## Friday, August 17, 2012

### On Erosion (3): The Simple Things

Next, we need to look again at CMDEBT relative to GDP, the relation on the graph we started with. Krugman's graph. But I want to look at it three different ways.

I want to see nominal CMDEBT divided by nominal GDP. This will look just like Krugman's.

I want to see real CMDEBT divided by real GDP, where the inflation adjustment is applied to aggregate numbers, just as real GDP is figured.

And I want to see real CMDEBT divided by real GDP, where real debt is figured by incremental adjustment, as described above.

The first two I can do in FRED:

 Graph #1: Two Lines in the Same Location Click graph for FRED source page
Blue: Nominal debt divided by nominal GDP. Red: Real debt divided by real GDP.

The blue line on Graph #1 here is almost entirely hidden by the red line. I started the red line just a bit late, and stopped it just a bit early, so you can see there actually *is* a blue line on the graph.

The two lines are identical.

The blue line shows CMDEBT relative to GDP using "nominal" values, exactly as Krugman has it on his graph. I even multiplied by 100 (as Krugman did) to convert the ratio values to percent values. (The "99.993" in the second formula is the price number for 2005, the base year for FRED's GDPDEF series.)

The red line shows CMDEBT relative to GDP using "real" values -- numbers with the price level divided out of them. Debt is adjusted on this graph by the same inflation-adjustment calculation that is used all the time for GDP. In other words, GDP and CMDEBT are adjusted the same way and for the same amount of inflation. As a result, the Debt/GDP ratio after adjustment is equal to the ratio before adjustment, and the red line ends up in exactly the same location as the blue line.

The graph shows absolutely no "erosion" of debt resulting from inflation. But this is absurd. The inflation adjustment of debt on this graph is most certainly wrong.

What the above graph shows is that anything divided by itself equals one.

REAL/REAL = 1 = NOMINAL/NOMINAL

Perhaps this is the relation Sumner had in mind when he ignored the effect of inflation on debt for the 1964-1984 period.

Scott Sumner's analysis of Krugman's graph, seemingly accurate on its face, is deeply flawed. The analysis ignores the effect of inflation on debt. It pretends there is no such thing as "erosion" of debt. It misinterprets the effect of inflation, reading it as a significant reduction in new borrowing.

Marcus Nunes builds upon Sumner's error, creating a plausible story about optimism to explain the reduction in borrowing during the Great Inflation. But the reduction in borrowing is something that never actually happened.

If the simple things are not laid out correctly, then everything built upon the simple things is at risk of being wrong.

...the error is to be found not in the superstructure, which has been erected with great care for logical consistency, but in a lack of clearness and of generality in the premisses.
- J.M. Keynes