Inflation-Adjusted Additions to Debt, and their Hodrick-Prescotts: An Exploration

I got a bunch of numbers from FRED -- the GDP deflator, and some measures of debt. All annual values, so the "additions" noted in the post title are annual additions. The debt numbers are "end of period" values, presumably the greatest accumulation debt reached each year. The deflator is the average of the year's values.

The FRED graph doesn't look like much, but it got me lots of numbers to work with. I took those numbers, selected from them half a dozen different measures of debt and, for each, I figured each year's change from the previous year in billions of dollars, took the inflation out of that number, and plotted the result:

Graph #1: Inflation-Adjusted Additions to Debt

Even though the inflation has been stripped out of the numbers, there is a definite increase as the years go by.

I thought maybe looking at annual percent change for the above graph might be useful. Silly me:

Graph #2: Percent Change from Prior Year for the Values Shown in Graph #1

There are some pretty healthy spikes of various colors on this graph. But you can't really see much else. So I figured I'd zoom-in, chop off a lot of the tall spikes, and maybe get a better look at the general activity:

Graph #3: A Close-Up of Graph #2

Still not much to look at.

So I gave up on that approach. I decided to look at the Hodrick-Prescott paths of the data-sets shown in Graph #1, the annual change (in billions of inflation-adjusted dollars) for each debt category:

Graph #4: The Hodrick-Prescott Values for the Data Shown in Graph #1

Okay. I thought maybe we'd see different lines showing peaks in different time periods for different debt categories. I don't see a lot of that, but this graph is easier to look at than Graph #1. It's clear that everything but Farm Business debt is going up, and the paths are simplified.

One thing clear on Graph #4 is a simplified picture of the size of Federal deficits, the orange line. It increases until about 1986, then decreases until about 1998, then goes up again. FWIW.

Above, we looked at the additions to debt in billions (Graph #1) and then at the percent change in those numbers (Graph #2). And the second graph was not very useful. Same here. Graph #4 looks at the H-P paths of the additions to debt in billions. Graph #5 shows the percent change in these numbers. It doesn't look useful:

Graph #5: Annual Percent Change in the Hodrick Prescott Values from Graph #4

Farm business debt (the brown line) shows some unusual spikes in the 1980s and 1990s. And the red and blue lines both show unusual declines related to our recent troubles. I note that the fall in the red line -- finance -- comes before that of household debt, the blue line.

Oops, I forgot to move the dates down out of the way.

In Graph #6 I zoom in on Graph #5, like before, to get a better look at the general activity.

Graph #6: A Closeup of Graph #5

Now it's getting like a Jackson Pollock painting: it's a pretty picture, but not a pretty picture of anything. Like abstract art, it's starting not to convey information. Let's zoom in more:

Graph #7: A Closeup of Graph #6

Anything?

The red line goes down until the end of the 1980s, then up for a few years, then falls. The brief up-disturbance reminds me of the 1990-93 disturbance in my Debt-per-Dollar graph. The red line is Financial debt.

Household debt (blue) perhaps follows the same pattern, but it would be pretty easy to call the trend "flat" until just before the disturbance. The blue line is also lower, suggesting a slower rate of debt growth than seen in the red line.

The orange line -- based on the annual change in Federal debt -- peaks around 1971, then falls dramatically, dropping off the graph in 1995, during the latter years of Clinton.

Inflation-adjusting deficits

It's easy to inflation-adjust deficits, as opposed to debt. A deficit is annual: This year's deficit doesn't include any of last year's deficit, or any other year. So adjusting deficits is like adjusting GDP: Multiply by 100 and divide by the price index. That's it.

Here's the record of Federal government deficits:

Graph #1: The Bigger the Deficit, the Farther Down the Line Goes

The line goes down more as the deficits get bigger, because they're deficits. I find it confusing, though. Just casually looking at it, I want the bigger deficit to be higher. So I inverted the graph. Also, I'm chopping off the years before 1940 because I'll be using another time series doesn't go so far back in time.

Graph #2: The Bigger the Deficit, the Higher Up the Line Goes

As noted above, to strip away the inflation from these numbers, I just have to multiply by 100 and divide by the price index:

Graph #3: Graph #2 Corrected for Inflation

Corrected for inflation, the Federal deficits start increasing in the late 1960s, and trend upward all through the 1970s. The trend runs flat through the 1980s, then falls in the 1990s.

The increasing size of deficits means a faster-growing debt. This confirms what we saw the other day, that a correctly inflation-adjusted Federal debt does not run flat from World War Two to the Reagan years.

