## Sunday, May 6, 2012

### Debt and Inflation (1): How Is Inflation Removed?

I want to look at the growth of debt, and the "erosion" of debt due to inflation during the Great Inflation. I want to use zero inflation as a conceptual yardstick.

People these days think zero inflation is not realistic. I don't want to argue about that but I need to look at debt with inflation stripped away. I have been confused by it.

Suppose we start with a look at "real" GDP, inflation-adjusted GDP. Compared to "nominal" GDP, which is based on actual prices.

Inflation means prices are going up. So when you take the inflation out of a number set, the numbers go up slower. So we see the blue line -- GDP with inflation removed -- goes up slower than the red line, which is GDP with nothing removed:

 Graph #1: Inflation-Adjusted GDP (blue) and Actual-Price GDP (red)
After you adjust for inflation, you still have to express the numbers in dollar values. The red line on Graph #1 uses dollar-values that change. The blue line uses dollar-values that are "fixed" and unchanging. The two lines cross at the year 2005 because in that one year, both lines use dollar-values from 2005.

Where the lines cross is not significant. The numbers cross at the "base year". We could force the lines to cross at any year we want by using the desired year as the base year. On the graph we have, the base year happens to be 2005. The lines cross that year because the value of the dollar on both lines is the same for that year.

How is inflation removed from a number set? Basically, it is divided out.

Typing price index into the search box at FRED returns 5514 results. Top three among these are the Consumer Price Index (twice) and the GDP Deflator. It seems the deflator is the relevant choice when looking at GDP, so I'll go with that.

The deflator is a sequence of numbers that go up as time goes by. So dividing by the deflator will give results that get smaller as time goes by. Smaller, as compared to the numbers you start with.

I took the red line from Graph #1 and divided it by the deflator. What happened then was the red line looked like a flat line down near the bottom of the graph. (The "base year" 2005 value of the deflator was 100. So in 2005 where the red and blue lines are supposed to be the same, the red line was low by a factor of 100.)

To correct for this, I multiplied all the red values by 100. Now the red line follows exactly the same path as the blue line:

I stopped the red line two years short at each end so you can actually see that there is a blue line on the graph, and that the red line follows exactly the same path.

Now let's do the same arithmetic with Total Debt instead of GDP. I don't know whether the CPI or the deflator is more appropriate. I'll use the deflator to be consistent with what I've done above.

Look at the second line of text in the top blue border on Graph #3 below, and compare it with the second line on the top border of Graph #2 above. The calculations are the same. Only the original numbersets differ. The one is TCMDO; the other is GDP.

 Graph #3: TCMDO debt (blue) and Inflation-Adjusted TCMDO (red)
I'm not sure that inflation-adjusted debt is a meaningful calculation, by the way.

Oops. On Graph #1 the blue line has the inflation adjustment. On Graph #3, the red line has the inflation adjustment. But in both cases, the inflation-adjusted line goes up more slowly than the unadjusted line. The unadjusted lines go up faster. The unadjusted numbers start out lower and end up higher than the adjusted numbers, because prices have been going up.

So that's the arithmetic of it.

#### 1 comment:

Jazzbumpa said...

I think the adjustment is valid.

In any given year there is a stock of debt. New debt is a flow into that stock, payoff a flow out.

That stock has value, denominated in terms of the current year's dollars.

To compare across time, it's appropriate to adjust for inflation, which is basically correcting or the changing value of money across time.

Makes sense to me.

BTW, in case you haven't looked back, I responded to your corporate tax post from Friday.

Cheers!
JzB