Friday, January 18, 2013

Spurious Detrending, and How We Describe Our Recessions


Consider this image:*†

Capture of Spuriously Detrended Real GDP from the 12-10-15-21 Businessweek

Graphs with a trend line like this are fairly common. They are used to present the view that 1) things used to be better, and 2) current conditions are worse.

This chart is deceptive.

It does one good thing: note that at the top it notes that a logarithmic scale is used. Using that scale — which is the mathematically correct thing to do — will tend to keep us from exaggerating our current state relative to the past.

And yet there’s the Great Recession, highlighted in pink, and circled three times (like it’s throbbing). Why is it so exaggerated if they did what they were supposed to do?

You see, this chart is also doing a bad thing: it fits a (single linear) trend through the data. Now, as explained in the handbook you may be correctly estimating the trend with your software, but if you are misapplying the idea in the first place, those nice looking estimates are junk. This is called spurious detrending, and this is an example. In this case, the spurious detrending accentuates the Great Recession.‡

Who would have an interest in making a misspecification like this? Mostly Democrats. Notice how the pink starts right after Bush takes office, and gets worse until Obama takes office. Also, note that the black shading corresponds mostly to the 1964-1981 period – with the Democratic presidents Johnson and Carter the bookends for that period (and economically liberal Republicans Nixon and Ford in the middle). It also shows the late Clinton years in black.

But Republicans might like this shading too: it makes the Reagan years look good.

The bottom line is that the shading just isn’t truly representing anything well. To see this, think about recessions. Every recession is lousy at the time, and should show up in pink when we look at the data retrospectively. But, they don’t. The postwar recessions are all there as dips in the jagged line: 1948-9, 1953-4, 1957-8, 1960-1, and 1981-2 (all correctly shown in pink), but what about 1969-70, 1973-5, 1980, 1990-1, and 2000-1 which are all shown in black! Would you be willing to go and tell all the people who were out of work in those periods … that those were the good times? And yet, that is exactly what this magazine is doing implicitly (note that the 1973-5 recession was every bit as bad as the Great Recession of 2007-9). They can get away with this because most people haven’t taken a class (like this one) where this sort of thing would be brought to their attention.

It also does a pretty bad job with the good times. Those 1950’s that people remember wistfully? They’re crap according to this chart. The boom in Clinton’s second term … is bad too. And the Bush expansion, which was rather long, and awfully good in 2005-6 … is all pink too.

* From pp. 28-29 of the October 15-21 issue of Bloomberg Business Week. Obviously, the hard copy was not interactive. You can see the interactive graphic here (although this one doesn’t do anything that you’re required to check out). What I pasted above is a screenshot of the interactive graphic.

† I could not get the interactive graphic to load in Firefox, but Chrome worked fine.

‡ I wonder whether this chart is even worse: they may not have estimated a trend at all … maybe they just drew the trend to make their point.

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