Friday, August 31, 2018

Cecchetti Mohanty & Zampolli and the effects of inflation on debt

This is the post I was talking about the other day when I said "I'm working on something that's taking forever." Now it's done. The post is so damn long that I can't read it all in one sitting. So grit your teeth and get through it as fast as you can.

Or maybe go the other way, and let the reading take forever, like the writing did.

The real effects of debt (PDF), the 2011 paper by Stephen G Cecchetti, Madhusudan Mohanty and Fabrizio Zampolli, includes a graph of debt adjusted for inflation. The inflation-adjustment of debt is a topic of great importance to me, and is the focus of today's post.

In this article I will be using the symbol "N2R" to mean "nominal-to-real". I discuss two different N2R calculations: the "standard" calculation, SN2R, and the Arthurian alternative, AN2R.

Cecchetti Mohanty and Zampolli (CMZ) get to inflation adjustment early in their paper. Under the heading "Rising debt: a preliminary examination" they write:
Graph 1 shows the aggregate non-financial sector debt of advanced economies and its composition since 1980. Two facts stand out: first, total non-financial debt as a percentage of GDP, as well as its sectoral components, have been rising steadily for much of the past three decades (left-hand panel)...

The right-hand panel of Graph 1 shows [that] adjusting for inflation does not change the message: real corporate debt has risen by a factor of roughly 3 (an average annual compounded growth rate of 3.8%); government debt by about 4½ times (5.1% annual rate); and household debt by 6 times (6.2% annual rate). Overall, real debt of the non-financial sector in advanced economies has been growing steadily at a rate of slightly less than 4½% for the past 30 years.
Their focus is the growth of debt.
What these panels show is that the surge in non-financial debt preceding the recent crisis is not a new phenomenon. It is merely the continuation of a trend...
Their focus is the growth of debt.


When the topic is GDP and you want to measure growth, getting good measurements requires inflation-adjustment of GDP. If you fail to remove the inflation, you measure the combination of output changes and price changes. How then can you evaluate growth? You cannot!

When the topic is debt and you want to measure growth, getting good measurements similarly requires inflation adjustment of debt. It makes sense that CMZ consider inflation-adjusted debt, because their focus is the growth of debt.


The BIS page that offers The real effects of debt for download also provides the accompanying dataset as an XLS file. That's a nice touch.

I wanted to take their data and see if I could duplicate their graph of inflation-adjusted debt. I couldn't do it. It was just too much work.

Their Excel file doesn't include raw numbers for debt. They give debt as a percent of GDP. I could convert back to debt in billions, if they provided GDP. But they don't.

They provide Real GDP per capita, and population data. I could work backwards from the per capita numbers to get Real GDP. But to convert to debt in billions I need Nominal GDP. That means I need a price index, so I can convert Real to Nominal GDP.

For a price index, CMZ provide only the annual change in consumer prices. I could use that, but it seems wrong. I'd want to use the GDP deflator to convert Real GDP to Nominal.

I noticed that their source for both Real GDP per capita and Population was the Penn World Tables 7.0. So I went to Penn World for Nominal GDP. I got tcgdp, which is described as "Total PPP Converted GDP, G-K method, at current prices".

I was only pretty sure it was the right data. But at least I could use it to convert "debt as a percent of GDP" to debt in billions.

But the next step would be to take inflation out of the debt. And all I have from CMZ is the CPI. Actually, not even. Their Excel file provides annual percent change values. I'd have to use those numbers to reconstruct a price index, then use the price index to deflate the debt.

I don't like it. The CPI is useful for consumer prices, consumer spending, and household debt. Not for government debt, not for corporate debt, and not for private or total non-financial debt. As I see it, anyhow.

I could go on ...


It was too much. I couldn't do it. So I set my duplicate-their-graph project aside for a while. And then I had a thought.

I can do all this finagling to get the CMZ data into the form I need for all sixteen countries that they average together, for all five different measures of debt for each country, and for all 30 years for each measure of debt. Or I can just go with the average annual compounded real growth rates provided by CMZ: 3.8% for corporate debt, 5.1% for government debt, 6.2% for household debt, and about 4.5% for the whole non-financial sector.

I went with Plan B.

My first graph today is CMZ's first graph, the two-panel graph they use to emphasize the growth of debt:

Graph #1: Debt Goes Up.
The Left Panel Compares the Size of Debt to the Size of the Economy
The Right Panel Shows the Growth of Debt after removing Price Increases
Debt goes up.

My second graph shows CMZ's average annual compounded real growth rates. I start each debt measure at 100 to mimic their indexing (1980=100), use the growth rates they provide, and stop after 30 years. I was surprised to get such a satisfactory result. Really:

Graph #2: My "Plan B" Graph
The lines are smooth curves; they don't show the variations in debt growth that we see on Graph #1. But I expected smooth curves, because these lines arise from constant growth rates.

