Debt and Inflation (3): Nomenclature

Suppose I borrow a dollar when the price index is 80. If I pay it off when the price index is 125, the erosion of debt by inflation is easy to figure. We can do it two ways.

We can multiply the debt by 80 and divide by 125. That tells us how much the dollar is worth, that we are paying back: It is worth 64 cents of the dollar we borrowed.

Or we can multiply the debt by 125 and divide by 80, This tells us how much we would have to pay, to pay back equivalent purchasing power: In this case, about $1.56.

But suppose I borrowed a dollar when the price index was 80, and borrowed another dollar when the price index was 115, and I pay it all off when the price index is 125. Now the calculation is not so simple.

Or suppose I borrowed a dollar at price index 80 and started paying it back the next year. And maybe I had it half paid off some years later when the price index was 115 but at that point I borrowed another dollar. And I've been making payments every year since. And now, when the price index is 125, I want to see where I stand.

Now the calculation is even more complicated. To be accurate, the calculation must use price indexes from all the years, because there were transactions in all the years.


Consider any particular year. The new debt created that year should be adjusted the same way GDP is adjusted for that year.

The problem is that the total debt number for that year includes both the new debt from that year and a lot of older debt, and we should really separate out the new debt before making an inflation-adjustment on it.

I want to do this for all the years that I know about, adjusting each year's new debt and adding it to the previous year's total. This leaves me with just one problem: the first year of the series. Since this is the first number I have, I cannot separate out the prior years' debt. So the first inflation adjustment is a fudge.

However, debt has increased a lot (as we know) so the first year's debt is a relatively small number. So, maybe the fudge will be insignificant.

And anyway, the calculation I want to do for the first year is the standard calculation used to make inflation adjustments. So my adjusted numbers will begin with exactly the same value that the "standard usage" calculation starts with. Only the subsequent numbers will differ.


I made up some numbers and went over the calculation a few times in Excel, and it's simpler than I thought. Actually, I use the same standard calculation as everybody else, except I separate new debt from existing, and apply each year's price level only to that year's addition to debt.

I did struggle with that, a bit. What happens if you borrowed some money some years ago, then later you paid off half of it but also borrowed some more?

It's less complicated than I thought. If I pay off some debt and borrow more that same year, both of those transactions will use the price index for that year. Yes, I paid back some debt with inflated dollars. But I also borrowed more of the same inflated dollars. Since we (crudely) figure the price level is the same for the whole year, the payback and the new borrowing is a wash. Only the net difference, only the change in total debt will affect my calculation of inflation-adjusted debt.

So again, I will take only the new debt for that year, and apply that year's price index to it. And I will add that adjusted number to the previous year's adjusted total to get the new adjusted total.

It's easier to do in a spreadsheet than in words.


I want to create some terminology we can use to distinguish my inflation-adjustment calculation from the one that is standard usage.

My calculation adjusts each year's debt separately, translating the "nominal" values into "real" values. So I will call this the "Annual Real Translation" (ART) calculation. The standard calc I will refer to as the "Standard Usage Recalculation for Real" (SURReal) adjustment.

Next, we will look at some spreadsheets.

Debt and Inflation (2): Background

I want to look at the "productivity" of debt, and at eroding the real value of debt by inflation during the Great Inflation. But first I want to evaluate the notion of the real value of debt and the inflation-adjustment of debt.

I looked at inflation-adjusted debt a while back, in Iffy, Piffy:

Graph #1: Inflation-Adjusted Gross Federal Debt

At the time, I said this:

This graph shows that before about 1981 the growth of the Federal debt kept pace with inflation, and since that time the growth of the Federal debt has far exceeded inflation. The change is surprisingly distinct.

Okay. However, in that post I also expressed this conclusion:

If the Federal debt only keeps up with inflation, then the debt is not excessive. By this measure, until 1981 the Federal debt was certainly not excessive.

Today, I am not certain of that.


I went looking for other examples of inflation-adjusted debt graphs.

