Debt and Inflation (3): Nomenclature

Suppose I borrow a dollar when the price index is 80. If I pay it off when the price index is 125, the erosion of debt by inflation is easy to figure. We can do it two ways.

We can multiply the debt by 80 and divide by 125. That tells us how much the dollar is worth, that we are paying back: It is worth 64 cents of the dollar we borrowed.

Or we can multiply the debt by 125 and divide by 80, This tells us how much we would have to pay, to pay back equivalent purchasing power: In this case, about $1.56.

But suppose I borrowed a dollar when the price index was 80, and borrowed another dollar when the price index was 115, and I pay it all off when the price index is 125. Now the calculation is not so simple.

Or suppose I borrowed a dollar at price index 80 and started paying it back the next year. And maybe I had it half paid off some years later when the price index was 115 but at that point I borrowed another dollar. And I've been making payments every year since. And now, when the price index is 125, I want to see where I stand.

Now the calculation is even more complicated. To be accurate, the calculation must use price indexes from all the years, because there were transactions in all the years.


Consider any particular year. The new debt created that year should be adjusted the same way GDP is adjusted for that year.

The problem is that the total debt number for that year includes both the new debt from that year and a lot of older debt, and we should really separate out the new debt before making an inflation-adjustment on it.

I want to do this for all the years that I know about, adjusting each year's new debt and adding it to the previous year's total. This leaves me with just one problem: the first year of the series. Since this is the first number I have, I cannot separate out the prior years' debt. So the first inflation adjustment is a fudge.

However, debt has increased a lot (as we know) so the first year's debt is a relatively small number. So, maybe the fudge will be insignificant.

And anyway, the calculation I want to do for the first year is the standard calculation used to make inflation adjustments. So my adjusted numbers will begin with exactly the same value that the "standard usage" calculation starts with. Only the subsequent numbers will differ.


I made up some numbers and went over the calculation a few times in Excel, and it's simpler than I thought. Actually, I use the same standard calculation as everybody else, except I separate new debt from existing, and apply each year's price level only to that year's addition to debt.

I did struggle with that, a bit. What happens if you borrowed some money some years ago, then later you paid off half of it but also borrowed some more?

It's less complicated than I thought. If I pay off some debt and borrow more that same year, both of those transactions will use the price index for that year. Yes, I paid back some debt with inflated dollars. But I also borrowed more of the same inflated dollars. Since we (crudely) figure the price level is the same for the whole year, the payback and the new borrowing is a wash. Only the net difference, only the change in total debt will affect my calculation of inflation-adjusted debt.

So again, I will take only the new debt for that year, and apply that year's price index to it. And I will add that adjusted number to the previous year's adjusted total to get the new adjusted total.

It's easier to do in a spreadsheet than in words.


I want to create some terminology we can use to distinguish my inflation-adjustment calculation from the one that is standard usage.

My calculation adjusts each year's debt separately, translating the "nominal" values into "real" values. So I will call this the "Annual Real Translation" (ART) calculation. The standard calc I will refer to as the "Standard Usage Recalculation for Real" (SURReal) adjustment.

Next, we will look at some spreadsheets.