Monday, September 7, 2015


We ended up last time looking at debt relative to debt. Maybe you don't like that so much, because in this world things are always shown "relative to GDP".

Hmm. Debt was growing a lot faster than GDP for more than half a century. So debt numbers are way bigger than GDP numbers. So, what you use for context might depend on what you want to see.

If you want to make the Federal debt look small, you could compare it to a big number like total debt. If you want to make it look big, you compare it to a small number like GDP.

Of course, you might just want to find out about the Federal debt (or whatever data you're looking at) without trying to make it look small or anything like that. I suppose you could compare it to GDP and also to total debt, as I did in the previous post.

And, all data aside, you should want to think about the context variable. You should want to think about whether GDP is always and everywhere the right variable to use when you're looking at things "relative to" things.

Of course GDP is not always and everywhere the right variable to use.


Irony of ironies: Turns out I'm going back to "relative to GDP" for this post. Truth be told, I got motivated to write the previous post because I happened upon my old Change in Debt post, which shows changes in debt relative to GDP.

The old post has an "old" style FRED graph. Here's the updated version:

Graph #1
The green line shows the Federal debt, relative to GDP. We looked at that last time, except last time it was accumulated Federal debt relative to GDP. This time it is change from year ago values, relative to GDP. So the numbers are not as high this time. But maybe it's easier to see changes.

The red and blue also show "change in debt" relative to GDP. Blue shows changes in total credit market debt (or credit market "instruments" as they are now called). Red shows changes in "other" credit market debt -- by which I mean all of it except what the Federal government owes.

Looking at Graph #1, I find a couple interesting things. One is that, in the years before 1970, the Federal debt was tangled up with the zero line, meaning almost no growth of Federal debt ("relative to GDP"). But "other" debt was running close to the 10% line -- meaning that debt other than the Federal debt was growing nearly 10% every year.

That's a big difference. If you start with $1 in (say) 1952 and it grows zero percent every year until 1970, in 1970 you still have just $1. But if you start with $1 in 1952 and it grows ten percent every year until 1970, then in 1970 you have $5.56.

So, in the years before 1970 on Graph #1, we can guess that the Federal debt grew about 5½ times slower than everybody else's debt. Or turn it the other way and say everybody else's debt grew about 5½ times faster than the Federal debt.


After 1970 or so, the growth rates on Graph #1 pick up the pace. Federal debt growth moves up to around 5%. "Other" debt varies, but reaches as high as 30%. In my view, the 20 years or so when the Federal debt was not growing, and everybody else's debt was growing around 10%, those 20 years of disparate debt growth created imbalances in the economy. The imbalances reduced economic growth, which led to a higher rate of Federal debt growth. That's why we see the Federal debt running higher between 1970 and 2000 than in the years before 1970.

But that's just what I think. It's not what this post is about.

This post is about the two different debt growth rates -- the rate for Federal debt and the rate for everybody else's debt. 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.

Instead of describing what all six and a half decades might look like, it is much easier just to show the graph. Unfortunately, these are "change from year ago" values. We're looking at changes. And sometimes the changes are large and sudden. So when I take "other" debt from Graph #1 (red) and look at it relative to Federal debt from the same graph, it comes out like this:

Graph #2
Two of the values are so large, and most of the other values are  so close to zero, that no discernible pattern appears on the graph.

I think I know what the decade of the 1980s should look like on Graph #2, but there is nothing there to see.

I could change the start- and end-dates on the graph and probably get something useful. But then I'd be missing five and one-half decades of the pattern I want to see. So I need a different strategy.


Oh, by the way: I'm taking "100 times Other Debt divided by GDP" and dividing it by "100 times Federal Debt divided by GDP". When I do that I have 100 on the top and 100 on the bottom, so they cancel out. And I have GDP on the bottom and GDP on the top, so they cancel out, too. So I'm left with Other Debt divided by Federal Debt.

No GDP for context!


I downloaded the excel file from FRED for the data in Graph #1 ... deleted the blue line for total (Federal plus Other) debt ... and made a graph in Excel to show Federal and Other (separately). The two are a good match to the green and red lines on Graph #1. (I check my work.)

Then I figured Hodrick-Prescott values for the two debt series, to smooth out the lines. I'm thinking when I recreate Graph #2 using the smoothed-out numbers, I won't get those crazy spikes. So I'll be able to see the pattern of Other relative to Federal for the whole period of the graph. Hopefully.

Just a reminder: If I'm successful we'll be looking at "change from year ago" of "other" debt as a multiple of "change from year ago" of the Federal debt. And we should be looking at better results than we have on Graph #2.


The FRED data I started with is quarterly. The recommended "lambda" value for the Hodrick-Prescott calc is 1600 for quarterly data. But that smooths the numbers out much more than I want. So I switched right away to a lambda of 100 -- the recommended value for annual data. Messed with it a bit and reduced the lambda values to 10. Now the H-P lines hug the FRED data pretty closely:

Graph #3
Now the next step is to do the "Other divided by Federal" again, this time using the Hodrick-Prescott data values.

Oh, by the way, I did my Hodrick-Prescott twiddle using Kurt Annen's HP-Filter Excel Add-In.

So I made the graph, and it wasn't much different than #2 above. Changed my lambda numbers back to 50, messed with it, and stuck with 50.

I don't know what to make of the result:

Graph #4


The Excel file with graphs, data, calcs, and Kurt Annen's H-P code is available for download at Google Drive.

// Monday Morning Update

I looked at Graph #4 this morning and decided to just graph the section between the really high spikes.

Graph #5
Well that's better! Looks like the spikes die as recessions arise. We might have expected that. What's more interesting, I think, is that the height achieved  by the spikes drops consistently, over a range of five spikes and for a 30-year period (1963-1993). We can say that a dollar increase in the Federal debt produced less and less of a private-sector response throughout that 30-year period. That's interesting, I think.

// The revised Excel file.


The Arthurian said...

probably important to keep in mind that we're not looking at debt numbers, but hodrick prescott numbers.

The Arthurian said...

also interesting:
between 1961 and 1973, the three low points all come at about the same level, between 5 and 10, maybe 7½ or 8.
between 1973 and 1993 the three lows are again about at the same level. but that level is 5 points lower than the 1961-1973 lows.

jim said...

I don't think there is much new info to be gained from the (change in other debt)/(change in federal debt) graph. All it says is that when federal deficit is near zero you get huge spikes in the graph and when the federal deficit is farthest from zero you get small spikes.

The Arthurian said...

I don't know, Jim. Take the 1980s for example. Jazzbumpa and I have been arguing for weeks whether it is the high level of debt in the 1980s, or the period of increase leading up to that, which qualifies as an "explosion" of Federal debt.

But I don't see much of either on that last graph, there.

The graph might at least be worth pondering.