I find Graph #2 satisfactory because all the lines start at 100, and
  • Household debt ends at 600.0, both on Graph #2 and on the right-hand panel of #1;
  • Government debt ends a little above 400.0 on both;
  • Total Non-Financial ends a little below 400.0 on both; and
  • Corporate debt ends around 300.0 on both.
The lines start and end in the right place. This is not my doing. It arises from the average growth rates CMZ provide. Their average growth rates must be right. Funny, because they seem low to me.

Their graph also shows "Private sector" (Total Non-Financial less Government, or Household plus Corporate) debt, which I omitted from Graph #2 to simplify my life.

I want to use Graph #2 as a yardstick, a measuring device to compare to US debt. The US numbers will not be identical, and may not even be similar, as Graph #2 shows average debt for a group of 16 nations. But I expect the US data to be comparable. In the ballpark. Similar enough to Graph #2 that I can find similarity without a great deal of effort.

So I went to FRED and gathered the debt data for households, non-financial corporations, and government, and for the non-financial sector in total. I indexed them to 1980=100 and showed the 1980-2010 period on Graph #3:

Graph #3: US Debt by Sector, 1980-2010, Indexed 1980=100
To identify the data I used, click the text "Graph #3" for the FRED source page.

I was looking at the graph and scratching my head because these debt measures stop in 2010 at values between 600 and 1200. On Graph #2, my yardstick, they range from 300 to 600. Half as much. Why, I wondered, are my numbers so far off?

I set the question aside for a few days. Then the answer just popped into my head: Graph #3 shows nominal data. I failed to make the adjustment for inflation.

Owa tagu siam.

For the next graph, I figure inflation-adjusted US debt measures as CMZ did, or as I imagine they did, using the same nominal-to-real calculation that is commonly used to convert between Nominal GDP and Real GDP, and using the CPI rather than the GDP Deflator as the measure of inflation.

For the CPI, I use CPIAUCSL, which is the first dataset returned when I search FRED for CPI. (It's also the dataset I ordinarily use when I need the CPI, because it was first among the search results when I was looking for a CPI to use, some years back.)

Here's the graph of US debt, CPI-adjusted for inflation:

Graph #4: Real US Debt by Sector, 1980-2010, Indexed 1980=100
This graph shows the same data as Graph #3, except CPI has been used to remove the inflation. You can see the same differences on both graphs: The red line runs high from 1982 to 2000; the green runs high and the blue runs low after 2000; and red jumps up at the end.

With inflation removed, the numbers are smaller. On Graph #3 the ending values were between 600 and 1200. Here they range between 240 and 480.

Compare #4 now to my yardstick: The 2010 values on Graph #2 range from 300 to 600. For Graph #4, the US data, I got values between 240 and 480. The US numbers are about 80% the size of the yardstick values. 80 percent: That's in the ballpark. Just on the low side.

I notice that on page one, CMZ say:
Using a new dataset on debt levels in 18 OECD countries from 1980 to 2010 (based primarily on flow of funds data), we examine the impact of debt on economic growth. Our data allow us to look at the impact of household, non-financial corporate and government debt separately.
There is a footnote:
Flow of funds data should provide a more accurate picture of indebtedness than bank credit data, which exclude several forms of debt including securitised debt, corporate bonds and trade credit. The difference is likely to matter in countries such as the United States, where a large fraction of credit is granted by non-bank intermediaries.
Does the footnote mean that the US numbers are low compared to the other countries? Or does it mean that the US numbers are not low, because they caught the discrepancy? I can't tell. But if the US values are low, this could explain why Graph #4 comes up short of the yardstick.


Note: Their dataset covers 18 OECD countries, but their first graph figures the average debt for only 16 of them. Not sure why. It might be because some data is missing. In Footnote 26 they say "All debt series begin in 1980 – with the exception of the household debt series of Denmark and Norway." Maybe they just left those two countries out of the average.

To create Graph #4 I started with #3 and brought in the CPI data. Ordinarily, to convert nominal to real, you take the nominal data, divide the prices out of it, then multiply by 100. I didn't do that.

It is dividing by the price index that changes or re-shapes a nominal series into real values. That part of the calculation, I did. I got that covered.

Multiplying by 100 takes the re-shaped series and floats the whole thing up higher on the graph, until it and the original series (the nominal values) are equal in the "base year". I didn't do that, because CMZ's method doesn't depend on a base year. They set the 1980 value to 100 by indexing. I did the same: Divide nominal debt by the price index, then index the ratio.

For the record, the two methods create the same changes and show the same results in the data. Going back to GDP as an example (because it's easier to think about inflation adjustment for GDP than for debt) dividing nominal GDP by the price index and multiplying by 100 makes the nominal follow exactly the path of Real GDP. The other method, dividing nominal GDP by the price index and indexing both the ratio and Real GDP on the same index-date, also makes the nominal follow exactly the path of Real GDP. The two methods are equivalent in this regard.