Checking my facts after spewing them

In mine of 6 November I wrote:

Very little of the Federal debt of 1970 was due to the borrowing of 1970. Most of that debt was from prior years.

Sounds right, doesn't it?

I don't think I ever looked at it though.

So... I can get a post out of that!

If I take FRED's Gross Federal Debt (FYGFD) and look at the increase for one year, 1970 say, that's the deficit for that year. If I look at the total for that year, it's the debt.

If I look at the increase for that year divided by the total for that year, and it's a low number, then I can fairly say "very little of the Federal debt" that year "was due to the borrowing of" that year. Got it?

Also, it might be interesting to see the trend.

Graph #1: Annual Addition to Federal Debt as a Percent of the New Total

Apart from the World War Two years, the Federal deficits have for the most part been less than 10% of the accumulated Federal debt. I think it's fair to say: that's a low number. At least, it means that the common, incorrect inflation adjustment of debt has the calculation right for only about 10% of accumulated debt, and it miscalculates the other 90 percent.

Regarding the trend, note that the increasing size of the deficits (again, apart from WWII) occurs mostly in the 1970s (and after 2000); and that the 1980s shows a trend of decreasing size. Again, this contradicts the notion that the deficit exploded under Reagan.

Son of a bitch, there it is again!

What site was I at? They had two graphs from Wikipedia -- the one, showing Federal debt held by the public and gross Federal debt for comparison. My mind goes back to this graph, and to my recent pie charts comparing components of debt.

Here it is. Found it at Wikipedia:

U.S. debt from 1940 to 2011. Red lines indicate the "debt held by the public" and black lines indicate the total national debt or gross public debt. The difference is the "intragovernmental debt," which includes obligations to government programs such as Social Security. Stated as a formula, National Debt = Debt held by the Public + Intragovernmental Debt. The second panel shows the two debt figures as a percentage of U.S. GDP (dollar value of U.S. economic production for that year).

The top panel is deflated so every year is in 2010 dollars.

Son of a bitch! "The top panel is deflated so every year is in 2010 dollars."

Pick a year: 1970. The Federal debt for 1970 included borrowings from 1969 and 1968, and from 1965 and 1960, and from the Korean War and World War Two, and for all I know it included borrowings from back to the time of Andrew Jackson.

For the Wikipedia graph, when the value for 1970 is "deflated" it is converted from 1970 dollars to 2010 dollars. In other words, all of that accumulated debt as of 1970 is assumed to have been originally borrowed in 1970. That's obviously wrong.

Very little of the Federal debt of 1970 was due to the borrowing of 1970. Most of that debt was from prior years. So deflating the debt as if all of it had been newly borrowed in 1970 is an error. A gross error. You can't swing a dead cat without seeing people make that mistake.

Now, the post I had in mind to write:

The Growth of the Gross Federal Debt

People are always showing the Federal debt:

Graph #2: Federal Debt Held by the Public

People are always saying that's not right, that's just the part of the debt held by the public. And it does exclude the "intragovernmental" debt that Wikipedia mentions:

Graph #3: Federal Debt without (blue) and with (red) the "Intragovernmental" Debt

You know what else it excludes? It excludes everybody else's debt:

Graph #4: Measures of the Federal Debt (red, blue) and Total Credit Market Debt (green)

The green line shows "credit market debt". It includes everybody else's debt other than the Federal government, and it includes the blue, "held by the public" debt of the Federal government. It does not include the "intragovernmental" debt. Everything from the blue line up to the green line is debt other than Federal.

We can subtract the blue line from the green line, and add in the red line to get a measure of debt that includes all of the Federal debt, here in orange:

Graph #5: All the Debt I Know About (orange)

That's all the debt I know about.


Now...

I want to take all the debt I know about, subtract out the gross Federal debt, and compare what's left to all the debt I know about. And to make it a little more interesting, I'll also compare the gross Federal debt to all the debt I know about:

Graph #6: The Two Parts of All the Debt I Know About

Why can't we get the Federal government's debt down? Because everyone else's debt is so high. The money we could be paying in taxes to the government (for doing things like providing us the dollar) goes instead to lenders for providing us with credit.

Can't swing a dead cat...

So I found this site
this dramatic site that uses the Great Seal
a version of the Great Seal of the United States
with the words Slaying the Dragon of Debt overlaid on the image...

I'm looking at their About page...

