The Federal Debt Graph with a Constant-Growth-Rate Denominator

I was saying Noah's picture of debt growth is distorted by a wandering denominator: by a GDP that suffers from a variable and inconsistent rate of increase.

It occurs to me that we could get a better picture of debt growth by faking the GDP numbers. Rather than using actual values, we can calculate a set of values that approximate the GDP numbers, but are based on a constant rate of growth.

I didn't do any of that "least squares" crap or anything like. I just picked 1947 for a startpoint and 2000 for an endpoint, and figured out a constant growth rate that would get me from the 1947 GDP number to the 2000 GDP number. It is completely subjective (or arbitrary, really) and if you know how, you could probably come up with a better series of constant growth rate values. Meanwhile, I got what I got and I'm going with it.

Graph #1

Graph #1 shows actual (often called "nominal") GDP in red, and my constant-growth-rate numbers in blue. You can see that the lines cross some time around the year 2000. (Exactly in the year 2000, actually, as that year was one of the defining points of the blue curve.) By design, the lines also cross in 1947, though we would have to "zoom in" to see it clearly.

The lines also cross around 1977, but this is not because I pinned them together at that point. Actually, that is information the graph gives us. (That is the reason for making the graph!) Now, looking at those three crossing points, we can say the red line runs below the blue for some years before 1977, then above the blue until the year 2000, then again below the blue.

In more familiar terms, we might say GDP growth was less than average before 1977, above average from 1977 to 2000, then again below average. Obviously this is not correct. It is the result of picking 1947 and 2000 as my arbitrary start- and end-dates. If I had picked 1966 or 1973 as an end-date, the whole rest of the blue line after that date might have been above the red.That would have been a better look at economic growth.

But the purpose of this exercise is not to find the point that economic growth began slowing. The purpose is to approximate the GDP we actually got, using a constant rate of growth. For that purpose, the blue line looks about right to me, up to 2007 anyway.

You with me? Do not imagine that Graph #1 shows periods of better-than-average and worse-than-average growth. It does not.


Saturday's post showed this comparison of growth rates for actual GDP (red) and the Federal debt (blue):

Graph #2. Click Graph for FRED Source Page

It is pretty easy to see that the Federal debt jumps up above GDP growth just after the 1982 recession. But if you take a second look you might notice that the red line wanders upward until the late 1970s, which makes the simultaneous increase in the blue line appear less significant. And then the red line wanders downward for 20 years or so, making the increase in the blue line look more significant. The changes in actual GDP contribute to making the change in Federal debt seem like a sudden increase that occurs after 1982.

Like Noah, we are deceived.

The growth rate of actual GDP varies, as the red line on Graph #2 shows. The growth rate of my "constant growth" GDP does not. This approximate measure (the blue line on Graph #1) has a constant annual growth of about 7.25%. Plotted on a graph, the growth rate is a flat (horizontal) line.

I took the numbers I used for Graph #1, worked out the annual growth rate values for them, and made a new graph:

Graph #3

The proportions of Graph #3 differ from those of Graph #2 but, that difference aside, the blue lines on the two graphs are the same. (Both blue lines represent the growth of Federal debt.) But on Graph #3, I show the growth rate of the "constant growth rate" GDP approximation. A flat, red line near the 7.25% level for the full period shown on the graph.

On Graph #3 it is pretty easy to see that the Federal debt jumps up above GDP growth just after the 1974 recession. That's the 1974 recession, not the 1982 recession. It is now quite obvious that a sudden increase in Federal debt growth occurs some eight years earlier than we thought!

The difference is not due to any changes I made to the blue line. I made no such changes. I only changed the red line from a wiggly worm to a constant (average growth rate) value, so that the red line does not obstruct our view of the blue line.


Almost done.

We've been looking off-and-on lately at a picture of the Federal debt relative to GDP, this FRED graph from Noah:

Graph #4: The Federal Debt Relative to GDP

It shows the Federal debt relative to a wiggly worm. According to our Graph #1 above, the wiggly worm ran low in the years before 1977, and then high till the year 2000. Running low before 1977, it makes the Federal debt look falsely high. (Low as it is in those years on Graph #4, it is falsely high.) Running high between 1977 and 2000, it makes the Federal debt look falsely low.

I'm saying that the growth of Federal debt was less than we think in the years before 1977, and more than we think in the years after. We are deceived. Why are we deceived? Because we think of the Federal debt in comparison to the wiggly path of actual GDP.

But now we can fix that. We can use the "constant growth rate" approximation of GDP in place of actual GDP. This will give us a version of Federal debt relative to GDP that is similar to Graph #4, without the distortions arising from variations in GDP growth.

Graph #5, below, shows in red the same "relative to actual GDP" data that we see on Graph #4: In particular, the red line shows the increase beginning around 1982, the increase Noah calls "the explosion in U.S. government debt".

The blue line on #5, which shows the same Federal debt but shows it relative to the "constant growth rate" approximation of GDP, shows that increase beginning around 1975. That is the same difference we noticed above, comparing Graphs #2 and #3.

The Federal debt, relative to actual GDP (red), and relative to a constant-growth approximation of GDP (blue):

Graph #5

The two lines are very similar. That says the two measures of GDP are very similar. And we would want that to be true, so we can have confidence in the approximation.

But the two lines also differ. In the years before 1977 the blue line is lower. In the years between 1977 and 2000, the blue line is higher. But look also at the transition from downtrend in the 1960s to uptrend in the 1980s. The red line (using actual GDP) hits bottom around 1974 and runs flat until 1982, and then suddenly starts on its upward journey.

We know that, of course: Noah pointed it out.

The transition from downtrend to uptrend is different for the blue line. It is earlier. Instead of going suddenly flat in 1974 like the red line, the blue line begins its uptrend there. That uptrend is definitely stronger after 1982; so if you were wanting to blame Reagan for the big increase in Federal debt I guess you can still do that. But 1982 is not where the uptrend starts. Not for the blue line. Not for the Federal debt.

And the only difference between the red and blue lines is that the red line is shaped by vagaries in both debt growth and GDP growth. The blue line is not. The blue line is the better measure of Federal debt growth.

And the postwar increase in Federal debt growth started before 1982.

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The Excel file at Google Drive