Recalculatin debt service

In the test-and-development version of Wednesday's post there remain some notes. This one,

ALSO
TOTAL DEBT WE BORROW IS GREATER THAN THE REPORTED NUMBERS BECAUSE WE ARE ALWAYS PAYING DEBT DOWN

and a handful of links to other debt service posts I've done.

In Debt service (3 July 2016), Graph #5 shows "Principal Repayment as a Percent of Household Debt" running near 4.5% all thru the 1990s, and averaging perhaps near 4.5% even after the 1990s. Independently, 4.5% was also my best guess number for principal repayment as a percent of household debt in mine of 22 January. So I thought I was onto something.

I was thinkin maybe I could use that graph for principal repayment numbers all the way back to the 1950s. Unfortunately, when I checked Graph #5, it turned out to be based on FRED's TDSP debt service, which means it only goes back to 1980. So the graph gains me nothing.

So then I was wonderin: How could principal repayment vary so much from a fixed percentage of the debt we owe?

It would vary with economic conditions, probably. If the economy was good, people could better afford to pay down debt. If the economy was bad, people could less afford to pay down debt. That could be part of it. Or the other way around: Maybe when the economy is good, people feel less urgency about paying down debt. But when things suddenly go bad, as in 2008, people feel more urgency, and make paying down debt a higher priority, so the repayment ratio goes up.

I don't know what to do with that.

Maybe it varies with "short term loans", loans that last less than a year. On average, maybe half of those are paid off before the end-of-year roundup when stats are tallied.
// But they do it Quarterly, Art.
Still, some of that short-term debt must slip through the cracks and miss being counted as debt.

If short term debt varies as a percent of debt, then the "slip through the cracks" number would vary as well.

I don't know how much sense this all makes, but it flashed thru my mind quicker than I could write it down, and I made a graph comparing "principal repayment as a percent of debt" to "short term loans as a percent of debt". I see some similarity:

Graph #1: Principal Repayment (blue) and Short Term Loans as Percent of Debt (red)

Some pattern similarity, yeah. Notice, though, that the red line references the right-hand scale, and the right-scale numbers are substantially bigger than the left-scale numbers. So, maybe substantially less than all of the short term debt has influence. As I imagined above.

I divided the red numbers by 6 and added 0.25 "to make the two series comparable", as Milton Friedman would say. I changed the frequency to annual, to get rid of the jiggies. And voila:

Graph #2: The same, but better

It's not a perfect match, red to blue, but it is interesting. I see the red runs higher than the blue coming out of the recessions of the early 1980s and thru the good period that followed, and again in the "goldilocks" of the 1990s. Some relation of red-above-blue to a good economy? Maybe. (BTW it looks like the red is about to go above the blue again just now.)

In the early years, the red line reaches 6.5%, over one third more than the 4.5% figure I noted above. At that rate, using the short term loan number instead of the constant value 4.5% should increase my estimate of principal repayment by as much as 30% or more. So I want to use this data, the red line here, as a guess at principle repayment as a percent of debt owed.

Yeah, you know what? The red line is higher on the left (when debt was low) and lower on the right (when debt is high). Makes sense, we can pay off a greater percentage of our debt when we don't have so much of it. I'm goin with this.


This is what I did on the 22nd:

"I can set up a calculation where I take interest paid, add some percentage of existing debt, and divide the total by disposable income."

This is what I'm doing today:

"I can tweak the percentage number..."

And again:

"The percentage number I get will be a rough estimate of how much debt we repay each year."

and it'll be based on "Short Term Loans as Percent of Debt".

I'll take my graph from the 22nd, duplicate the red line in green, then eliminate the 0.045 (4.5%) as percent of debt repaid and use the other thing.

Here's what I get:

Graph #3: Debt Service using a Guestimated Variable Measure of Principal Repayment (green)

Damn! It sure doesn't look like a 30% increase, going from red to green. Almost not worth the trouble of figuring.

I had the same trouble yesterday. Oh, first I had trouble with the short-term-loan calculation. (I was trying to do it without coffee.) Then when I finally got it right and plugged it in to the repayment-of-principal calculation, I got the same tiny increase you see in that last graph above.

I fiddled with it yesterday and couldn't get it to come out as I expected, so I set it aside. That delayed this post till today, and I put up the "tiresome warnings" post instead. This morning I created the graph again, along with my 3AM coffee.

I got the same result today, so maybe it's not wrong. But it sure doesn't look like a 30% increase. I have to check some numbers. I want to start with the red high points on Graph #2: 1950 (6.55837) and 1973 (6.49469), both well above the 4.5% of my prior calculation.

Table #1: Checking the High Points on the Red Line of Graph #2:

Year	1950	1973
Household Debt	74.845	613.133
Est. % of Debt Repaid	6.558	6.495
Est Debt Repaid (billions)	4.909	39.821
Household Interest Paid	4.155	48.779
Principal & Interest (billions)	9.064	88.600
DPI (billions)	214.823	1008.383
Principal & Interest as Percent of DPI	4.2	8.8

Checking next the percentages that are not 30: Reading off Graph #3 at FRED, for 1950 the red line's value is 3.50196. The green's value is 4.21911, or 20.5% more than the red. For 1973 the red is 7.57358. The green, at 8.78644, is 16.0% higher than the red value for 1973.

These values are figured for the dates with the highest estimates of "principal repayment as a percent of household debt" on Graph #2. As the values fall, the principle repayment percentage also falls from 20.5% (or 16.0%) to lower values. On average, then, on Graph #3 the green values are nowhere near 30% higher than the red values.

And Graph #3 is right. But why is my 30% guess so far off?

1. We add principal repayment and interest payment together to get the debt service payment. If we reduce the principal repayment but do not change the interest payment, the debt service payment changes by a smaller percentage than the principal repayment.
2. Where the values are expressed as "percent of DPI" rather than percent of household debt, those values are affected by the changes in the Debt-to-DPI ratio. When the ratio is less than 1.00, as it was for all years before 2002, the payment is a smaller percentage of DPI than of debt.

These factors, and perhaps others, push the calculated percentages down below my 30% estimate.

Looking at this picture a different way, my "short-term-debt"-based estimate of the principle repayment percentage (red line, Graph #2) is high early and low late. I think this is realistic. When the debt accumulation is small relative to income, it is fairly easy to repay a higher percentage of that debt. But when the debt accumulation is large, repaying even a small percentage of that debt consumes a large portion of income.

I wouldn't be surprised if the actual principle repayment percentage value was substantially higher in the early years than what my graphs show.

Meanwhile, having these numbers to look at is better than nothing.