"Slaying the Dragon of Debt" is a research project by the Regional Oral History Office of The Bancroft Library at the University of California, Berkeley. The first year of the project was funded under the auspices of the Shorenstein Program on Politics, Policy, and Values.

Berkeley used to be a cool place.
I'm not getting that vibe from this site.

The question of how much national debt the United States can bear is one of the most divisive issues in contemporary American politics. After reaching a postwar historic low at the end of the 1970s, the national debt has risen to a level that many observers consider unsustainable. Why has the debt grown during this time? What accounts for the federal government’s almost chronic inability to balance the budget? How worried should we be about these developments?

It is irrefutable that the national debt --
by which I presume they mean the Federal debt --
is a divisive political issue today.
It's a political issue, but it's not a political problem.
It's an economic problem. Or an economic non-problem, maybe.

Clicking their TimeLine menu item brings up a timeline graphic.
You can click different parts of the graphic to bring up a relevant page.

The first one I clicked was the Omnibus Budget Reconciliation Act of 1981
which brought me to this page, and this graph:

I didn't need to read the bold print. The flat spot that runs from World War Two to Reagan told me at a glance that I was looking at debt corrected for inflation.

Debt incorrectly corrected for inflation. You can't swing a dead cat without hitting the incorrect inflation adjustment of debt.


What's the point of "correcting" a graph for inflation? Isn't the point to show what the true number would have been, if there had been no inflation?

If inflation erodes debt, the debt burden becomes less because of inflation. So if there was no inflation, the burden would be more than it actually is.

How much more?

Suppose you borrowed $1000 at a time when the price level was 1.0. Later, when the price level was 2.0 you pay back the loan. You pay back $1000. You get off easy, because prices have doubled. $1000 buys only half what it used to buy. To make the inflation adjustment, take the 1000, divide the old price level (1.0) out of it, and multiply the new price level (2.0) into it.

The inflation-adjusted value of the $1000 you borrowed is $2000, because prices have doubled. If you only have to pay $1000 to pay off the loan, well, the other thousand dollars of value just got eroded away!

But suppose we change our mind and decide not to pay back the loan when the price level is 2.0. Instead, we borrow another $100, so now we owe a total of $1100.

Later, when prices have doubled again we pay off the loan. We pay $1100. How much of the original value has eroded away?

We could do the same calculation we did before, but with the new numbers. We could divide 1100 by the old price level (2.0) and multiply by the new price level (4.0). In fact, that's how the inflation-adjustment of debt is typically done. That's how it's done for the "Slay the Dragon" graph. But it's wrong: 2.0 is the old price level for the $100 you borrowed... 1.0 is the old price level for the $1000.

Let's work it out. Divide 1100 by the old price level 2.0, you get 550. Multiply 550 by the new price level 4.0, you get 2200. So we're saying the inflation-adjusted value of the $1100 is $2200. It makes sense at first, because prices have doubled. But wait a minute...

Prices only doubled once after you borrowed the $100. But prices doubled twice since you borrowed the $1000. You have to take the 1000, divide by 1.0, the price level when you borrowed the 1000, and multiply by 4.0 to get the right adjustment. And you have to take the 100, divide by 2.0, the price level when you borrowed the $100, and multiply by 4.0 to get the right answer for the second loan. And then you have to add the two adjusted numbers together, add $4000 and $200 together, to get the right answer.

Each year's addition to debt has to be adjusted separately, to convert from that year's price level to the "base year" price level you want to use. If you lump it all together, you get it all wrong.

In our little example, the correct answer ($4200) is a lot higher than the original amount we borrowed, $1000 plus $100 or $1100 total. The correct answer is also a lot higher than the incorrect answer of $2200.

When people use the wrong method of inflation-adjusting debt, often their answer is significantly below the correct answer. Keep that in mind when you look at my "Three Views" graph below.


I got annual numbers from FRED for the Gross Federal Debt (1939-2012) and the GDP Deflator to use as a price index (1947-2012). Uploaded to Google Drive.

First I want to duplicate the "Slay the Dragon" graph. Theirs starts at 1940 but I can only start at 1947 because of the price index numbers I got. And theirs ends around 2007, but I can go all the way to 2012. But that's okay.

