## Wednesday, September 9, 2015

### Following up

On Monday I showed this graph:

 Graph #1
and tried to describe one particular decade of it:
Consider, for example, what the graph shows between the years 1980 and 1990. It shows the Federal debt (green) running at around 5% increase, and relatively stable at that level. It also shows everybody else's debt (red) climbing from near 10% annual increase to near 30%, then falling back to below 10% during the decade.

So, I'm thinking if I look at the red line relative to the green line -- "other" debt relative to Federal -- I'd see during that decade "other" debt starts at about two times Federal, rises to about six times Federal, then falls back to around two times Federal or something less. And that's just the 1980s.

I want to follow up now by comparing two different graphs of that particular decade: one, the ratio of change from year ago values; the other, the ratio of Hodrick-Prescotts of those values.

Looking at it a little more closely now, what I described as the 1980s appears to be more like the 1982-1992 period. I hope you'll forgive that sloppiness.

Anyway, I took Graph #1 and reduced it to run from 1980-01-01 to 1992-01-01:

 Graph #2
As you may remember, the blue line is "total credit market debt" relative to GDP. The red and green are two portions of that: Green is the Federal government's portion of that debt, and red is everybody else's; both, again, relative to GDP.

I ignore the blue line, and look at the red relative to the green:

 Graph #3
This is a reduced-date-range version of Monday's Graph #2, which showed two grand spikes, a few squiggles, and nothing in the 1980s.

My description of what I expected to see in the 1980s --

during that decade "other" debt starts at about two times Federal, rises to about six times Federal, then falls back to around two times Federal or something less

is not too far off (if you go from 1983 to 1992). But my intent here is not to compare the graph to my guesstimate and conclude that I'm a good guesser. My intent is to compare Graph #3 to Graph #4:

 Graph #4
Now it gets subjective: I think #4 is a good representation of #3.

Just to clarify what's in my mind... I've been wanting for quite some time to work with Hodrick-Prescott values, smoothed-out versions of raw data. Using smoothed data in ordinary economic calculations (rather than using the raw data) just seems like it might give more easily interpretable results.

The two posts, Monday's and this follow-up, are my first opportunity to try it.