Debt and Inflation (4): Recalculating

Far as I know, it is GDP that is most often expressed as 'real' values. The conversion takes GDP values for a number of years, strips away the inflating prices from each value, and replaces it with the price-level of some "base" year.

FRED's GDP Deflator uses a base year of 2005.

FRED's Consumer Price Index uses a base period of 1982-84 -- a base that, remarkably, must be older than some economists!

The 1982-83 edition of the Statistical Abstract -- back when we were still using GNP instead of GDP -- used 1972 as a base year for the deflator, and 1967 as a base year for the CPI.

The Bicentennial Edition of the Historical Statistics used 1967 for the CPI and 1958 for the deflator.

But you can use any year for a base year, if you have the data. Pick the year you want to be the base year. Then divide each year's GDP by that same year's deflator, and multiply by the deflator for the year you picked. That's it. The year you picked is the base year for your results.

The blue line on Graph #1 below is the gross Federal debt. The other three lines show inflation-adjusted Federal debt, using three different base years. The red line uses the default 2005 base year, and maybe you can see the red and blue lines cross just at 2005 on the graph.

Graph #1: The Gross Fededal Debt (blue) and Three Surreal Adjustments

The gold line shows the same Federal debt and uses the same calculation for inflation adjustment as the red line, but with a base year of 2010. The whole gold line is scaled up a little from the red one, because prices went up a little between 2005 and 2010. And the gold and blue lines cross in 2010.

You can see that the red and gold lines are similar, and that both show the trademark flatness before Reagan came to office (as noted in an earlier part of this series). The unadjusted blue line lacks that flatness through the 1970s, the worst of the inflation.

The green line shows the flatness in the years before Reagan. Like the red and gold, the green line shows the same inflation-adjusted debt data with a different base year. This time the base year is 1947; this means the green and blue lines cross at 1947.

Basically, the green line is a scaled-down version of the red and gold.

All three versions of inflation-adjusted debt rely on the same calculation that is commonly used when the inflation adjustment is made to GDP. This is the calculation I've been calling surreal, the one that I say produces erroneous results when used for inflation adjusting debt.


Graph #2 presents two improved calculations of the inflation adjustment of debt, the green and gold lines.

Graph #2: Alternatives to the Surreal Calculation

First off, the blue line is the gross Federal debt, unadjusted.

The red line is inflation-adjusted -- by the surreal calculation -- with a base year of 2010, meaning the lines cross in 2010. But here's the thing: If inflation erodes debt, then they shouldn't meet in 2010. The red line should be higher in 2010. The 60-plus years of erosion by inflation should have made "the debt we owe today" less than "the debt we would have owed if there was no inflation."

The standard calculation used for inflation adjustment, the surreal calculation, tells us that there has been no erosion of debt. More precisely, it tells us that there has been no erosion in the base year, but that there *has* been erosion in other years. The surreal calculation cannot possibly be valid for inflation-adjustment of a stock like debt, that carries over from year to year.

Again: When we use the most recent year as the base year, the surreal calculates out the same as nominal debt in that year. This cannot be correct. It means there was no inflation adjustment. But the original purchasing power borrowed must have been greater than the outstanding debt today, if there was a loss to inflation.

Certainly, a different calculation is needed.

The gold line presents the result of one such calculation. It begins with the 1947 value, unadjusted. (Thus, the gold line has 1947 as base year.) For the next year, 1948, I adjusted the 1947 total for one year's inflation, and to it added the new debt for 1948, unadjusted.

For 1949 I take the total from 1948 and adjust it for one year's inflation, then add to that the new debt of 1949. I followed these steps repeatedly for each year, all the way through. At the end, in 2010, the inflation-adjusted value for gross Federal debt came to $20,152.3. That is half again as much as the unadjusted Federal debt.

In other words, this calculation shows that there has been erosion of debt by inflation.

The green line shows another alternative to the surreal calculation of debt. Here, we begin by adjusting the 1947 value using 2010 as the base year. (This makes the green line start at exactly the same level as the surreal calculation's red line, by the way.) For the next year, I carry forward the previous year's adjusted value and add to it the new debt for 1948, after adjusting the new debt for inflation through 2010.

For 1949 and after, this process is repeated, so that the inflation-adjusted total always reflects base-year 2010 values. At the end, in 2010, the inflation-adjusted value for the gross Federal debt comes to $20,152.3 -- exactly the same as for the gold line.


You know when I knew for sure I was onto something with this? When I saw Graph #2. Four lines, four different sets of numbers, but only two starting points, and only two end points.

The source data for this post is from FRED.

The worksheet I used to generate Graph #1 is in this Google Docs file.

The worksheet I used to generate Graph #2 is in this Google Docs file.