowdown of some unknown magnitude, wouldn’t you agree?

 

– I guess most of you reading now are nodding. And – worryingly – the charts above show the same pattern (we should expect all quarters to grow equally, at least over longer samples); weak Q1 and strong Q2, while Q3 and Q4 are similar – and it doesn’t matter much how you change the sample ranges.

But how should we go about investigating this more formally? – Well, academics have already come to our rescue, and the preferred approach is actually quite straightforward; just run the time series of your choice through the seasonal adjustment process a second time! If there is no residual seasonality then, by definition, the seasonal factors must be ‘0’![1] The preferred choice for double-adjusting in previous studies seem to be the Census X-12 method, but when trying to emulate their results, we find that the ARIMA X-11 method produces very similar findings (which is not strange, since the methods are basically the same). Lo and behold, when double-adjusting with the X-11 procedure in the Macrobond application, a considerably more stable quarterly profile emerges:

[1] Pro-tip: US is not the only country with seasonal adjustment troubles. Do double-check a statistical agency near you.

 

Now, we can imagine a host of ways of better fitting the seasonal adjustment, but I do urge you to remember that a seasonal adjustment procedure normally needs at least 20-30 years of data (five is considered an absolute minimum) to perform well. Also, do note that structural changes are already taken into consideration in the more advanced seasonal adjustment procedures Macrobond supplies.

The graph below shows the first quarter seasonal factors between 2003 and 2018. As we noted above, if the seasonal adjustment procedure was perfect, this would be a straight line at ‘0’. It is not.

 

So, when all is said and done are the weak Q1-numbers just a statistical quirk that will recoil in Q2. No, not that easy I’m afraid. The most recent study referred to above, conveniently only plotted the double adjusted Q1 numbers (as I have in the graph above). With the risk of sounding like a party-pooper (which I probably am anyway) that kind of takes away important information. Let’s rather look at the whole story:

 

Clearly, there are still some repetitive patterns in the data, but whether this is yet another change to the seasonal patterns, or just a twist of fate, remains to be seen. Anyway, the pun here is that hassling Hassett was perhaps a tad premature. ‘Real’Q1 GDP-growth is probably stronger than whatever the BEA will be reporting, and in particular Q2 will probably come across as stronger than what it ‘really’ is. As if this forecasting stuff wasn’t sufficiently complicated…

Do you know what? – Maybe there is something to be said for that unadjusted % YoY-number us Europeans are using after all! It is too bad the BEA doesn’t supply it.

 

 

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