econcrit: The Nominal-to-Real calculation

Wednesday, August 22, 2018

The Nominal-to-Real calculation

Start with GDP:

Graph #1 (Click the Graph or the Caption for a Better View)

The black line shows GDP, sometimes called Nominal GDP or NGDP. The fat blue line, well hidden by the red, shows inflation-adjusted GDP (Real GDP or RGDP). And the red shows the result of the standard calculation that converts NGDP to RGDP.

The calculation, given in the upper border of the graph, is GDP divided by the price index and multiplied by 100.

When they figure the price index, they could take care of the 100 as the last step. Then, when we convert nominal to real, we would only have to divide by the price index. But they don't take care of it for us, so we have to remember to do it ourselves.

And if your memory is not so good, like mine? Don't worry; the graph will remind you. Instead of ending near 18000, the red line will end near 180, with the whole line shrunk down to match. 180 is not as far above zero as where our black GDP line starts. So it will be obvious when you see it, that you forgot to multiply. And you curse your memory again, and fix your calculation again, and you're good.

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Now the mind-blower: Let's pretend we're looking at debt, not GDP.

It's just numbers to work with. I need numbers to work with. And it is representative: Typically, when people convert nominal debt to real debt, they use the same calculation, the standard calculation that is used to convert nominal GDP to Real GDP. Plus, that's the calculation I want to look at today, the nominal-to-real conversion.

So the black line is debt. The fat blue line is Real Debt, or so people say. And the red line shows the calculation. The same calculation that is used to convert GDP to Real GDP.

According to me, as a way to convert nominal to real, that calculation is perfectly good when used to convert GDP, but completely unacceptable when used to convert debt.

Maybe that blows your mind even more. Maybe it should.

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One difference between debt and GDP is that when we figure GDP we start again at zero every year. GDP is never a total for more than one year. Debt is not like that. Debt is always a total for more than one year. When we figure debt, we take the end-of-year balance and use it as the start-of-year balance for the next year. And by "we" I don't mean me; I mean the experts who work up the numbers.

Debt is reported every year, just like GDP. But the number is a multi-year accumulation. One year's debt includes the borrowing of many years, and reflects the prices of many years.

GDP is never a total for more than one year. Debt is always a total for more than one year. This difference is the reason the standard calculation works for GDP but does not work for debt. Why? Because the price index gives the price level for one year at a time. There is no price index for the many years of borrowing that are accumulated in one year's debt.

There is no price index that measures the price level for a multi-year accumulation of debt. So the standard nominal-to-real calculation gives the wrong answer when you use it to figure real debt.

To convert nominal debt to real, a different calculation is needed. One like this.

In Round Numbers

In an inflationary economy, which ours has been, the dollar loses value over time. A dollar a year ago was worth more than a dollar today. A dollar five years ago was worth even more.

Since the late 1990s, inflation has been roughly two percent a year. Call it two percent. So a dollar last year was worth 2% more. A dollar five years ago, 10% more.

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Now: How old is our debt? Just a guess, but I'm saying five years old on average. More than five, I think, but say five years old. And that's for newly reported totals: Debt totals announced this morning encompass debt that is on average five years old, or more.

If we have 2% annual inflation, in five years that's about 10% inflation overall. If our debt is five years old on average, then debt reported this morning has already seen about 10% inflation. The dollars we borrowed and spent were worth 10% more than a dollar is worth at the moment.

So if we're doing inflation adjustment, the adjustment could be about five times bigger for debt than for GDP.

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The annual addition to debt is generally in the neighborhood of five to ten percent of the total accumulation. That means that 90 to 95 percent of debt is old debt -- money borrowed on average five years ago, when the dollar was worth about 10% more. At any given time, then, 90 to 95 percent of debt represents spending that was done when the dollar was worth 10% more.

When we look at the value of debt in dollars that don't lose value over time (which is really what inflation adjustment is all about) we have to say the adjustment is substantially greater for debt than for GDP. Because debt always has that extra 10% and GDP doesn't.