## Thursday, August 13, 2015

### Debt is built in many layers, each with its own price level

Format it like a sentence, and the title of Nathan Tankus's recent post looks like a reply to something somebody said:

No, inflation doesn’t erode the burden of debts.

His opening sentence makes his topic clear:

It is commonly argued that inflation erodes debts.

His next sentence makes his position clear:

However, the usual defenses amount to little more than circular logic.

Then he provided an example from Paul Krugman. In short:

the burden of debt has been aggravated by falling inflation

And now we know to whom Nathan Tankus was replying in his title.

Tankus explains the problem:
The source of the confusion here is that it is popular to divide key economic variables by abstract measures of the prices across the economy (such as the Consumer Price Index). This makes sense sometimes but in other situations become nonsensical. Debt is one such example.

The source of confusion, he says, is the common practice of calculating the inflation-adjusted (or "real") value of debt. The calculation, he says, divides debt by a price measure "such as the Consumer Price Index". I picked up on that right away. Not only is that calculation common. It is also wrong.

Tankus lays out the mathematical relation for us, and identifies ways the burden of debt can be reduced:
In the United States most people have debts denominated in U.S. Dollars. A useful proxy for the burden of debt is the ratio between an individual’s or sector’s nominal debt to its nominal income.

The burden of this debt falls when they can refinance at a lower nominal interest rate, their nominal income rises or they default.

It's not just a proxy. I'd call the debt-to-income ratio a way to actually measure the burden of debt. But Nathan Tankus and I are in the same ballpark.

His next sentence I'm not sure about:
In most discussions the “real value of the debt” is discussed while still talking about nominal income (or at least being unclear about the measurement of income).

Could be. I've seen people divide a nominal quantity by an inflation-adjusted quantity and use it as evidence that labor costs drive inflation. I've seen Milton Friedman divide a nominal quantity by an inflation-adjusted quantity and draw the conclusion that printing money is the cause of inflation.

That's the way that calculation works: Whatever nominal thing you divide by an inflation-adjusted quantity, you can make a specious argument that your nominal thing is the cause of inflation. So I am highly sympathetic when Tankus says he doesn't trust ratios that use both "real" and "nominal" values.

Then he says
It is basic math that dealing with such a ratio you have to divide the numerator and the denominator from the price level to stay consistent. However, from that point of view it becomes clear the exercise is nonsense.

After that he loses me. In the next sentence following the word "nonsense" Nathan is suddenly talking of "falling productivity" and "oil". So instead of reading more, I went back to the part that made sense. I agree when he says you have to divide both the numerator and the denominator by the price level to be consistent. Yes. Otherwise you're just factoring the price level into your results.

But Nathan says it is okay to use the "consistent" calculation with debt. I disagree. Debt is almost always an accumulation of multiple borrowings from multiple years. The consistent calculation divides each year's debt number by only one year's price level. There is no thought given to multiple-year accumulations of debt.

My debt today includes money I borrowed last year to buy a car, and money I borrowed several years back when I bought a house. To figure my "real" debt correctly I would have to divide part of my debt by last year's price level and part of it by the price level when I bought the house. The common calculation does not do that, not even the "consistent" version. The common calc divides this year's total outstanding debt by this year's price level. It divides last year's total outstanding debt by last year's price level. It divides any one year's total outstanding debt number by that year's price level. There is no allowance for multi-year accumulations of debt. The common calculation converts from any one year, to a "base" year, and that's it.

In addition to the problem of dividing nominals by reals, which Nathan Tankus points out, there is the problem that the common calculation does not allow for multiple-year accumulations. In plain English, when you use the common calculation to inflation-adjust debt, you get the wrong answer.

Jazzbumpa said...

My debt today includes money I borrowed last year to buy a car, and money I borrowed several years back when I bought a house.

So far, so good.

To figure my "real" debt correctly I would have to divide part of my debt by last year's price level and part of it by the price level when I bought the house.

No. Your real debt today = exactly your nominal debt today, because inflation has no effect in the instant, and that is where you live.

What you actually owe on any given day is the sum of your car debt and house debt and credit card debt and whatever else you might have borrowed from somebody else last week. The inflation rates on the days that you bought the car the house and whatever are irrelevant.

You owe exactly what the sum of your debt statement say you owe, not some finagled, fictional number.

These real vs nominal adjustments only make sense when you are trying to normalize some measure across time, so that you can compare the value at t(1) to the value at t(2) and not be thrown off by the changing purchasing power of money.

But you are going at the whole thing backwards. If you want to inflation-adjust debt, you can't start from some arbitrary t(0) in the past and calculate up to now, By doing that you get an unreal debt which is greater than your actual debt. And it will be different for every t=0 that you might chose.

You have to run your calculations the other way, and inflation adjust the past with t(0) = now, and all the other t's as negative.

But what does that get you?

What are you trying to accomplish?

Cheers!
JzB

The Arthurian said...

"Your real debt today = exactly your nominal debt today, because inflation has no effect in the instant, and that is where you live... You owe exactly what the sum of your debt statement say you owe, not some finagled, fictional number."