The advantage of indexing, in this particular case, is that it's the way CMZ look at their inflation-adjusted debt data. I'm following their method. So I get lines that meet in the index year (1980) just like CMZ gets. If I had done the usual thing (multiplying by 100 at the end) my lines would meet in the base year, be it 2009 or 2012 or the unwieldy 1982-1984.


I said above that I figured the inflation-adjusted US debt measures "as I imagine they did, using the same nominal-to-real calculation that is commonly used to convert between Nominal GDP and Real GDP" and using CPI rather than the GDP Deflator as the inflation measure. I also said I wouldn't have used the CPI.

What I didn't point out above is that I would not have used the nominal-to-real calculation that is commonly used to convert GDP from nominal to real. I would have used a different nominal-to-real calculation for the inflation-adjustment of debt. I would have used a calculation that is appropriate for a "stock" rather than a "flow".


Common reasons to evaluate debt are budgeting, planning, and paying the bills. The evaluation can be as simple as
  • The debt I owe at present is X;
  • The balance due just now is Y; and
  • The income I have to work with is Z.
I might even skip the first step, figuring X.

Looking at present balances and present income is a "current moment" evaluation: I need Y dollars at the moment, and have Z.

We sit down on payday, perhaps, to make this evaluation. We will sit down again next month and next year to re-evaluate. But it is always a current-moment evaluation. My debt X may have accumulated over many years, but I am focused on the current balance, along with the current payments I have to make and the money currently available for paying the bills.

For a current-moment evaluation, nominal values are entirely appropriate.

But there are other reasons to evaluate debt, reasons such as CMZ's desire to show the growth of debt. Or you may wish to estimate the boost to economic growth that is created by a growing debt. Or you might want to examine the notion that inflation erodes debt -- the idea that "inflation is good for borrowers and bad for lenders". To satisfy such curiosity, inflation-adjusted values are needed.

However, when the inflation-adjustment of debt is done by the same calculation that is used to convert GDP from nominal to real, the debt-to-income ratios turn out identical. When the same calculation is used, the ratio of real debt to real income is identical to the ratio of nominal debt to nominal income. And if the two ratios are identical, no "erosion" of debt can be discovered by comparing them. This may tempt you to conclude that inflation does not erode debt, and that inflation is neither good nor bad for either borrowers or lenders.

Myself, I'm not tempted. I bought a house during the Great Inflation of the 1970s. My mortgage had a high interest rate, near 8 percent. Still, I watched my mortgage payment remain unchanged year after year while my take-home pay went up and up along with Great Inflation prices. So I know from personal experience that inflation is good for borrowers. I know for a fact that inflation erodes debt.

Okay, maybe things are different these days. Inflation doesn't erode debt because incomes no longer increase with inflation. But that doesn't mean the commonly used nominal-to-real calculation is the right one to use to figure real debt. That calculation does not show the erosion of debt, period, whether there is any or not.

The standard calculation SN2R does not show erosion of debt, even for the 1970s. The calculation is obviously not right. To adjust debt for inflation, a different calculation is needed.


GDP is a "flow". Debt is a "stock". Technical terms. The obvious "bathtub" example can explain the difference: A "flow" variable measures how much water flows into the bathtub during a specified period of time. A "stock" variable measures all the water that's in the bathtub at a specified moment in time.

You could have "almost enough" water in the bathtub, then run the faucet for just one minute more, and then you might have "exactly enough" water in the tub. Before and after we run the faucet we have "stock" measurements, evaluations of all the water in the tub. Running the faucet for a minute is a "flow" that changes the "stock" of water in the tub.

For a perhaps more relevant example, consider the Federal debt and deficit. The Federal debt is a "stock" variable. It measures all the water in one particular bathtub -- all of the debt owed by the Federal government -- at some particular point in time.

The Federal deficit is a "flow" variable. It tells us how much water we're adding to the bathtub while the faucet is on. In this case, it tells how much we add to the Federal debt over the course of a year.

By definition, the Federal deficit begins every year at zero. If there is already a deficit at the start of the year, it is the prior year's deficit. By contrast, the Federal debt can never get to zero unless the whole thing is paid off. Debt is important because it measures the whole thing. The deficits are important because they tell us how much the debt changes each year.

A "stock" variable measures the whole thing. A "flow" variable measures changes in the stock.

Like the deficit, GDP begins every year at zero. If GDP gets to $20 trillion by the end of the year, it means we produced $20 trillion of output during that year. GDP is a "flow" variable. It measures the flow of goods and services into society during a period of time. During a year. And it starts at zero.

