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) |

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.)

## 1 comment:

I one way of looking at the data doesn't give a clear picture, it can be sliced another way.

Denominators can both provide context and be misleading, depending on the circumstances.

Since you're interested in growth rates, why not look at that aspect directly?

http://research.stlouisfed.org/fred2/graph/?g=qjd

I think I riffed on this graph a couple of days ago at another post.

Cheers!

JzB

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