Conclusions

A lot of graphs here lately, looking at the federal debt as a percent of GDP. I hope these posts don't frustrate you. I hope you find them interesting. For some reason, I seem to think it necessary to share with you an example of the "struggle with numbers" that occupies so much of my time.

Maybe that is part of the "being more personal" thing that was among my New Year's resolutions this year.

See, now I think that is funny.

You may notice, in these recent posts, that I do a lot of looking at the numbers, but not a lot of drawing conclusions from them.


If we lived in a society where everybody thought they would live forever if only they could get to the moons of Jupiter, astronomy would be different than it is today. It would be more like economics.

Everyone who has touched money has "experience" with the economy and "views" about it. And this personal aspect of our subject affects the conclusions we reach.

And I think the conclusions we reach -- or at least the conclusions that policy-makers reach -- are clearly, obviously, outstandingly wrong.

I think it is easy to get the conclusions wrong, when you have "experience" and "views" and a vested interest in a thing.

I do my best to avoid reaching conclusions. I try to look at evidence until the conclusions presenting themselves become undeniable.

I do not jump to conclusions. I jump away from them.

Doubting the Numbers

Then I got email from my son Jerry:

Hey,
I'm trying to figure out your post numbers problem... Could you try using
(gross federal debt from "hist07z1") / (nominal GDP from measuringworth)
instead of
(gross federal debt as a percentage of GDP from "hist07z1")
and see what happens?

Jerry thinks the discrepancies in the numbers may arise because the "federal debt relative to GDP" table has embedded GDP numbers that differ from the Measuringworth numbers I'm using. It was a good idea, I thought.

So I made another copy of the first spreadsheet, deleted everything but the original source table, and started over.

Took the Gross Federal Debt numbers from the "hist07z1.xls" source the Supporting Evidence site provides. Deleted the "TQ" row right away.

Took the Nominal GDP numbers from Measuringworth, as Jerry suggested. And calculated my own "Federal Debt Relative to GDP" numbers from the two sources.

Then to satisfy curiosity, I compared my calculated numbers to those given in the "hist07z1" table, for the 1955-1973 period:

GRAPH #1

The one is consistently lower than the other; this is exactly the problem that kept recurring in the previous analyses. I think Jerry has identified the problem. The discrepancy is in the GDP numbers. Not in my arithmetic. Well, that's a relief.


Next step was to generate a "best-fit" exponential trend based on the 1955-1973 years of the improved "Federal Debt Relative to GDP" numbers. I also have to grab the exponential formula from Excel:

y = 0.6854e^-0.0381x

The R-squared value came out at 0.9891, even higher than I had before. So that's good.

GRAPH #2

Using this formula in my Google Docs sheet, the base-period comparison looked good:

GRAPH #3

And the full-period trend will look familiar by now:

GRAPH #4

The next step is to calculate the hypothetical output for which growth is fast enough that the gross federal debt declines along the exponential curve. To do this I'm using federal debt numbers from the "hist07z1" divided by the exponential curve number, again following Jerry's suggestion.

I generated the GHP numbers and made graphs comparing hypothetical output to actual ("nominal") output. First, the base period 1955-1973:

GRAPH #5

I was relieved to see that the two lines cross repeatedly in these years, just as they do in Graph #3 above. Finally, the little things were taken care of, and I could move on. Only the big thing remains:

GRAPH #6

But before I go, here again is a close-up of the start of the Federal Debt problem:

GRAPH #7

Say I have Four Numbers...

"I have four numbers..." Call them N, D, R, and T.

I know that N/D=R.

And I know that T is close in value to R, perhaps a little above or a little below.

Let me take as an example N=12 and D=3. Then R=4. And T is close to 4, so, maybe 6.

Now I create a new number X such that N/X=T.

In my example, T > R. Therefore (N/X) > (N/D).

I think -- I'm out of school a long time now, but I think that if N/X > N/D, then X/N < D/N.

And I think I can multiply both sides of the inequality by N, so X < D.

So, if T > R then X < D. And conversely, if T < R then X > D.