Like the Federal debt, total non-financial debt begins each year exactly where it left off at the end of the year before. There is no resetting of debt to zero every year, the way there is for GDP. Debt is a "stock" variable. It measures an accumulation. It doesn't reset to zero. It accumulates.

When we evaluate a debt-to-income ratio, we are comparing a number that has been increasing for many years, to a number that starts at zero every year.

"Ideally," CMZ write, "we would prefer to measure either a stock relative to a stock or a flow divided by a flow." That's revealing, I think. But it is easy to see that the debt-to-GDP ratio will go up and up and up, because GDP starts every year at zero, and debt starts every year where it left off the year before.


 If you're using annual data, you have one price level for the whole year. Then, when the ball drops, that price level is suddenly replaced by a new one, good for the whole new year. This is the same for debt and for GDP, or for whatever annual data you are using. For prices, it is a compromise with reality. Prices change all the time, not only at midnight on New Year's Eve. But the "sudden replacement" method is an approximation that doesn't trouble me at all, because it gives me data to work with.

SN2R, the standard calculation to convert nominal to real, is simple: Divide one year's nominal value by the price index for the same year, and you get the real value for that year. Remember to multiply by 100.

But there is something else to remember. GDP for 2017 counts the value of stuff produced in 2017; this makes the 2017 price level the relevant one. But debt for 2017 counts all the debt still outstanding at the end of 2017, even if it is debt from prior years. So the 2017 price level is only useful for converting the 2017 addition to accumulated debt. Not for the debt carried over from prior years.

See the problem?

To remove the price changes from GDP, use the GDP number and the price index number for the same year and you're good. There is no prior-year stuff in GDP with different price levels to be worked out.

To remove the price changes from debt you have to deal with multiple price levels, because the debt number includes not only the one year's borrowing, but also the outstanding debt from prior years when prices were different.

You cannot assume that converting nominal debt to real is just like converting nominal GDP to real. It isn't. Not all of the debt reported for 2017 was created in 2017. If you assume that it was, and use the calculation commonly used for GDP to adjust debt, your real debt numbers will be real wrong.


Not done yet. I want to see some more graphs. First, GDP and Real GDP:

Graph #5: Nominal and Real (SN2R) GDP
The black line shows GDP, sometimes called Nominal GDP or NGDP. The fat blue line, well hidden by the red, shows inflation-adjusted GDP (Real GDP or RGDP). And the red is the result of the standard calculation that converts NGDP to RGDP.

Nothing wrong with that. Now let me show a similar graph for debt. I'll use...

You know what? I'll use Household Debt. That's one that seems to worry CMZ, what with their "rather stark point that real household debt tripled between 1995 and 2010, dwarfing the accumulation of debt in other sectors of the economy." Yeah, let's look at Household debt.

Here again, I'm showing US data only:

Graph #6: Nominal and Real (SN2R) Household Debt
The black line shows household debt as reported by FRED, which is "nominal" debt. The red line shows nominal Household debt divided by the same price index used to create the red line on Graph #5. Most people would say that the red line is real debt. I don't agree.

There is no blue line this time, as FRED offers no data series for Real Household Debt.

The path of the black line on #6 curves upward (and, after the crisis, downward) more dramatically than the black on #5. So, debt is not the same as GDP. But we knew that.

Nonetheless, the relation of red to black is the same on Graph #6 as it is on #5. In both cases, red and black meet in 2012. In both cases, before 2012 the red is higher. And in both cases, after 2012, the red is lower.

In both cases also, the gap between red and black widens until about 1965. From 1965 to 1980, or maybe 1990, red and black run roughly parallel on both graphs. Finally, after 1990 the red and black lines draw closer to each other. Both graphs show this pattern.

The red line differs from the black on both graphs. But the red/black differences on Graph #6 are similar to those on Graph #5. The similarity of these differences is not surprising. In both cases the red line differs from the black because of inflation. Both graphs use the same measure of inflation. And both graphs use the same calculation, the standard N2R calculation (SN2R), to remove the inflation.

This comparison is an attempt to make the obvious, obvious.

One result of using the same measure of inflation and the same SN2R calculation on graphs #5 and #6 is that the ratio of reds, real debt relative to real GDP, is identical to the ratio of blacks, nominal debt relative to nominal GDP. See for yourself:

Graph #7: To see it bigger, click the graph
Identical: The red line runs dead-center on the black. Why?

We assumed that inflation had the same effect on GDP and debt. We used the same price index to adjust both. Then we divided inflation-adjusted debt by inflation-adjusted GDP. Our arithmetic divides the price index out of the numbers. If you write down the formula and rearrange it, you will see the price index disappear. You will see why the ratio of nominals and the ratio of reals are identical.

If the two price indexes differed, that difference would be brought into the picture. If we go back and change Graph #6, Nominal and Real Household Debt, using Cecchetti's choice -- the CPI -- for the price index, the result is no longer similar to Graphs #5 and #6:

Graph #8: Household Debt, with CPI Inflation Removed
The black line is the same, but the red is different this time.

