Friday, June 22, 2012

By the numbers

Here's how to take inflation out of GDP: Divide each year's GDP number by the same year's price-level number.

That's it. That's the whole calculation.

When you've done all the years, a graph of your numbers takes on a different shape. That's because you have removed the inflation from the numbers.

Usually, we do a second step: We multiply all the values by 100, or we pick a base year and multiply all the values by the base year price-level.

The second step scales the numbers up, so you can visually compare your results to the numbers you started with. But this "scaling up" really has nothing to do with removing inflation from the numbers. That all happens in step one.

To make an inflation-adjustment of debt, we should do exactly the same thing: Divide each year's debt by the same year's price number. The trouble is that when you take any one year's total debt, it is not the debt of just one year. It is the debt of many years.

If we take the GDP number for 1980 and divide it by the price number for 1980, that's fine. But if we take total debt for 1980 and divide it by the price number, our answer is wrong. Total debt for 1980 includes debt from 1979 and 1978 and 1977, and even some left over debt from 1965 when prices were much lower. Our calculation does not allow for that. So our answer is wrong.

If you are taking the price level out of debt, the 1980 price level only applies to 1980's additions to debt. To remove the price level from the debt that still remains from 1965, you have to divide it by the 1965 price level. For all the years, you have to do this.

But nobody does this.

If you're looking at debt for 1980 and you divide the total debt by the price level for 1980, the adjustment of left-over debt from 1965 is understated. This understatement changes the shape of the graph. When you make the graph, the old debt is shown falsely low. And then, the "erosion of debt by inflation" appears to be less than is actually the case.

Every year's debt has to be figured separately, just as every year's GDP is figured separately. What you have to do is start at the beginning, adjust each year's addition to debt separately, and total up the adjusted numbers as you go.

A few days back Nonny presented this graph, which is not adjusted for inflation:

Graph #1: Total Debt as a Percent of GDP

Nonny said one can use the graph to "pinpoint the timing" of the big changes. Jazz responded: "Yep - Reagan and Bush, Jr." Jazz refers to the big increase from 1980 to 1986, and the big increase after the year 2000.

There is nothing wrong with the graph, except that it includes the effects of inflation. If inflation was always the same, it wouldn't matter. But inflation is not always the same. Therefore, inflation changes the shape of the graph. So we don't really know if the big increase from 1980 to 1986 was due to a big increase in debt, or if it was due to the ending of the Great Inflation.

What's missing from Nonny's graph -- or not missing, but hidden within it -- is inflation. When we look at this graph we are not so much seeing the relation between debt and output as we are seeing the different effects of inflation on debt and output.

Nonny says:

The plots of debt/gdp or debt/income are all time plots of the nominal measures of both components, combined into a ratio at the time of collection; that is, inflation (or deflation) comes out in the wash.

Yes, it is true there is inflation in the numerator and denominator both. So you would think the inflation gets divided out of the picture, or "comes out in the wash" as Nonny says. But the the size of the effect of inflation is greater for debt than it is for output, because today's total debt includes debt from a time when prices were lower.

For any given year, there must be two different inflation adjustments: one for GDP, and another for debt. Because the two calculations differ, inflation does not simply "come out in the wash" when you look at debt relative to GDP.


Jazzbumpa said...

Let's see if I'm getting this.

Debt is a stock.

GDP is a flow.

The rate of inflation is also a flow.

Does that make CPI a stock (of accumulated inflation?)

Then isn't GDP/CPI a flow/stock?

Then Debt/CPI is a stock/stock?

The generalized form of the question is -- how do you inflation adjust a stock?

What you propose is to adjust each years addition to debt (a flow) by that years inflation rate (also a flow.)

Then to get gross current debt, you total the adjusted debt values for all the years in the series.

This has it's own internal logic.

Have you done a comparison graph? Seems like maybe you did, but you post faster than I can read, so I'm not sure.

My head is starting to hurt. I feel there may be a shifting reference in here somewhere.


The Arthurian said...

Thanks, Jazz. Comparison graph 4AM tomorrow.

1. I assume it is possible for inflation to "erode" debt (Krugman's term).

2. By the standard inflation adjustment (as used for GDP) the real and nominal values are equal in the base year.

3. However, for debt, if the real and nominal values are equal, THERE HAS BEEN NO EROSION OF DEBT.

4. Therefore, the calculation that shows them to be equal must be wrong.

The Arthurian said...

"The rate of inflation is also a flow.
Does that make CPI a stock (of accumulated inflation?)"

That's pretty interesting, actually.

"The generalized form of the question is -- how do you inflation adjust a stock?"