Those graphs, again

I have a couple questions about the result I got in yesterday's post. The five graphs from yesterday's post are reproduced at right. Graph #1 shows FRED's "Federal Surplus or Deficit" series (FYFSD) with the numbers inverted and the inflation stripped out of them.	#1, from November 10
Graph #2 and #3 show the Federal debt, said to be corrected for inflation. Graph #2 shows both the "gross Federal" debt (black) and the debt "held by the public" (red). It's easy enough to see the flat spot pre-1980 on the these graphs. Easy to see the sudden change, and the sharp increase after 1980.	#2, from Wikipedia
The post-1980 increase seems steeper on Graph #3 than Graph #2, because Graph #3 is taller. The uptrend is stretched upward to fill up the space in the taller graph. Graph #3 exaggerates. Again, these graphs show essentially no increase in real Federal debt between World War Two and 1980; then a sudden change, and a persistent, rapid increase in real Federal debt. I say these graphs are wrong.	#3, from Slaying the Dragon of Debt
Like the two previous graphs, the red line on Graph #4 shows the Federal debt "corrected" for inflation. I argue in the November 5 post that the calculation used for the red line gives incorrect results: Not only this red line, but also Graphs #2 and #3 are incorrect. The yellow line on Graph #4 is the correct result.	#4, from November 5
The result I got yesterday: Graph #5 shows the accumulating total of inflation-adjusted Federal deficits on Graph #1. The blue line here curves up gradually through the 1960s and '70s, like the yellow line on Graph #4. The uptrend continues through the 1980s. There is no sudden change around 1980 as there is in Graph #2 and Graph #3 and the red line on Graph #4.	#5, from November 10

So I was saying: I want to check a couple things in Graph #5.

For one thing, the blue line on Graph #5 starts out at zero (or slightly below zero, actually). Given that the start-of-data is 1947, this blue line starts after the end of the second World War. After the end of the second World War, Graph #2 and #3 run flat, but well above the zero level. Why the difference?

Easy answer: The line on Graph #5 starts at zero because it doesn't include the Federal debt accumulated during the second World War. Nor does it include the Federal debt that was existing prior to that war. So it starts at zero, because it starts at zero.

My other concern about yesterday's result is a bit more involved. The blue line on Graph #5 curves upward to a maximum in the mid-1990s. After that, the line actually falls for about five years before turning upward again.

Can I explain the downtrend in yesterday's result graph? That downtrend lasted for half a decade. Obviously it's not a glitch. Is there an explanation? I think so, yes.

What I think is this: The original data from FRED, the FYFSD data, accumulates not to the gross Federal debt, but to the debt held by the public. It accumulates to the lower measure of Federal debt. I think. That's just a guess at this point, but it's the only thing that makes sense to me.

Graph #6: Federal Debt Held by the Public (red) and the Gross Federal Debt (blue)

The red line on Graph #6 trends down for about 5 years starting in the mid-1990s. The blue line does not. If the deficit numbers from Graph #1, added up, look like the red line on Graph #6, then I have a good answer to my question: The inflation-adjusted line trends down because the unadjusted line trends down.

I downloaded the numbers from Graph #6 and the "Federal Surplus or Deficit" numbers used to develop Graph #1 above. In Google Drive I inverted the deficit numbers (to make increasing deficits go up) and converted all units to billions. Then I added up the deficit values and compared the accumulation of deficits to the red and blue versions of the Federal debt from Graph #6:

Graph #7: Sum of Deficits Compared to Two Measures of Federal Debt
The Google Drive Spreadsheet is available

The yellow line here is a good match to the red line. The sum of deficits is a good match to Federal debt held by the public. Both lines trend down for a few years in the late 1990s.

The yellow line runs a bit below the red for all the years shown on the graph. But again, that is because prior years' debt is included in the debt measures, but not in the deficit numbers.

So we know the deficit numbers do sum to a close approximation of Federal debt held by the public. This explains the late-1990s decline visible on Graph #5.