The red line runs above the black before they cross, and below after, as before. But this time the two lines cross in the early 1980s. This difference comes from using a price index with a different base year. (The lines cross between 1982 and 1984, because that, somehow, is the "base year" for the CPI.)

If I use this red line for real debt in the ratio of reds, this time the ratio of reds will not be identical to the ratio of blacks.

Graph #9: I had to multiply by 180 rather than 100 to float the red line up.
But for the later years, even 180 was not enough.
That differs from what we saw on Graph #7. Here the difference arises because we used a price index that measures inflation differently. But you could also get lines that differ if you used a different N2R calculation.

Come to think of it, the alternative N2R calculation that I use is one that creates its own price index on the fly, a price index weighted by the amount of borrowing done each year.


Note: I said above that I wouldn't have used the CPI for the N2R conversion. CMZ do use it. But they use it for all their N2R conversions, so they are not creating false differences as I did on Graph #9. Their lines are somewhat more like the red on #9 than the black. But all their lines are like that.

They use a price index that I wouldn't have used, but at least they use it consistently.

Here is my idea of an acceptable N2R calculation for debt. For each year in turn, calculate that year's addition to accumulated debt, adjust that year's addition for that year's inflation, and then total up the adjusted amounts. For example, to figure real Federal debt, adjust each year's Federal deficit separately for inflation, then add up the adjusted amounts to get the real Federal debt.

Nobody does this.

For real household debt, for each time period take the change in billions, divide by the price index for that period (and multiply by 100), then total up the adjusted amounts. Nobody does N2R this way.

I can show it on a graph, but not a FRED graph. To make it similar to Graph #6, I'll use the GDP Deflator rather than the CPI.

Here's an Excel graph showing nominal Household debt (black) and the "standard calculation" real measure (red) exactly as shown on Graph #6 above. In addition, this graph shows real debt where the nominals are inflation-adjusted by the alternative nominal-to-real calculation, AN2R, with the adjustments based on the year of borrowing rather than the year of reporting:

Graph #10: Comparing Nominal and Two Measures of Real Household Debt
The standard calculation (SN2R,  red) has real debt crossing nominal debt in the base year (2012) just as we saw on Graph #6. This means that, as of 2012, there had been no "erosion" of debt by inflation, even though the earlier years show that real debt had more value -- more purchasing power -- than the nominal.

You can't have it both ways. It defies logic.

The alternative calculation (AN2R, blue) has real debt starting out at the same value as the standard calculation. But adjusting each year's borrowing separately for inflation pushes real debt above the number that the standard calculation provides.

The red and blue lines run very close together until the mid-60s. After that, for about 20 years, the blue line continues its seemingly exponential increase while the red line falls behind. It is no coincidence that the gap widens during these years: It was the time economists call the "Great Inflation". AN2R measures inflation differently than SN2R, and shows a greater difference from nominal when inflation is greater.

Looking at the blue from Graph #10 relative to the red, the blue's more rapid increase during the Great Inflation stands out clearly:

Graph #11: The Alternative N2R relative to the Standard N2R
The influence of the Great Inflation is obvious on this graph. As for the significance of the earlier and later periods, I leave that as an exercise for the reader.

"Seemingly exponential," I said of the blue line on Graph #10. In other words, AN2R shows household debt growing at a consistent pace since the early 1950s. SN2R shows debt growth lagging during the Great Inflation. People tend to see the slow debt growth of that time as a good thing. But as AN2R shows, debt growth in those years was not actually slow.

But does the increase of AN2R-adjusted debt follow an exponential path? It comes pretty close, based on data for the 1951-2006 period, according to this graph:

Graph #12: Showing an Exponential Trend Line for the AN2R-Adjusted Debt
Inflation-adjusted debt runs above the exponential path from the late 1970s to the early 1990s, then falls below it. But one key fact this graph shows is that AN2R-adjusted debt closely follows the exponential for a decade or more after the onset of the Great Inflation. By contrast, SN2R-adjusted debt (red) falls behind the exponential curve as soon as the Great Inflation begins. Conclusion: SN2R incorrectly measures the effect of inflation on debt.

An increase in the severity of inflation appears as a difference between AN2R- and SN2R-adjusted debt. Conclusion: SN2R incorrectly measures the effect of inflation on debt.

Many people notice the red line running relatively flat from the mid-1960s to the early 1980s and say the growth of debt was not rapid in that era. But as both the blue and the black lines show, debt growth was rapid in that era. The discrepancy arises because the standard N2R calculation gives an incorrect result when used to remove the inflation from a "stock" variable like debt.


The gap between nominal and real is a measure of the "erosion" of debt or, alternatively, of whether inflation is good or bad for borrowers or lenders.