Jazz, you're not confused by the unfortunate word "real" are you???

jim said...

I'll admit I'm confused by what you mean by real

You seem to be saying that if there was no inflation AND everything else remained the same your debts would be a lot higher.

But that seems a bit backwards to me. If there was no inflation then your income and the price you pay for things would be lower and debt would remain the same.

The Arthurian said...

Jim: "You seem to be saying that if there was no inflation AND everything else remained the same your debts would be a lot higher. But that seems a bit backwards to me. If there was no inflation then your income and the price you pay for things would be lower and debt would remain the same."

If debts are higher and everything else is unchanged... If debt is unchanged and everything else is lower... Either way, the debt-to-GDP ratio goes up. The two scenarios you describe differ because of the choice of base year -- either near the start of data, or near the end. That's why the one scenario seems "backwards" relative to the other.

Jazzbumpa said...

Art -

No. My comment to the earlier post made explicit that I grok the difference between "real" and real! You are obfuscating.

I don't have a vocabulary problem.

I have a problem understanding that when the real (i.e. factual and documented) total of your outstanding debts is \$10,000 you perform a calculation that says it's "real" (i.e. inflation adjusted) value is \$14,275. This is why Nathan said you were being incoherent.

Your problem is conceptual. You can never inflation adjust a current value. Your debt level is what it is, and your income level is what it is, all in today's dollars.

Otherwise, I will be delighted to lend you \$10,000 tomorrow morning and have you pay me back \$14,275 in the afternoon.

Cheers!
JzB

The Arthurian said...

Jazz: "You can never inflation adjust a current value."

Really?

Jazzbumpa said...

OK. But compare this graph.

https://research.stlouisfed.org/fred2/graph/?g=1DjX

Notice that in the base year nominal and inflation adjusted GDP are identical. That's what I was getting at. From the 2009 perspective, 2015 is the future.

All this is saying is that if we measured 2015 GDP in 2009 dollars, the number would be smaller because 2009 dollars were bigger than 2015 dollars. Thus, we can talk about the current year in the context of some base year. This allows us to estimate what the value of GDP, etc, would be if the size of the measuring stick hadn't changed.

That is all inflation adjustment is good for. It provides a context, but one that is confusing, and can be easily misunderstood or abused.

Also notice that the inflation adjusted value of 2015 GDP is LESS than the nominal value, not more than, as per your algorithm.

The previous base year was 2002, IIRC. That would give you a completely different set of even smaller post-2002 numbers. So any inflation adjustment is a totally arbitrary exercise. And, again, will be different for any selection of base year.

If the Fed decided to use 2015 as the base year, the allegedly "real" values all will change again, with "real" and nominal values identical for 2015.

This is suggesting to me that there is a conceptual flaw in inflation adjusting a stock.

I'll ask again, why do you think inflation adjusting debt is worth doing, has any meaning - practical, theoretical or abstract; and what do you expect to do with it?

JzB

The Arthurian said...

"Thus, we can talk about the current year in the context of some base year. This allows us to estimate what the value of GDP, etc, would be if the size of the measuring stick hadn't changed."

Yes. If we want to see how much the economy has really grown, for example, inflation adjustment is useful. That's why I say "Real" numbers provide the better measure of growth.

"Also notice that the inflation adjusted value of 2015 GDP is LESS than the nominal value, not more than, as per your algorithm."

But I don't use my algorithm for GDP. I use it for debt, because debt is an accumulation over many years. Each year's addition to outstanding debt must be inflation-adjusted separately.

Suppose we set debt aside, and consider GDP for a moment. Let me take your graph g=1DjX, change the frequency to annual for simplicity, and download the data from FRED. Now I have a set of "flow" values in two forms: actual values, and inflation-adjusted values.

Now pretend there is another variable that people talk about: Aggregate Output. This would be the accumulation of GDP over many years. Here is the relation that concerns me:

Deficits are to GDP as Debt is to Aggregate Output.

My algorithm applies to Debt and to Aggregate Output, not to Deficits or GDP.

If I take the FRED numbers for Real GDP and add them all together, the number I get will be inflation adjusted Aggregate Output

When I make a graph showing Aggregate Output and Inflation-Adjusted Aggregate Output, the Inflation-Adjusted line runs higher,even at and after the base year.

"I'll ask again, why do you think inflation adjusting debt is worth doing, has any meaning - practical, theoretical or abstract; and what do you expect to do with it?"

Krugman says inflation erodes debt. If that is true, then I should be able to show it on a graph. I have shown it. The inflation-adjusted line is higher, even at and after the base year. If the graph turned out like your g=1DjX graph, with the inflation-adjusted numbers lower than the nominals after the base year, then it would show no erosion of debt by inflation. My algorithm shows inflation-adjusted debt is higher, which is what we would expect from Krugman's statement.

Noah Smith asks Why did rich-world deficits start exploding around 1980? A big part of the answer to that question is that the Great Inflation came to an end at that time. Noah fails to deal with that.