Mark Wieczorek looks at the national debt, adjusted for inflation, and writes:

In 1950's dollars, our debt is currently $887,445,036,515.72 or 887 billion dollars, which is 3.45 times the size of the debt in 1950. Here's just the inflation-adjusted debt from 1950 - 2003. This graph paints a very interesting picture about the past few administrations.

At Technorati, Steve Kosoris provided graphs of the U.S. National Debt, also adjusted for inflation. And at Bearwatch, Sackerson looked at US public debt since 1945 - inflation-adjusted. Sackerson writes:

For a long time, US public debt increased no faster than consumer price inflation, then under Reagan it appears to have started its steep rise. The causes are presumably complex...

And the Supporting Evidence site looks at the Federal debt, showing both current and inflation-adjusted values:

Source: Supporting Evidence

Oddly, all of the inflation-adjusted debt graphs I found were for the government debt. None showing total debt. Not even mine.

I still wonder what can and cannot fairly be said about these graphs and about the inflation-adjustment of debt. My first thought was: Wow, Reagan really increased government spending! But that's not right -- or, at least, it isn't what the graphs show.

If increased government spending was the cause of the change in trend, it would show up in current spending. It would show up in the deficits immediately. But it would appear in accumulated debt only after a lag. Cumulative numbers change slowly.

So if increased government spending caused that distinct change in the debt graph, we should look for the increase not in the years after 1981, but in the years before. And we should look not at the accumulated debt, but in the annual deficits, the additions to accumulated debt. Mark Wieczorek, quoted above, shows the additions to debt:

Additions to the National Debt, Adjusted for Inflation

The increase appears to begin in the mid-1960s, concurrent with the increase of inflation. Not concurrent with Reagan in the 1980s.

Note that the increase in deficits is not explained by inflation, for the graph shows inflation-adjusted deficits.

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:

Graph #2: Calculating Inflation-Adjusted GDP

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.

The Inflation Adjustment of Debt

The typical inflation-adjustment of GDP takes the total dollar value of one year's output and converts it to the dollar value of another year. For example, if a basket of goods used to cost $80 but now costs $125, you take GDP now, multiply by 80, and divide by 125 to convert the current value to the value of that other time.

If for another year the basket cost $115, well, multiply that year's GDP by 80 and divide by 115. (Basically, the arithmetic un-distorts output by one year's price level and re-distorts it by a different year's price level. When all the years are distorted by the same price level, economists call that "real" output.)

Using this method, GDP for any set of years can be evaluated as if prices had not changed. That lets you distinguish changes in prices from changes in the amount of stuff we produce, to get a more accurate picture of how output has grown over time.

The GDP Deflator is a series of numbers that are conversion values for a whole series of years. That's where you find values like my examples 80 and 115 and 125, but actual numbers for all the years. So that works.

The thing is, when you look at GDP you're looking at the value of one year's output. It makes sense to use the deflator number for that year when you do the calculation.

But when you look at debt and try to make the same conversion of values, there is a problem. Debt is typically created and accumulated over a number of years rather than a single year. If you look at the debt you have today and this year's deflator number is 125, that's probably not the right number to use for all your debt. Maybe you took on some of that debt last year or the year before that, or the year that the deflator value was 115, or maybe even the year the deflator value was 80. This complicates the calculation.

With GDP, the number is the total value of stuff created on one year. So the standard conversion works fine. But with debt, which accumulates over many years, the standard calculation must give a wrong answer.


In my next few posts, I will consider the inflation adjustment of debt.

Why we do graphs

A graph from How fiscally prudent is "lower the rate and broaden the base"? by Craig Gurian at remappingdebate.org:

Pretty sure I've looked at both the series shown on this graph, separately. But putting them together makes an interesting picture. Funny thing, though: To my eye the graph does *not* show what it claims to show. It does not show that "As effective rates go down, so does tax revenue as a share of GDP". Not to my eye.

Oh yeah, the orange line -- the effective corporate tax rate -- shows a consistent downhill run from start to finish.

And yeah, the blue line -- Corporate taxes as a percentage of GDP -- shows a parallel downhill run. But only until 1982. After that, the blue line runs flat.