The gap between black (nominal) and blue (AN2R) shows the cumulative benefit borrowers receive from inflation, or the loss to lenders.

The gap between black (nominal) and red (SN2R) shows that there was some benefit to borrowers, except that as of the base year, no such benefit had ever existed. It defies logic, as I said.

Furthermore, if you use the standard N2R calculation to figure real debt using a different base year, the "no such benefit ever existed" date changes with the base year. Clearly, the standard calculation is not to be trusted for the inflation adjustment of "stock" variables like debt.


Moving on, suppose we compare the ratio of reals to the ratio of nominals, using the household debt to GDP ratio.

Graph #13
The black line shows the ratio of nominal values, the one you are most likely to see. The red line shows real to real: inflation-adjusted household debt as a percent of inflation-adjusted GDP, where both debt and GDP are adjusted using the standard (SN2R) calculation.

The blue line also shows real to real, but the debt has been adjusted using the alternative (AN2R) calculation.

Red and black both show essentially no increase between 1964 and 1984 -- again, the years of the Great Inflation. The Great Inflation is the reason there is no increase in the black line. Erroneous use of a calculation meant for flow data, to remove inflation from debt (which is not a flow, but a stock) is the reason there is no increase in the red line.

The blue line does show increase between 1964 and 1984, as it does in general before 1990 and as it does after the 1990s, until the Great Recession. The blue is oddly flat in the 1990s. That's pretty interesting. It suggests that the growth of household debt was actually slow at that time. There was no Great Inflation in the 1990s, after all.

After the 1990s we see a persistent, rapid increase in household debt until it could rise no more. That increase appears much larger than any other in the blue line. It appears to "dwarf" the other increases of that line. But I wonder.

The increase is bigger, yes, but the line is also higher. Suppose we take the blue line thru 1990, before it goes flat, and put a trend line on it. A straight-line trend:

Graph #14
That dashed line should make you want to tip your head to make the line look flat. When you do, the flat of the 1990s becomes a decline. And the increase after the 1990s becomes less steep. These changes since 1990 are still obviously larger than earlier changes. But then, the dashed line is still rising.

I worked backwards from the trend line to get trend line values. Then I made a graph showing the blue AN2R/RGDP values as a percent of the trend line values. This graph:

Graph #15
Again here we see the flat of the 1990s as a decline. And the increase after the 1990s is readily visible, but now half of it is below trend! (The trend is based on data ending in 1990, remember.) And the decline since 2008 or so puts the ratio lower than it has ever been. That's lower than it has ever been.

And the peak, the 2008 peak, is no higher than the 1958 peak. And we didn't have a debt problem in 1958.

So maybe this should tell you something. Maybe it should tell you that looking at debt, relative to the trend of debt, is not reliably informative.

I have never been comfortable with the idea that you can compare debt to the trend of debt to see whether debt is high or low. When debt goes high, the trend soon follows. Then, when you find a spot where debt is a little below trend, you are able to say "Debt is low!" It's pure nonsense.

It's worse than nonsense. But up till now, I didn't have evidence to show that you can't use the trend of debt as a context for debt. Now I do. Graph #15 is evidence.

But this is off-topic, dammit.


Anyway, Graph #14 shows that the growth of real household debt is not something that only started after 1980. The graph shows that it was already up to speed in the 1950s. The size of the debt wasn't yet a problem in the 1950s. But the growth of debt made it certain, even then, that the size of debt was going to be a problem.

You can worry all you want that "real household debt tripled between 1995 and 2010". What you're telling me is that you don't have a good idea what happened before 1980. Hell, you say it outright:
One clear limitation of our dataset is that it starts in 1980. It is sufficient, however, to look back at the history of the United States (for which long back data are easily available) to understand how extraordinary the developments over the last 30 years have been. As Graph 2 shows, the US non-financial debt-to-GDP ratio was steady at around 150% from the early 1950s until the mid-1980s.
You don't have good data before 1980. But you are satisfied to look at the US data for those early years, ignore real debt, observe that the "debt-to-GDP ratio was steady" during that time, and call the matter settled. I don't know whether to laugh or puke.

And by the way, the debt-to-GDP ratio was steady only during the latter half of the 1950-1980 period, and only because of the Great Inflation. During the early half of that period, the ratio was rising at a rapid clip. Very sloppy work, Cecchetti.

Don't be like that, Art.


CMZ's abstract opens with these words:
At moderate levels, debt improves welfare and enhances growth. But high levels can be damaging. When does debt go from good to bad? We address this question ...
Mm. But they address the question by looking at debt relative to GDP, without considering that the debt-to-GDP ratio is greatly influenced by great inflation. They mistake the low debt of the 1965-1984 period for a fact about debt when really it is a fact about inflation.

