Following up

On Saturday I showed consumer debt on a log scale. It showed pretty much a straight-line increase.

Then I said the log scale graph provided no context for consumer debt, and that in context the graph would show much less of a straight-line increase. So I showed a graph of consumer debt relative to GDP, consumer debt in context. And sure enough, the graph showed much less of a straight-line increase.

Something's been bothering me for two days now. I remember Stuart Staniford saying it's hard to read changes in small growth rates on a log graph. And I'm concerned that my first graph hides changes because it's a log graph. I'm concerned that my second graph shows much more deviation from the straight-line increase because it's *not* a log graph.

So I went back to FRED and looked at "consumer debt on a log scale" again. And this time I put "consumer debt relative to GDP" on the same graph. And I made sure to show the log values of the second line this time.

Graph #1: "Consumer Debt" on a Log Scale (blue) and Log of the "Consumer Debt to GDP" ratio (red)

Consumer debt on a log scale shows a straight-line increase. Consumer debt in the context of GDP does not show a straight-line increase, and this is true even when Log values are shown.

So yes: "Consumer debt relative to GDP" fails to show the straight-line increase because of the context variable: because of GDP. It's the context that distorts the picture.

(At FRED, when you have the ratio of two series, you cannot show the values "on a log scale". To get the same effect you have to take the Log of the values. I'm not sure why that is, really. But I did look into it. The two methods are equivalent.)