## Saturday, August 15, 2015

### GDP, the GDP deflator, Federal debt, and time

"... inflation erodes the real value of debt." - Paul Krugman

A few days ago I showed a graph of Federal debt relative to GDP. Showed the ratio of nominals, and also the ratio of reals. The two are not the same because the calculation of reals for debt differs from the calculation of reals for GDP, because debt is a stock and GDP is a flow.

This graph.

 Graph #1: Ratio of Nominals (blue) and Ratio of Reals (red)
In a comment on that post, Jazzbumpa reacted:

I find the whole concept of inflation adjusting debt to be deeply troubling.

You end up with a "real" debt/GDP value that is greater than the real [i. e. currently factual] value. What does that even mean?

What does it mean? It means inflation erodes debt. The inflation-adjusted (or "real") value is greater than the inflated value because inflation erodes debt. The gap between the red and blue lines shows the extent of the erosion.

Come to think of it, we can look at the one line relative to the other. We can look at the blue line relative to the red: The inflated values as a percent of the inflation-adjusted values. On this new graph a value of 100% will indicate zero erosion of debt due to inflation. A value of 80% will indicate that 20% of the value borrowed has been lost to inflation. And 60% indicates that 40% has been lost to inflation -- or, that to pay off the debt would require only 60% of the total value borrowed.

 Graph #2: The Blue Line from Graph #1 as a Percent of the Red Line from Graph #1
The only variables we're using here are GDP, the GDP deflator, Federal debt, and time. So it can only be these that influence the pattern shown on the graph.

I'm having a hard time imagining how changes in the data would be related to the changes visible on the graph. I'll have to look into that.

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This Excel file contains the above graphs and the source data.