They say the growth of debt after 1980 was "extraordinary" -- in context, meaning that the growth of debt before 1980 was slow. But this judgment is based on the debt-to-GDP ratio without regard to the effects of inflation. Yes, they do look at real debt to gauge debt growth. But they don't look at real debt before 1980.

And they use a nominal-to-real calculation that gives erroneous results. At least, I think they do. I couldn't duplicate their graph, so I can't really be sure what they did.

Wednesday, August 22, 2018

The Nominal-to-Real calculation

Start with GDP:

Graph #1 (Click the Graph or the Caption for a Better View)
The black line shows GDP, sometimes called Nominal GDP or NGDP. The fat blue line, well hidden by the red, shows inflation-adjusted GDP (Real GDP or RGDP). And the red shows the result of the standard calculation that converts NGDP to RGDP.

The calculation, given in the upper border of the graph, is GDP divided by the price index and multiplied by 100.

When they figure the price index, they could take care of the 100 as the last step. Then, when we convert nominal to real, we would only have to divide by the price index. But they don't take care of it for us, so we have to remember to do it ourselves.

And if your memory is not so good, like mine? Don't worry; the graph will remind you. Instead of ending near 18000, the red line will end near 180, with the whole line shrunk down to match. 180 is not as far above zero as where our black GDP line starts. So it will be obvious when you see it, that you forgot to multiply. And you curse your memory again, and fix your calculation again, and you're good.


Now the mind-blower: Let's pretend we're looking at debt, not GDP.

It's just numbers to work with. I need numbers to work with. And it is representative: Typically, when people convert nominal debt to real debt, they use the same calculation, the standard calculation that is used to convert nominal GDP to Real GDP. Plus, that's the calculation I want to look at today, the nominal-to-real conversion.

So the black line is debt. The fat blue line is Real Debt, or so people say. And the red line shows the calculation. The same calculation that is used to convert GDP to Real GDP.

According to me, as a way to convert nominal to real, that calculation is perfectly good when used to convert GDP, but completely unacceptable when used to convert debt.

Maybe that blows your mind even more. Maybe it should.


One difference between debt and GDP is that when we figure GDP we start again at zero every year. GDP is never a total for more than one year. Debt is not like that. Debt is always a total for more than one year. When we figure debt, we take the end-of-year balance and use it as the start-of-year balance for the next year. And by "we" I don't mean me; I mean the experts who work up the numbers.

Debt is reported every year, just like GDP. But the number is a multi-year accumulation. One year's debt includes the borrowing of many years, and reflects the prices of many years.

GDP is never a total for more than one year. Debt is always a  total for more than one year. This difference is the reason the standard calculation works for GDP but does not work for debt. Why? Because the price index gives the price level for one year at a time. There is no price index for the many years of borrowing that are accumulated in one year's debt.

There is no price index that measures the price level for a multi-year accumulation of debt. So the standard nominal-to-real calculation gives the wrong answer when you use it to figure real debt.

To convert nominal debt to real, a different calculation is needed. One like this.

In Round Numbers

In an inflationary economy, which ours has been, the dollar loses value over time. A dollar a year ago was worth more than a dollar today. A dollar five years ago was worth even more.

Since the late 1990s, inflation has been roughly two percent a year. Call it two percent. So a dollar last year was worth 2% more. A dollar five years ago, 10% more.


Now: How old is our debt? Just a guess, but I'm saying five years old on average. More than five, I think, but say five years old. And that's for newly reported totals: Debt totals announced this morning encompass debt that is on average five years old, or more.

If we have 2% annual inflation, in five years that's about 10% inflation overall. If our debt is five years old on average, then debt reported this morning has already seen about 10% inflation. The dollars we borrowed and spent were worth 10% more than a dollar is worth at the moment.

So if we're doing inflation adjustment, the adjustment could be about five times bigger for debt than for GDP.


The annual addition to debt is generally in the neighborhood of five to ten percent of the total accumulation. That means that 90 to 95 percent of debt is old debt -- money borrowed on average five years ago, when the dollar was worth about 10% more. At any given time, then, 90 to 95 percent of debt represents spending that was done when the dollar was worth 10% more.

When we look at the value of debt in dollars that don't lose value over time (which is really what inflation adjustment is all about) we have to say the adjustment is substantially greater for debt than for GDP. Because debt always has that extra 10% and GDP doesn't.

YearGDP InflationDebt Inflation
The Current Year0%10%
One Year Later2%12%
Two Years Later4%14%

The standard calculation understates real debt. There's no getting around it.

Sunday, August 19, 2018

Another break in the silence

It's been a week.

The definition of the word "accumulation" provided by the Cambridge English Dictionary and returned by Google is
1. an amount of something that has been collected: 2. the process of gradually increasing in amount, or the increased amount...
Either an amount of something, or the process of increasing. An amount, or a process.

