## Thursday, August 16, 2012

### On Erosion (2): Ada and Ida

The first thing I want to do is duplicate Krugman's graph from yesterday's post.

His:
 Graph #1: Krugman's Graph

Mine:
 Graph #2: My version of Krugman's Graph

Not bad. If you see differences, it is because I downloaded "annual" data from FRED, and Krugman probably used the default "quarterly" data. Both graphs show the same "face" -- a nose in the 1980s, a chin before that, a neck in the early 1960s. Even indications of eyes and hair can be seen in the graph.

Next, I want to graph the raw debt numbers (not divided by GDP) along with "real debt" numbers figured the way "real GDP" is figured:

 Graph #3: The Raw Numbers, and "Real" Debt Figured by Aggregate Debt Adjustment

The relation between the two lines shown on Graph #3 is similar to the relation between Nominal GDP and Real GDP, which you have probably seen many times. The two lines cross in 2005, because the price deflator used for the conversion has 2005 as its base year. The red line is higher than the blue in the years before 2005, and the blue line is higher in the years after 2005.

Suppose you wanted to use this graph to learn something about inflation's ability to "erode" debt. After all, some people do call for a higher inflation target -- increased inflation -- to help reduce the burden of debt.

But in 2005 the lines cross. The real and nominal values are equal in 2005. In other words, in 2005 there was *no* erosion of debt, despite all the inflation we had between 1950 and 2005. That is wrong, of course. But that is what the graph shows.

It is the calculation used to figure "real" debt that is incorrect.

Next, I want to do the graph again, using the incremental inflation adjustment described in yesterday's post.

 Graph #4: The Raw Numbers, and "Real" Debt Figured by Incremental Debt Adjustment

Here, "Real" debt is significantly higher than nominal debt at every point on the graph. The red line is higher than the blue, by the amount that debt was eroded by inflation. If you are looking to see the erosion of debt, this graph shows it. Incremental Data Adjustment (IDA) of debt shows it.

David Blake said...

i have read this and the previous post twice and cannot understand the point you are making.
Why does it matter when debt was issued?

David Blake said...

It seems to me you are confusing debt, which is a stock, with the deficit, which is a flow.
BTW, I entirely agree that private not public debt is the problem for the economy.

The Arthurian said...

David, it seems to me that everyone else is "confusing debt, which is a stock, with the deficit, which is a flow." :)

A flow number (like GDP) represents one year's accumulation. Therefore, to calculate an inflation-adjustment for it, we need divide out only the one year's price level.

A stock number (like debt) represents an accumulation of many years -- many years' deficits, say. But each year's deficit was created at a different price level. Therefore, to adjust total debt for inflation, it is necessary to adjust each year's piece of it separately.

The full force of a dollar borrowed and spent in 1964 was far different from one borrowed and spent 20 years later!

I have assembled a PDF from the four parts of this "On Erosion" series. I put it on Google Docs. You should be able to download it from there, if I did it right.

I could be wrong about this, but I can't see it. Thanks for keeping an eye on me. "It is astonishing what foolish things one can temporarily believe if one thinks too long alone..."

Anonymous said...

I'm pretty sure you ARE wrong about this. When people talk about inflation eroding debt, they mean that the value of the debt now is being reduced. When the debt was contracted does not matter, because current debt is the sum of all previous deficits.
If you bought government bonds in 1982 and have held them for 30 years, those bonds will of course have been eroded by inflation more than bonds issued last year have been. But that simply tells us about the distribution of losses as the debt is eroded. It does not tell us anything about the question of the value of the debt today compared to the size of the economy, which is what people are talking about.

The Arthurian said...

Hi, Anon. I think you and I are very close to agreement, except for your first sentence!

In your second sentence at the end I would add "relative to what it was", which raises the question about how far back in time we look for un-eroded values.

Your 3rd and 4th sentences contradict each other, I think. To me, *when* the debt was contracted does matter, because that is what determines the original (un-eroded) value of the debt.

I definitely agree with your last sentence, that the value of the debt compared to the size of the economy is the way to measure erosion of debt. But if real debt and real gdp are calculated the same way, the ratio of reals is identical to the ratio of nominals, and there can be no erosion of debt. In order to have erosion of debt relative to gdp, inflation must affect debt and gdp differently.

Jerry said...

Anon -
Say for the sake of argument that you never get a "real" raise, but your wage keeps pace with inflation. You make \$10 an hour in 2012 dollars (or whatever - deflator 1.0).
Say the deflator in 1995 was 2.0, and in 1980 was 3.0.
Say that your creditor charges 0% interest. (these are all oversimplifications to make it easier to get at the relevant point.)

Say that you work 100 hours a year.

You borrowed 100 hours worth of wage (100% of your income) in 1980 - in nominal dollars that is 100*10/3 = \$333.33.

You didn't pay it back. In 1995, you borrowed another 100 hours worth. In nominal dollars, that is 100*10/2 = \$500.00

So the total "dollars" that you borrowed was 833.33.
The total "hours of labor" that you borrowed was 200.

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Question: In 2012, how much has that debt been eroded by inflation?

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The right answer should be...
If there were no inflation, you would owe:
(200 hours of wage) = \$2000
So the erosion is:
2000 - 833.33
= 1166.67

or, it was eroded by:
(2000 - 833.33) / 2000
= 58.3%

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If you calculate it Art's way (basically: integrating the "real deficit"), you get that you borrowed 100% of your yearly income in 1980 and another 100% in 1995, for 200%. So the "real debt art-wise" would be \$2000. So you get the right answer (2000-833 is the erosion, so as a percent it's 58.3).

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If you calculate it "the normal way", you would say... i don't even know what. Can you fill this part in for me? I don't think it even makes sense enough to write down an answer. What calculation would you do to see how much the debt has been eroded?

But, in any case, if you get a different answer than the "art method", then your answer is wrong.