After 1982 the blue line runs flat while the orange line continues to run downhill. And it is pretty easy to see that the two lines get closer and closer together after 1982.

This is what I think: I think it makes sense to say "As effective rates go down, so does tax revenue as a share of GDP". I think that is what we would expect to be true. But the graph seems to show that it is not true, or anyway that it is no longer true.

It is particularly striking that the change comes just at the start of the Reagan era. Lots of people might not want to admit that Reagan appears to have stopped the decline of corporate tax revenue as a percent of GDP. But then, it is right there on the graph.

It is possible that what the graph really shows is a sudden slowdown in the growth of GDP after 1982, which pushed up the blue line enough to make it run flat.

It is possible that what the graph really shows is that there was a sudden increase in corporate taxables as a share of GDP after 1982, which pushed up corporate taxes enough to make the blue line run flat.

But it is not possible that "As effective rates go down, so does tax revenue as a share of GDP", because after 1982 the effective rate continued to fall and tax revenue did not.

Private Debt 2012 (18): The Limits to Debt

People have to see their parents doing well and their grandparents retiring well, or all is for naught.

Yes, you can put the stranglehold on, and eke out a few more dollars of interest for a few more years, but nobody likes that too much and people will turn against you, and turn against your economic system. Not only will they abandon their underwater homes. They will also give up on the concept of economic growth.

Don't expect people to be "rational".

Nick Rowe and NGDP Targeting

I don't care what you want to target. NGDP LT? Hot item these days. I don't care. Let me look at Nick Rowe's response to David Andolfatto on the subject, at a theme that runs through Rowe's post.

1. "NGDP targeting provides a 50-50 aggregate sharing of aggregate risk between creditors and debtors. If real GDP falls 10% below what was expected, the price level rises 10% above what was expected..."

Rowe is talking about the effects of inflation on debt -- the erosion thing. What he points out, however, is that NGDP targeting offers no assurance of growth.

If real output turns out 10% low, then inflation just goes 10% high. If real output goes 50% low, then inflation goes 50% high. NGDP targeting does nothing for growth.

2. "Many New Keynesian models assume Divine Coincidence. They assume that if monetary policy is successful in keeping P on target it will also, as a happy side-effect, keep Y on target too."

P is the price level; Y is real output. Nick Rowe says these models assume that if policy keeps prices on target, real output growth will stay on target too.

That's a criticism of inflation-targeting, not NGDP targeting. But the same logic applies to both; NGDP targeting does nothing for growth. NGDP targeting is policymakers telling us: If you don't want inflation, then make sure you generate real growth.

But that's not how you get real growth.

NGDP targeting is a policy choice that finds inflation and real growth to be equally acceptable alternatives. As Rowe says, "An unchanged target P.Y will allow P to rise so Y won't fall as much." If real growth falters, an unchanged NGDP target will allow prices to rise so real growth won't fall as much.

Of course I am sure that no economist, and no one else either, would say inflation and real growth are equally acceptable. But that is what NGDP targeting (the policy) says.

3. "When a negative AD shock hits, both P and Y will fall. When AD recovers both P and Y will rise. But we know very little about how that rise in AD will be divided into a rise in P and a rise in Y."

Nick Rowe says that we have little control over the outcome of an NGDP-targeting stimulus. If aggregate demand (AD) falls below target and policy provides stimulus, "we know very little" about how that stimulus will be split up between real growth and mere inflation. This theme runs all through Rowe's post.

Actually, I think we know quite a lot about that. Knowing nothing, I think we can assume that everything will go to inflation and nothing will go to growth.


Nick Rowe is arguing that, given all of the unknowns, NGDP targeting would give better results than inflation targeting. I'm not disputing that.

I'm pretty sure the argument is that inflation is an inducement to spend, and spending boosts aggregate demand, and higher AD leads to growth. Well, I'm no economist and it is beyond my abilities to out-argue economists about such things. Anyway, I think it's probably at least half true.

So where's the problem? The problem is the problem you already know: The growth we get is inadequate. Same problem we've had since before Reagan:

"Reaganomics" was the most serious attempt to change the course of U.S. economic policy of any administration since the New Deal. "Only by reducing the growth of government," said Ronald Reagan, "can we increase the growth of the economy."

