Friday, October 12, 2012

JzB, meet bJZ

Jazzbumpa considers Debt and Growth. His third graph:
Graph 3 is a scatter plot of GDP vs TCMDO YoY % change for each, FRED quarterly data from Q4, 1952 through Q2, 2012, with a best fit straight line included.

Graph 3 GDP vs TCMDO, YoY % Change

The relationship is quite clearly positive.  The R^2 value at .39 is rather low, but not terrible.  There is quite a bit of scatter in the data.

His third graph is similar to one I did a few weeks back, that did not make it to the blog. Similar, and different. Jazz's graph uses quarterly data. Mine uses annual data. I did mine again now, at FRED:

Graph #1: GDP vs TCMDO, YoY% Change (annual data)
Click graph for FRED source page #bJZ

I made the plot area taller than usual, more like a square so that a 45-degree line would look like 45 degrees. Dunno, seems appropriate for a scatter plot.

Just by eye, the annual numbers seem a lot less "scattered" than the quarterly numbers. Maybe it's just because the dots are bigger. Or maybe a given dollop of new debt needs more than three months for its effect to show up in growth.

There are two "tails" to the left of the main cluster, and one "tongue" sticking out to the right. The highest dot, part of the upper tail, is start-of-data, 1951. It probably displays effects of transition out of WWII.

The lowest dot is part of the other tail, near the end of the data. This low-GDP-growth, low-debt-growth tail displays what's been going on since the financial crisis.

The two rightmost dots, near 15% debt growth, are part of the tongue. Those two dots show the rapid debt growth of the mid-1980s.

If we were to omit the anomalies and put a trendline on the cluster...

It did not occur to me to split up the numbers into different periods as Jazz did in his Graph #4. That was a good idea -- especially if we are considering the effects of accumulating debt on the relation of debt to growth.


Jazzbumpa said...

Dang! I didn't know you could do a scatter plot at FRED.

Less scatter in annual data isn't a surprise, since it will automatically smooth the 4 qtrs.

"Or maybe a given dollop of new debt needs more than three months for its effect to show up in growth."

In my next yet-to-be written post, I'll look at time lags in YoY growth in GDP vs TCMDO, and TCMDO vs GDP (Y-axis factor, by tradition the dependent variable listed first.)

As it turns out, the slope and R^2 responses of GDP to TCMDO are highest in the current Q, and fall off rapidly in succeeding Qs.

But for TCMDO as a function of GDP, the slope and R^2 actually increase slightly for 2 Q's, then are only slightly below current Q after a full year.

Does this suggest that YoY TCMDO is a function of GDP, rather than the other way around?

I can easily believe in a bivariant feedback loop, but this still surprises me.

Very little in the tank today, and I don't feel much like writing, so it might be a few days before the post goes up.


Jerry said...

One thing that jumps out at me is - i think you guys're looking at rates-of-change (is the "YoY" year-on-year change?). So, really, you are seeing correlation between deficit and growth. Not debt and growth. But you could also look at debt (normalized somehow - tcmdo/gdp?) versus gdp growth (or something), right?

The Arthurian said...

Oh, I like that "normalized debt" idea. (I got in trouble with normalizing last time I tried it, though. Jazz got on my case. Correctly, I think.)

I think that most people associate the word "deficit" with the Federal deficit, rather than any increase in debt. So to avoid confusion I often avoid the word. Good point, though.

Well, I think I'll go normalize something.

Jazzbumpa said...

Jerry -

You don't have the math quite right. Yes we are looking at rates of change - growth in debt, growth in GDP; but no, that is not any kind of deficit. Deficit is accumulated total debt - closer to an integral than a derivative.

Normalizing is worthy of consideration. Haven't gotten there in my analysis yet.

I see Keen looks at the derivative of debt growth, which seems quite abstract to me.


The Arthurian said...

Jazz --
"Deficit is accumulated total debt"

Well I never heard THAT before. Do you have a link to that definition?

nanute said...

And here I'm thinking that debt is the total of all deficits over time. When it comes to government debt, I'd say all the borrowing to spend beyond receipts (deficit spending), would equal the total accumulated debt.