On Erosion (1): Calculating Real Debt

The typical inflation-adjustment of GDP takes the total dollar value of one year's output and converts it to the dollar value for another year. To do this is fairly simple: divide the one year's price number out of the GDP, and multiply the other year's price into it.

For example, if a basket of goods used to cost $80 but now costs $125, take GDP now, divide by the current price-number, and multiply by the old price number.

This calculation is used all the time to figure what economists call "real" GDP. But what happens when you want to figure debt as "real" debt?

Consider any particular year. The new debt created that year should be adjusted the same way GDP is adjusted for that year: Divide it by the price level for that year, and multiply by the base-year price. But when we inflation-adjust debt, we often get the wrong answer.

The problem is that the total debt number for any one year includes both the new debt from that year, plus a lot of old debt left over from other years. The current year's price number is relevant only for the current year's addition to debt. For older debt included in the current balance, you have to use price numbers from prior years.

One good technique is to separate the new debt from the old debt. Then you inflation-adjust the new debt for the year just the same way you would inflation-adjust the GDP for that year. Next, you look at the old debt that you didn't adjust yet, pull out just the most recent year's debt remaining in it, and inflation-adjust that year's debt using that year's price number.

And you keep doing that, stepping back a year and adjusting just the one year's debt the same way you would figure "real" GDP for that year, then stepping back another year. You go back as far as you can go, adjusting each year's debt separately, and then add them up.

This method may be thought of as "incremental" adjustment of debt.


I don't mean to harp on it. But it seems most people think you can adjust debt for inflation the same way you adjust GDP for inflation. You cannot. It works for GDP, because GDP is a measure of one year's stuff. It doesn't work for debt, because any year's debt is almost always an accumulation of many years' deficits.


Recently, Krugman and Sumner and Nunes and Wojnilower and yours truly considered this graph from Paul Krugman:

Krugman sees "a dramatic rise in household debt, which many of us now believe lies at the heart of our continuing depression."

Sumner says "I suppose it’s in the eye of the beholder, but I see three big debt surges: 1952-64, 1984-91, and 2000-08."

Nunes writes, "Why does the share of debt rise? I believe it reflects peoples “optimism” about future prospects... During the 1950s and first half of the 1960s we observe a rise in household debt. People felt good about the future... Note, however, that as soon as inflation begins to trend up in the second half of the 60s, the future doesn´t look so bright anymore. Households’ don´t increase indebtedness..."

And, when Sumner reports that the first two debt surges were followed by golden ages and the third by a severe recession, and asks "What was different with the third case?", Joshua Wojnilower responds:

The difference is the aggregate amount of household debt compared with incomes... As the aggregate amount of debt rises, ...an increasing percentage of income and savings becomes necessary to cover interest costs and... pay back previous debt. These actions reduce the amount of income and savings available for consumption and investment, creating a drag on economic growth.

Wojnilower doesn't read anything into the graph. He doesn't chop it up into surges and remissions the way Sumner does. He doesn't attribute the surges to optimism, the way Nunes does. He doesn't even describe the increase as "dramatic" the way Krugman does. Wojnilower says only that debt was very high by the end. Then he lays out a scenario explaining some troubles that may arise when debt gets very high.

By contrast, Sumner presents a relaxed, eye-of-the-beholder evaluation of the graph. He points out three "big debt surges" and the remissions of debt growth following each. And yes, if you glance at the graph, you can see the surges clearly.

But Sumner's evaluation of the graph is too relaxed, and he misses an important detail. He calls the end of the first surge at 1964, and the start of the second at 1984. As luck would have it, Allan Meltzer calls the start of the Great Inflation at 1965, and its end at 1984. The Great Inflation fits very neatly between the first two of Sumner's surges.

Could Sumner have missed it? With all the ruckus these days calling for policymakers to raise the inflation target from 2% to 4% or more, simply to help erode debt, I don't see how Sumner could possibly have overlooked the Great Inflation.

The Great Inflation significantly reduced the burden of debt relative to GDP, and that is what you see between Sumner's first and second surge on Krugman's graph.

Perhaps Sumner would say that the inflation in the numerator (CMDEBT) and in the denominator (GDP) of Krugman's ratio simply cancel each other out. But if that was true, there could be no such thing as the erosion of debt by inflation!

// Related post: MICROBES