The big picture is wrong

A follow-up to my post of 31 August.

In mine of 11 August I compared Cecchetti Mohanty and Zampolli's average real debt growth of "slightly less than 4½%" to my 3.79%. But my number is for a different time period. CMZ's number is for 1980-2010. Mine is for the 1948-2017 period. This invalidates the comparison. I want a do-over.

It's been almost a month, so I downloaded a new dataset from FRED. Domestic Nonfinancial Sectors; Credit Market Instruments; Liability, Level (TCMDODNS) and Consumer Price Index for All Urban Consumers: All Items (CPIAUCSL). CMZ for some reason use consumer prices to deflate debt; I'll use this measure of CPI for that purpose.

As I'm using a new dataset here I want to check and see if I still get the same 3.79% growth figure for the 1948-2017 period. I do:

Graph #1: SN2R, 1948-2017

I'm taking the growth rate number from the trend line equation.

Okay, so now the 1980-2010 period:

Graph #2: SN2R, 1980-2010

That's a 4.05% growth rate. Higher than my original 3.79% but still less than CMZ's 4.5%. Why less? My number is for US debt. Theirs is the average for sixteen OECD nations. You'd expect the numbers to differ.

But I am troubled by my numbers for US data: higher for the period starting in 1980, lower for the period starting in 1948. Troubled, because my view is that debt growth was not slower before 1980. These numbers don't support my view.

Looks like we'll be doing a few more graphs today.

Oh, I should point out that I'm leaving the dates off the graphs so that my x-axis values start with 1, because adding x-axis dates changes the growth rate number. Starting with 1, Excel thinks I mean the first x value. Starting with 1980 or whatever, it seems to think that the first x value occurred back in the year 1 AD. Not sure why adding the dates changes the growth rate, but it does. Maybe because to show the date "1980" Excel needs a value like 29221. Excel date numbers are weird.

Okay, here's the period before CMZ's 1980-2010:

Graph #3: SN2R, 1948-1980

It shows a real debt growth rate of 3.81%. Low growth early. I'm not helping myself here.

And here is the period after CMZ's 1980-2010. This one we know is low:

Graph #4: SN2R, 2010-2017

It shows 2.33 percent growth for inflation-adjusted debt. That's low.

Here is the big picture:

Graph #5: Based on the Standard Nominal-to-Real (SN2R) Conversion

The black line shows CMZ's growth number for the OECD countries for 1980-2010. The three blue lines show my numbers for US debt growth before, during, and after the 1980-2010 period. The red line emphasizes the path of change.

My graph shows exactly what Cecchetti Mohanty and Zampolli said: Debt growth was rapid in the 1980-2010 period, slower before and after that time. So it looks like I was wrong, saying debt growth was not slower before 1980.

So it looks. However, we are looking at growth numbers for real debt, and the numbers are figured as if debt is a "flow" variable. Debt is not a flow variable. The calculation produces erroneous results. The big picture is wrong.


The debt growth rates above are based on inflation-adjusted debt. But the inflation adjustment is done incorrectly. It is based on SN2R, the standard nominal-to-real calculation. Let's see what happens to the growth numbers when we use AN2R, the calculation for "stock" variables that I went over last time.

First, look at the overall number. Using the same FRED data as above, this time I get a 4.74% growth rate for real debt. Last time I got 3.79%. Real debt growth is almost a full percentage point higher this time:

Graph #6

Okay, there is a discrepancy. In mine of 31 August when I figured my "yardstick" graph, I was satisfied with the result because the start-point and end-point were right. Here, the end-point is obviously wrong. My growth number must be too high, because the red line is too high at the end.

Probably should have been using a "compound annual growth rate" (CAGR) calculation. Well, we can do that some other time. Meanwhile, look at this graph with me.

• The two lines run close together until about Year 25. So from Year 1 to 25, the 4.74% number is good.
• From Year 25 to 43, real debt increases faster than the red curve. The 4.74% number is too low.
• From Year 43 to the end, debt growth is much slower than the red curve's estimate. Except that
• Between Years 55 and 61 the two lines run close together, so the 4.74% number is good.

Now look at the graph again, using Year 43 as a break point. Before Year 43 the CAGR must be greater than 4.74%. After Year 43 the CAGR must be less than 4.74%. In other words, real debt growth was faster in the early years and slower in the later years. This supports my view. So maybe I'm not wrong. Maybe Cecchetti and all are wrong about the growth of real debt.

Let's put dates on the graph and look at it again:

Graph #7

The two lines run close (and 4.74% is a good number) until 1972. Debt growth is faster than 4.74% from 1972 to 1988 about. Then after the late 1980s, real debt growth slows. If you make 1980 your break point, much of the rapid 1972-1988 growth gets counted in the 1980-2010 period. However, debt growth has been slowing since 1988. So I still want to say Cecchetti and all are probably wrong about 1980-2010 being the period of most rapid debt growth.

I left the trend line equation on the graph so you can see how it changes when dates are added to the x-axis. Obviously the growth rate doesn't really change just because you put dates on a graph. Ignore the trend line equation on Graph #7.

Let's break up the growth by period, as we did above. Before 1980:

Graph #8

 Before 1980, real debt figured my way shows 5.56% annual growth. That's more than a percentage point higher than CMZ's "almost 4.5%" claimed for the 1980-2010 period.

1980-2010:

Graph #9

For the 1980-2010 period, real debt figured my way shows a growth rate of 3.74 percent. This is three-quarters of a point lower than CMZ's 4.5% figure for the period, and nearly two percentage points less than debt growth for the 1948-1980 period shown on Graph #8.

2010-2017:

Graph #10

Two point one four percent real debt growth in the years after 2010.

And by the way, in these last three graphs the end-point discrepancy seems to have cleared up. The growth rate numbers are good.

To summarize these AN2R debt growth numbers:

Graph #11: Based on the Alternative Nominal-to-Real (AN2R) Conversion

There is a massive difference between this and Graph #5.

When real debt is properly calculated, its growth rate is seen to be slowing. Real debt growth is not fastest in the 1980-2010 period. It is fastest in the early period, and has been slowing since.

Now you have to rethink everything.