I'm using the same base year they used, 2000, so that my numbers are the same or close to theirs if I do everything the same way they did. It's a good match:

Graph #2: From the sheet named "Wrong" in the Google Drive Spreadsheet

Next I show three versions of the Federal debt: the raw numbers, the incorrect, slay-the-dragon style inflation adjustment, and the correct adjustment:

Graph #3: From the sheet named "Three Views" in the Google Drive Spreadsheet

The raw, unadjusted numbers are shown in blue They start out around $257 billion, hit $5628.7 billion in 2000, and end up at 16,051 billion in 2012.

The incorrectly adjusted numbers are shown in red. This line uses the same numbers as my Graph #2. The numbers start out around $1632 billion, reach $5628.7 billion in 2000, and end up at $12,517.7 billion.

The correctly adjusted numbers are shown in yellow. They start at 1632.2, reach 9348.2 in 2000, and end up at 18,080.2 billion.

If inflation erodes debt, the debt burden becomes less because of inflation. Corrected for inflation, the burden would be more than it actually is. So, let's check our numbers. Year 2000 is the base year; let's check that year.

The raw, uncorrected numbers (blue) tell us that we had a $5628.7 billion Federal debt in the year 2000. The incorrect numbers (red) also tell us that we had a $5628.7 billion Federal debt in the year 2000, after adjusting for inflation. This cannot possibly be right, because inflation erodes debt. Corrected for inflation, the year 2000 value of debt must be more than the raw numbers -- must be more, unless there was no inflation at all since the start of the graph.

But there certainly was inflation. For many years leading up to year 2000 there was inflation. So the correct inflation-adjusted number would have to be higher than the raw number. It has to be.

The yellow line shows that correcting for inflation pushes the gross Federal debt up from $5628.7 billion to $9348.2 billion. Thankfully, we only have to pay the lower number. But if you're gonna figure the inflation-adjustment of debt, you may as well do it right.

Before you ask... No, there's not a problem with the inflation-adjustment of GDP, not this problem anyway. The problem arises because debt accumulates over many years, and over those many years prices are changing. GDP only accumulates for one year, and the change in prices over one year is small compared to a long-term change. This small change is typically taken as an average for the year. So the problem identified here does not apply to the inflation-adjustment of GDP.

So, that snazzy snap-the-dragon site makes a big stupid mess of things with their flawed inflation-adjustment of debt. They claim that "the deficit exploded under Reagan." And their graph shows it.

But their graph is wrong.


// For more on the inflation-adjustment of debt (and other "it's a stock, not a flow" variables) download my 14-page PDF from MPRA.

Household debt as context

Here's the measure of debt people often show when speaking of "household" debt:

Graph #1: Household Debt

Here it is in context, relative to GDP:

Graph #2: Household Debt relative to GDP

Now look at household debt relative to financial debt:

Graph #3: Household Debt relative to Financial Debt

In the early years, when household debt was small, and small relative to GDP, it was still nine or ten times the size of financial debt.

Financial debt was tiny.

Today, household debt is high, and high relative to GDP, yet it is just about equal in size to financial debt.

Financial debt is tiny no longer.

With nothing particular in mind

Sometimes I wake up in the morning with nothing particular in my mind. I get a cup of coffee (or tea. Lately, more tea than coffee. Tea with honey) and sit down at the computer. Often, I end up at FRED.

Today is one of those days.

Graph #1: What's called "Household Debt" ... Debt of Households and Nonprofit Organizations

Blue: Household debt relative to GDP (relative to GDP, for context) (because everybody looks at household debt, and everybody looks at it relative to GDP).

Red: Percent change from year ago, of same.

The blue line rises to a mid-1960s peak... At that point the red line falls below zero (see the right scale) and remains below zero for a while, so that the blue line trends down for a few years.

In the 1970s there is a resurgence of debt growth, debt-to-GDP growth really, with the uppermost peaks of the red line trending uphill until the mid-1980s; and the blue line trending upward again also.

After the mid-1980s peak, the growth of the red line falls back toward zero (right scale). The blue line continues rising, but at a slower rate, through the 1990s.

A large spike in the red line around the year 2000, then a gradual tapering, appears in the blue line as a massive increase from 2000 to the 2009 recession. Decline thereafter in the blue line, as the red line again goes below zero.

//

I'm wondering if the uptrend from the latter 1960s to the mid 1980s has anything to do with the inflation of those years. Yes, yes, I know: The debt here is "in context". Inflation affected both the debt number and the GDP number, and it should have no bearing on the direction of trend.