N is the numerator: Gross Federal Debt.
D is the denominator: Gross Domestic Product.
R is the ratio N/D: Gross Federal Debt as a Percent of GDP.
T is my exponential trend value, calculated to be very close to R for the years 1955 through 1973.

This line

So, if T > R then X < D. And conversely, if T < R then X > D.

means:

If the Exponential Trend value is more than the "Gross Federal Debt as a Percent of GDP" value, then my value X -- which is the Gross Hypothetical Product or GHP -- is less than the Gross Domestic Product. And conversely, if the Exponential Trend value is less than "Gross Federal Debt as a Percent of GDP" then GHP is more than GDP.

In other words, it means that if this graph shows the two lines crossing:

then this graph also must show the two lines crossing:

But it doesn't.

Third Time's the Charm... Hopefully

So I make myself another copy of the first spreadsheet. I get rid of Sheet4, and Sheet3 and Sheet2. I keep Sheet1 and the Table. And I think about starting from the beginning.

Step 1: Delete the "TQ" year row from Sheet1. Now the year-numbers are consecutive, the "Gross Federal Debt as a Percent of GDP" numbers still correspond to the years, and the "Exponential Curve" column formulas each refer to the correct year-number. And the "break" is gone, in the graph of the exponential:

Just to be safe, I re-did the exponential calculation and checked that the graphs were using the numbers I wanted them to be using. Were good. And the exponential trend runs right through the center of the actual 1955-1973 numbers, as expected:

Next, as before, I wanted to calculate GHP, hypothetical output numbers with growth enough to keep the federal-debt-relative-to-output trend following the exponential downtrend. (That's on Sheet2.)

Next, on Sheet3 I compare actual GDP to the GHP numbers. Once again, the GHP numbers dwarf the GDP numbers:

But once again, GHP is never greater than GDP in the base period:

Okay, time out.

The "TQ" Year

OH WHAT A DOPE

It was when I deleted the "TQ" year from the spreadsheet. I think it shifted all the numbers out a year, or in a year. I think it moved the whole right end of the exponential curve up (or down) by a one-year increment. And I think that was enough to put my "Gross Hypothetical Output" numbers entirely below (or entirely above) the actual numbers for the 1955-1973 period. I think that would have done it.

I was sleepin. For about 3/4 of a second, my eyes opened wider and wider as the above thought went through my mind.

I looked at the clock right away. It was 3:08 A.M.

So it goes.

Made me laugh

Just a little poetry, to be found at Economics and Ethics

An Ongoing Exchange

Tschäff and I are going back-and-forth on money here.

In order to have a coherent thought, I find myself pruning off branches of the discussion that I really don't want to lose. So I will look at some of those branches in this post. Hopefully, it is all ONE branch, so we have a new coherent thought here.

Tschäff writes:

Money is always someone's liability, so by definition it is debt. The only exception is if you use cowrie shells, cigarettes, or some other commodity.

and (earlier) he says:

You're still thinking about money like it is some commodity, and missing the much bigger picture that it is always created as credit. By using double entry book keeping, you're able to find for every dollar that exists there is a creditor and a debtor.

But I think -- this is just a gut reaction, but I think it must be right -- even if we use cowrie shells for money, money is someone's liability. I don't think it is "what we use for money" that makes money a liability. I think it is keeping track of it in a ledger book that makes it a liablity. Or with accounting software. It is accounting that views everything as assets and liabilities.

And you can't get around it by saying, "Oh in places where they use cowrie shells for money, they are too primitive to do accounting." They can use sticks with notches.

//

Okay, Tschäff, I am picturing the "Federal Debt Relative to GDP" graph for some reason. The great peak of federal debt that is associated with World War Two. And the "golden age" which came soon after all that debt was created. And it was definitely "debt" to the government. But it was "money" to the recipients on the other side of all those government spending transactions.

But I want to look at the percentage of the federal debt that was held by the Federal Reserve. How much of it was "monetized" in other words -- and (it may be said) was no longer debt, perhaps.

//

And this is definitely a different branch now... But I must raise the question: "Why did the vast federal debt lead to an economic boom following World War Two, while the vast federal debt of recent times does not?"

