Real Accumulated Federal Deficits relative to RGDP

Back on 10 November, I showed Federal deficits corrected for inflation:

Graph #1: Federal Deficits, Corrected for Inflation
From the Inflation-Adjusted Deficits spreadsheet

I said:

I want to add up the numbers and see what the accumulating total looks like. If I add up Federal deficits, I get the Federal debt. So if I add up inflation-adjusted Federal deficits, I get the inflation-adjusted Federal debt.

I want to see what that looks like.

By the end of the post I had done just that. Graph #5 from that post, renumbered:

Graph #2: The Sum of Inflation-Adjusted Deficits as a Measure of Inflation-Adjusted Debt
From the Inflation-Adjusted Deficits spreadsheet

What this gives me is a picture of the Federal debt accumulated since 1947, adjusted for inflation. But it looks nothing like what you usually see when people show the Federal debt adjusted for inflation. Here's Wikipedia's picture of the Federal debt with the numbers "deflated so every year is in 2010 dollars":

Graph #3: From Wikipedia

My Graph #2 does not include World War Two debt, or any debt before 1947. So mine starts at zero where the Wikipedia graph in 1947 is already over two trillion bucks. But that's not the big difference.

The big difference is that the lines are not the same shape. Graph #2 shows continuous increase all through the 1960s, 1970s, 1980s, and into the 1990s. The Wikipedia graph runs flat or even downhill from World War Two to the early 1980s, then suddenly takes off upward.

The Wikipedia graph shows no increase until the end of the Great Inflation in the early 1980s. That is not because there was a sudden massive increase in Federal deficits at that time. It is because the Great Inflation came to an end, and because of the way they figure the inflation adjustment.

The Wikipedia graph adjusts the whole Federal debt as though all of that debt was newly created each year. All the debt existing at the end of the Great Inflation, for example, is adjusted for inflation since the end of the Great Inflation. But some of that debt was created before the Great Inflation, when the value of the dollar was more. The Wikipedia graph understates the purchasing power of older deficits.

The sudden change around 1982 on the Wikipedia graph is due in large part to the sudden slowdown of inflation.


For Graph #1 above, the inflation-adjusted deficits, I took the 1947 deficit and converted it from 1947 dollars to 2009 dollars. I took the 1948 deficit and converted it from 1948 dollars to 2009 dollars. When I got to it, I took the 1970 deficit and converted it from 1970 dollars to 2009 dollars. I converted each year's deficit from that year's dollars to 2009 dollars. That's what I did. Then for Graph #2, I added them up. But that's not how you get a graph like the Wikipedia graph.

To figure the year 1970 for the Wikipedia graph, you take all the deficits from 1947 to 1970, add them up, and convert them from 1970 dollars to 2009 dollars. When you're plotting the point 1971 on the graph, you add up all the deficits from 1947 to 1971 and convert the sum from 1971 dollars to 2009 dollars.

To get a graph like the Wikipedia graph, you take all the debt accumulated up to some date, and you convert from that date's dollars to "base year" dollars, 2009 dollars or whatever. To get a graph like the Wikipedia graph, you ignore the actual value of the money at the time it was borrowed. You just convert from the year you are plotting, to the base year. That's bad arithmetic, I think.


Today I want to look at debt relative to GDP. I want to look at the inflation-adjusted Federal debt, relative to inflation-adjusted GDP.

To do that I'll use a Google Drive graph. But let me start with the FRED graph I used to gather numbers.

Graph #4: Three Measures of the Federal Debt relative to GDP

The red line shows the "Gross Federal Debt" as a percent of GDP.

There are two other lines on Graph #4, green and blue, running close together. The blue line (which starts at 1970) shows the "Federal Debt Held by the Public" as a percent of GDP.

The green line shows Federal Debt Held by the Public, inflation-adjusted like the red line on the Wikipedia graph, divided by inflation-adjusted GDP. The green line is for all practical purposes identical to the blue line, which is *not* adjusted for inflation.

The green line shows a measure of accumulated debt (which is a "stock") relative to GDP (which is a "flow") with both measures adjusted as if they were "flow" variables.

Now I am ready. This post reviews two ways of inflation-adjusting debt: my way, as shown in Graph #2, and everybody else's way, as shown in the Wikipedia graph. Now I take these two measures of debt and show each one relative to inflation-adjusted GDP:

Graph #5: Two Measures of Real Federal Debt relative to Real Output
From the Inflation-Adjusted Deficit Accum and RGDP spreadsheet

The blue line on Graph #5 is the blue line from Graph #2, accumulated real deficits, divided by Real GDP. The green line on Graph #5 is the same as the green line on Graph #4.

The two lines are similar after about 1982. One rides a little higher than the other, but the two share the same general shape. Before 1982 it's a different story. Before 1982 the green line trends down, while the blue line trends upward. These two lines cannot both be correct.

The green line trends down because the calculation ignores the purchasing power of the borrowed money at the time of borrowing. The calculation is visible on Graph #4.