Oh -- but that's not really true. I looked at the erosion of debt before. Inflation today, or inflation on a given day, let's say, affects not only prices and borrowing at that moment, but affects also the cost of all pre-existing debt. (I bought a house back then, and after a few inflationary years my mortgage payment took a much smaller bite out of my weekly paycheck.) In those inflationary years, the cost of accumulated CMDEBT eroded as GDP and incomes were inflating. The ratio, the blue line should have been trending down.

But during most of the Great Inflation, the blue line wasn't trending down. It was trending up. That means debt must have been growing faster than GDP -- growing so much faster that it kept the blue line going up despite the inflation of those years.

Have a look at growth rates:

Graph #2: Percent Change from Year Ago for GDP (blue) and CMDEBT (red)

The red peak of the latter 1960s is lower than the blue peak. Household debt grew more slowly than nominal GDP in those years. This corresponds to the decline on Graph #1 between the mid-1960s and the 1970 recession.

Between the 1970 and 1974 recessions the red and blue peaks are nearly the same. The red is a little higher and maybe a little wider. CMDEBT, represented by the red line, grew a little faster than GDP. And sure enough, on Graph #1 the blue line goes up a little between the 1970 and '74 recessions.

Between the 1974 and 1980 recessions the red peak is clearly higher and wider than the blue. CMDEBT grew significantly faster than GDP in those years -- and again, the rising blue line on Graph #1 confirms this.

So yes: Debt was growing faster than GDP in the 1970s, despite the inflation of those years. And no: the uptrend on Graph #1 from the latter 1960s to the mid 1980s doesn't seem to be because of inflation. It seems to be despite inflation.

The 1970s was the time of the greatest excitement of the Great Inflation. Inflation was driving GDP up... Inflation was eroding the burden of debt... But did we take advantage of that erosion to pay off debt at a faster rate? We evidently did not. Debt grew faster in the early 1970s than in the late 1960s, and faster in the late 1970s than the early 1970s as Graph #2 shows; and, as Graph #1 shows, the ratio of CMDEBT to GDP rose through the 1970s. Not only rose, but accelerated.

Did I make an extra payment every so often on my old mortgage? I did not. Instead, sad to say, I started using credit cards. My debt went up faster than my income.

//

Graph #3 shows "percent change from year ago" growth of household debt (blue) and the rate of inflation as measured by the GDP Deflator (red):

Graph #3: The Growth Rate of CMDEBT (blue) and GDP Deflator Inflation (red)

Inflation (red) peaks twice in the 1950s, reaches a bottom at the end of the 1950s, and starts to climb rather early in the 1960s. This is where the Great Inflation begins.

During those years, the growth rate of household debt is slowing. It slows until the 1970 recession. It slows for the better part of a decade after inflation starts to rise. It was not the growth of debt -- not household debt anyway -- that turned the embers of inflation into a raging fire.

Do I find this disturbing? Of course I do. I need another look. Graph #4 shows the same measure of debt (blue) as Graph #3, and the rate of inflation as measured this time by the Consumer Price Index (red):

Graph #4: The Growth Rate of CMDEBT (blue) and Consumer Price Index Inflation (red)

Same story. Debt growth slows all through the 1960s; inflation picks up early in the 1960s. Why do I find this story disturbing? Because I blame debt for everything! But I cannot blame the slowing growth of household debt for the accelerating inflation.

It bothers me, yes. It doesn't bother me a whole lot, though, because I know there's gotta be costs somewhere that ignited the inflation. It's just that those costs are not to be found in household debt.

For the record, then, let's have a look at some other debt. I'll start with TCMDO, total credit market debt, and subtract CMDEBT out of it. Subtract out the household debt. Come to think of it, I'll subtract out the Federal debt, too. Everybody knows that the Federal debt is the source of all our troubles -- thinks they know -- so let's eliminate that source of troubles along with household debt, and take a look at the debt that remains.

And I'll show it with the red and blue lines both using the same scale, the left scale, so you can better judge how high the rate of debt growth was in the 1960s and '70s, as compared to the rate of inflation:

Graph #5: The Growth Rate of Debt Other than Household and Federal Debt (blue)
and Consumer Price Index Inflation (red)

I rest my case.

"The malign effect of high private debt"

The euro crisis: Debtors' prison at The Economist:

The malign effect of high private debt becomes apparent in the busts that follow credit-driven booms. Households that have borrowed too much in relation to their income trim their spending, the main component of GDP. Overleveraged firms avoid investing and concentrate on shrinking their balance-sheets by paying off loans. As bad debts erode their capital, banks become more reluctant to lend. These adverse trends reinforce each other, increasing the overall drag on growth.

Components of debt