Debt is built in many layers, each with its own price level

Format it like a sentence, and the title of Nathan Tankus's recent post looks like a reply to something somebody said:

No, inflation doesn’t erode the burden of debts.

His opening sentence makes his topic clear:

It is commonly argued that inflation erodes debts.

His next sentence makes his position clear:

However, the usual defenses amount to little more than circular logic.

Then he provided an example from Paul Krugman. In short:

the burden of debt has been aggravated by falling inflation

And now we know to whom Nathan Tankus was replying in his title.


Tankus explains the problem:

The source of the confusion here is that it is popular to divide key economic variables by abstract measures of the prices across the economy (such as the Consumer Price Index). This makes sense sometimes but in other situations become nonsensical. Debt is one such example.

The source of confusion, he says, is the common practice of calculating the inflation-adjusted (or "real") value of debt. The calculation, he says, divides debt by a price measure "such as the Consumer Price Index". I picked up on that right away. Not only is that calculation common. It is also wrong.

Tankus lays out the mathematical relation for us, and identifies ways the burden of debt can be reduced:

In the United States most people have debts denominated in U.S. Dollars. A useful proxy for the burden of debt is the ratio between an individual’s or sector’s nominal debt to its nominal income.

The burden of this debt falls when they can refinance at a lower nominal interest rate, their nominal income rises or they default.

It's not just a proxy. I'd call the debt-to-income ratio a way to actually measure the burden of debt. But Nathan Tankus and I are in the same ballpark.

His next sentence I'm not sure about:

In most discussions the “real value of the debt” is discussed while still talking about nominal income (or at least being unclear about the measurement of income).

Could be. I've seen people divide a nominal quantity by an inflation-adjusted quantity and use it as evidence that labor costs drive inflation. I've seen Milton Friedman divide a nominal quantity by an inflation-adjusted quantity and draw the conclusion that printing money is the cause of inflation.

That's the way that calculation works: Whatever nominal thing you divide by an inflation-adjusted quantity, you can make a specious argument that your nominal thing is the cause of inflation. So I am highly sympathetic when Tankus says he doesn't trust ratios that use both "real" and "nominal" values.

Then he says

It is basic math that dealing with such a ratio you have to divide the numerator and the denominator from the price level to stay consistent. However, from that point of view it becomes clear the exercise is nonsense.

After that he loses me. In the next sentence following the word "nonsense" Nathan is suddenly talking of "falling productivity" and "oil". So instead of reading more, I went back to the part that made sense. I agree when he says you have to divide both the numerator and the denominator by the price level to be consistent. Yes. Otherwise you're just factoring the price level into your results.

But Nathan says it is okay to use the "consistent" calculation with debt. I disagree. Debt is almost always an accumulation of multiple borrowings from multiple years. The consistent calculation divides each year's debt number by only one year's price level. There is no thought given to multiple-year accumulations of debt.

My debt today includes money I borrowed last year to buy a car, and money I borrowed several years back when I bought a house. To figure my "real" debt correctly I would have to divide part of my debt by last year's price level and part of it by the price level when I bought the house. The common calculation does not do that, not even the "consistent" version. The common calc divides this year's total outstanding debt by this year's price level. It divides last year's total outstanding debt by last year's price level. It divides any one year's total outstanding debt number by that year's price level. There is no allowance for multi-year accumulations of debt. The common calculation converts from any one year, to a "base" year, and that's it.

In addition to the problem of dividing nominals by reals, which Nathan Tankus points out, there is the problem that the common calculation does not allow for multiple-year accumulations. In plain English, when you use the common calculation to inflation-adjust debt, you get the wrong answer.