I have seen graphs of inflation-adjusted debt where people have used the same calculation that you would use for GDP: The value for any given year has that particular year's price level divided out, and the base year's price level multiplied in. That's fine for GDP.

It's even fine for annual deficits. But with debt, the value for any given year consists of borrowings from many prior years. Therefore, there is no one particular year's price level that can be used to remove the effects of inflation. To solve this problem, we can break up debt into annual deficits, inflation-adjust the deficits separately, and then sum them up to get inflation-adjusted debt.

If inflation-adjusting debt is worth doing, then it is worth doing right.

Greg said...

I think one issue here is conflating terminology between discussions of private debt and public debt.

Much of what you say Art is true regarding our public debt, but that is because it is consistently financialized and traded as an "asset" so its value does fluctuate with inflation. Prices of bonds rise as interest rates fall and interest rates falling are generally something thought of as a fight against deflation, hence inflationary. Since the govt is the one making the payments on the debt and there is never a question as to whether the payments CAN be made (in the US any way) there is some validity to looking at the changing value of the dollars you are getting in various years, hence there is some meaning to the terms "real" or "inflation adjusted"

Its mostly meaningless when discussing private debt. I borrow 10,000 today at 6% for 5 years my payments do not change regardless of the inflation rate. My ability to make them doesn't change unless my income changes. Are there inflation affects on my nominal income? Perhaps my salary has COLAs but if not, a rising cost of everything else (of necessity) mean my debt payment leaves me with less disposable income. That being said I think its not helpful to think of this in terms of "real" vs "non inflation adjusted". The debt payments aren't of any more or less value to the banks who are receiving them, they have already built interest into the equation. Its silly I think to talk about people paying inflation adjusted dollars to banks and inflation doesn't help borrowers pay their debts to banks unless they are having rising incomes during the inflationary times.

Thats my \$.02

The Arthurian said...

Greg, You mentioned about 30 things that I did not bring up, ceteris paribus and all that. None of what I was saying had anything to do with debt being financialized and traded as an asset, for example.

I am trying to make people understand that the calculation used to convert "nominal" GDP to "real" GDP gives the wrong answer if you use it to convert debt. It's not even economics, really. It's arithmetic.

Trying with little success, I should say.

BTW, did you see Brian Romanchuk's post?
http://www.bondeconomics.com/2015/08/inflation-and-debt-burdens.html

jim said...

Art wrote: "I am trying to make people understand that the calculation used to convert "nominal" GDP to "real" GDP gives the wrong answer if you use it to convert debt."

If you use that method to calculate real interest rates it will also
give you the wrong answer. To get real interest rates you just take nominal interest rate and subtract the rate of inflation. No multiplying or division.

I don't know why one might expect to calculate one thing the way one calculates another thing.

The Arthurian said...

Who the fuck was talking about "paying inflation adjusted dollars to banks", Greg?

The Arthurian said...

Thanks, Jim. I like that.

The upper graph on this Wikipedia page

https://en.wikipedia.org/wiki/File:USDebt.png

shows gross and public debt in trillions of 2010 dollars. In other words, inflation-adjusted debt. Everybody figures it the same way you'd figure real GDP from nominal.

I guess nobody ever stopped to think about it.

The R program used to generate the graph is also shown on that page. Can you read R ?

Greg said...

Whoa Art!

I admit my comment, like many of mine, was probably somewhat oblique, but I dont think it missed the mark as much as you think.

Lets look at your post and the comments, including mine.

You start out your post by quoting Nathan Tankus and his argument that inflation doesnt erode the burden of debts. He pulls a quote from Krugman where Krugman talks about falling inflation worsening the burden of debt.

Now I dont care about GDP deflators, CPI, or whatever a this point. Tankus is referring to private debt while Krugman is likely referring to public debt. Or.. Krugman is using the same framework for evaluating public debt and private debt...... which is DEAD WRONG! That is my first point.

Now you and Jazz go back and forth in the comments talking about how, when or whether to inflation adjust certain metrics and argue the merits of one or the other.

My next point is that inflation adjusting public debt metrics has some merit. I might disagree with some on exactly what the inflation adjustment eventually means but I think it is of some use to think about public debt from year to year and consider what inflation has done to it. The reason being, I think, is that public debt is held as an asset in private portfolios so the "value" of that asset is dependent on 1) real growth in value and 2) inflation. I would argue that it means nothing to the govt since it never affects their ability to pay, but it does ("it" being inflation) does matter to the private sector holder of the debt.

For private debt, one where people owe banks, I think inflation adjusting is a worthless concept and I started to explain why. Thats where I was talking about paying inflation adjusted dollars to banks.
You said;

"I am trying to make people understand that the calculation used to convert "nominal" GDP to "real" GDP gives the wrong answer if you use it to convert debt. It's not even economics, really. It's arithmetic."

I agree completely. But I want to take it a step further and say stop thinking about debt to GDP ratios for public debt the way you think about debt to income ratios for private debt. GDP is not the govts income!