- William A. Niskanen

Reagan was wrong about the need to reduce the growth of government, and anyway his policies proved unsustainable. But the point is, his objective was to increase the growth of the economy. Because growth was inadequate.

That was the problem then, and it is still the problem now. That's why we have the George W. Bush tax cuts. It's why we have people calling for austerity. It's why we have people calling for inflation. And it's why we have people calling for NGDP targeting. But NGDP targeting can do little or nothing to boost real growth, as Nick Rowe points out.


Why do we have trouble getting adequate economic growth? Is growth hindered by the fact that we don't use NGDP targeting? No. NGDP targeting is an approach that attempts to get the desired results without bothering to analyze the cause of the problem.

NGDP targeting is a manipulative policy. It uses people's reactions to inflation to induce spending and extort growth from the economy. Would it work?

Does it solve the problem? Well... Of course not. The problem is not simply that we don't get adequate growth. The underlying reason we don't get growth -- that is the problem. But NGDP targeting does not bother to investigate such things.

Act Naturally

From Scott Sumner's response to David Andolfatto:

The recent (2008-09) NGDP crash was the largest since the 1930s, and Lucas has argued that the Friedman and Schwartz story applies to the steepest part of that crash, in late 2008 and early 2009. However he also believes that the slow recovery is better seen as an example of the sort of stagnation that hit Europe after the 1970s, when natural rates of unemployment rose to a much higher plateau.

1. One would expect Sumner to speak of an "NGDP crash" as opposed to a GDP crash, because NGDP is part of Sumner's central theme. However, we really didn't have much deflation to speak of, so what is correctly described as an NGDP crash is also correctly described as a GDP crash or an RGDP crash.

No biggie. But Sumner's use of the term "NGDP crash" shifts focus to his theme and away from analysis of the problem. And it is never right to take eyes off the analysis.

I guess that's the problem with lots of solutions people offer: They want you to look at their solution, rather than at what the problem really is.

2. The biggie:

"...the slow recovery is better seen as an example of the sort of stagnation that hit Europe after the 1970s, when natural rates of unemployment rose to a much higher plateau."

You can't just make up something like "the natural rate of unemployment" and assume that it varies, and then throw numbers together based on these and other assumptions and call that evidence, and expect me to buy it.

The thing that you call the natural rate is something I see as a result of the interaction of your conflicting economic policies. But you never blame your policies. You act like your policies had nothing to do with the problems. You act like there's no way your policies could have done things to make the so-called "natural" rate go up.

Funny thing about that: If you guys made the natural rate go up, it isn't really a natural rate at all.

"infinitely better"

From Robert Reich's #21788301646:

...the real issue isn’t debt per se but the ratio of the debt to the size of the economy.

In their haste to cut the public debt, Europeans have overlooked the denominator of the equation. By reducing public budgets they’ve removed a critical source of demand — at a time when consumers and the private sector are still in the gravitational pull of the Great Recession and can’t make up the difference. The obvious result is a massive slowdown that has worsened the ratio of Europe’s debt to its total GDP, and is plunging the continent into recession.

A large debt with faster growth is preferable to a smaller debt sitting atop no growth at all. And it’s infinitely better than a smaller debt on top of a contracting economy.

Infinitely better. The words of a man who does not understand numbers. The chosen word should be interesting, perhaps aggressive, never irritating. Reich is irritating.

I like "the gravitational pull". Wealth has gravity, or something like. That's the reason people say it takes money to make money.

I don't so much like "the real issue" and "per se". Here: The problem is not the debt itself, but the ratio of debt to the size of the economy.

But Reich -- Santovenia once referred to him as "the diminutive Mr. Reich" -- isn't really talking about debt. He's talking about "the public debt" and that's a whole other animal. The way the economy responds to "debt" is by no means the same as the way it responds to public debt.

We can argue till the cows come home about more or less public debt and the benefit or harm of it. Twill solve nothing. Public debt is not the problem.

Refrain.