I ask, because I have the answer. The Great Depression caused (or was caused by) a great decline in the accumulation of private-sector debt. World War Two continued that decline (relative to the quantity of money). After the war, people had a great deal of money and very little debt. People were then perfect customers, so the economy was able to grow.

In recent times, however, the growth of federal debt has been accompanied by an even greater growth of private-sector debt. Until recently, we had no great decline in the accumulation of private-sector debt. Therefore, debt remains a burden that chokes off growth despite the growth of federal debt. And that is why I always call for policies to reduce the accumulation of private-sector debt.

Prune this!

Following up on yesterday's post

I got some satisfaction from yesterday's comparison of GDP and GHP. My GHP, Gross Hypothetical Product, looks to be very close to GDP for the period 1955-1973. Which it must be if my arithmetic is good, for the GHP trend is based on those years.

But here's a view of the period on which the trend is based:

I checked the numbers in the spreadsheet. In every case for the 1955-1973 period, every GHP value is less than the corresponding GDP value. I think that's wrong. I think the GHP trend should be centered on the GDP numbers. That how the R-squared gets minimized. As I said in the first of this series,

The two lines cross each other repeatedly, as though the exponential is centered on the actuals.

That's what I'm expecting to see in numbers based on the exponential calculation. But in today's graph, the lines don't cross.

Here -- here's the first graph from that earlier post:

GROSS FEDERAL DEBT AS A PERCENT OF GDP and EXPONENTIAL DECLINE

You can see that the red and blue lines appear to be intertwined, in that 1955-1973 range. Now I'm thinkin maybe that's an optical illusion? But it's not:

This close-up shows clearly that the lines cross repeatedly.

I must have got something wrong in the other calculations somewhere. I'll get back to ya if and when I find it. Otherwise, I have to set this topic aside.

Slept on it

I corrected for inflation too soon. That has to be it. That's the only change I made to the numbers. All the other stuff was just getting the numbers, or showing them.

Couple days back I looked at Gross Federal Debt as a Percent of GDP. Looked for a trend. Found one.

Or invented one. Whatever.

Looked at that trend, long-term. And wanted to find the economic growth that would have kept the federal debt number going down, kept it following the trend.

It's backwards from what everybody else does. Everybody else looks at Federal Debt Relative to GDP and says the federal debt is too high.

But the original complaint, remember, was that economic growth was too slow: GDP was not increasing fast enough. So to me, backward is the right way to go. Rather than focusing on squishing down the federal debt, I want to consider the growth we would have needed, to make the federal debt seem size-reasonable. Then I want to look at that growth and see if it is realistic.

Anyway, I'll make a new spreadsheet. And this time I'll correct for inflation later.


I'll keep the original sheet called TABLE, which has the source numbers untouched.

I'll keep my Sheet1, where I develop the numbers for the exponential trend.

And I'll keep my Sheet2, where I develop the Gross Hypothetical Product. But I'll delete from that sheet the GDP Deflator and the inflation-adjusted GHP. And I'll delete Sheet3 and Sheet4, where I used the inflation-adjusted numbers and my graphs went astray.

On Sheet2 I'm adding the column "Gross Federal Debt as a percent of GHP." That's redundant, because it'll give me the exponential trend numbers again. But at least I can do a graph, and I have numbers to use for GHP.

Let's compare GHP to GDP. No inflation-adjustment. The GDP numbers -- actual, or "nominal" this time -- again come from Measuringworth.

Wow. These numbers are big. The GHP makes the GDP look small. It doesn't look like "realistic" growth. What this means I guess is that debt really took off. And you can see some kinks in the red line, where it suddenly starts going up faster than it did before. That's driven entirely by the growth of federal debt.

That's not something you'd normally hear me say. But I have to say what the graph says. Still, it's much too early to draw any conclusions.

Let's cut off some of that right end of the graph, and look at it where the lines are closer. I'll stop this time at 1982:

There is a definite break with the trend. A closer close-up shows the break occurring between 1974 and 1975 or -- more accurately -- shows the change in 1975 and after:

"That is enough for today!"