When I talk about "the accumulation" of debt I definitely mean the huge amount of it. When I talk about "accumulation" of debt, sometimes I may mean the process.

What do Cecchetti, Mohanty and Zampolli mean when they say
The righthand panel of Graph 1 makes the rather stark point that real household debt tripled between 1995 and 2010, dwarfing the accumulation of debt in other sectors of the economy.
... and is it okay to use the "D" word?

What do they mean? To my ear, they mean the amount. Not the process. "Real household debt tripled", they say. They're talking about the increased size of household debt, not the process of increasing. But of course, you can't have the one without the other.

Let me back up just a little, quote their whole paragraph, and show their graph:
Graph #1
As shown in Graph 1, from 1995 to the middle of the last decade, public debt had been relatively stable as a percentage of GDP. But this period of relative public sector restraint was accompanied by a rapid rise in household and non-financial corporate debt. The righthand panel of Graph 1 makes the rather stark point that real household debt tripled between 1995 and 2010, dwarfing the accumulation of debt in other sectors of the economy.
Yeah, I think that's wrong. The size of household debt does not "dwarf" debt in other sectors of the economy. They make it sound like household debt is the biggest component. But household debt is the smallest of the components they are looking at, as the left-hand panel of their graph shows.

At the same time, the right-hand panel does show that household debt was the fastest-growing component of debt. So perhaps it is true that the "process" of accumulation of household debt dwarfs the others. It would be more clear, though, if they just said household debt grew the fastest.

The left-hand panel shows five measures of debt, in each case comparing the size of debt to the size of GDP. Since all the measures of debt are compared to the same standard, the left panel provides a good way to compare those debt measures to each other. The one that's biggest relative to GDP is biggest, period. The one that's smallest relative to GDP is smallest. From start to finish, except for two or three years between 2005 and 2009, household debt is the smallest.

The right-hand panel shows debt for the same five sectors. This time the debt numbers have been adjusted to remove inflation.

Here's something: When you want to see the growth of GDP, you take inflation out of the numbers. This lets you see the size of GDP so you can compare one year to another. Doing this, you are comparing GDP only to itself. Something similar is true for the right-hand panel: Forget the fact that there are several lines on the graph. Each line compares one measure of debt to itself. If the line goes up, the debt got bigger. This is what the right-hand panel shows.

If you put five lines like that together on a graph, it does NOT show that one pile of debt is bigger than another pile of debt. Each line compares one component of debt to itself.

The fact that the five measures all start with the same value allows us to compare the growth rates of the different debt measures. Because it is highest at the end, then, we have to say household debt was fastest-growing.

Household debt is the smallest but fastest-growing measure on Graph #1.

CM&Z's graph shows "total non-financial debt" and  components of it. It shows that household debt is the smallest component, but the fastest growing.

Let's look at it.

And what does it leave out, their graph of non-financial debt and components? Well, obviously, it leaves out financial debt, the debt of financial business.

Let's look at that, too:

Graph #2: Household Debt (blue) and Financial Debt (red). Data for the US only.
Close. They're close. Who knew?

And how do they compare for size?

Graph #3: Financial Debt as a Percent of Household Debt
Financial debt grew from 20% of Household debt, to 120%, and then started tapering off.

Household debt is the fastest growing component of non-financial debt. But Financial debt grew faster, from the 1950s to 2001. For half a century, financial debt grew faster than household debt.

Hey Cecchetti.


Financial debt, it was growing even faster than household debt.

Yeah, so?

You wanna show it on our graph?


Sunday, August 12, 2018

A follow-up note on the growth of debt

Before the silence resumes, an afterthought.

I'm looking at non-financial debt: Domestic Nonfinancial Sectors; Credit Market Instruments; Liability, Level at FRED. Annual data, downloaded to Excel. Looking for something I can compare to what I'm reading about the growth of non-financial debt in CM&Z's The real effects of debt.

They look at debt (first, debt relative to GDP, then the growth of inflation-adjusted debt) and they observe
... the surge in non-financial debt preceding the recent crisis is not a new phenomenon. It is merely the continuation of a trend that was ongoing over the entire period for which we have been able to assemble comprehensive data...
One clear limitation of our dataset is that it starts in 1980. It is sufficient, however, to look back at the history of the United States (for which long back data are easily available) to understand how extraordinary the developments over the last 30 years have been. As Graph 2 shows, the US non-financial debt-to-GDP ratio was steady at around 150% from the early 1950s until the mid-1980s.
They say that non-financial debt has been growing rapidly since the 1980s, but not before the 1980s. They are careless, though, offering no more than a "sufficient" argument. They evaluate the growth of inflation-adjusted debt for the post-1980 but not the pre-1980 years. Without looking at it, they say debt growth was relatively slow before 1980 -- specifically in the US -- and they want me to take their word for it. This I cannot do.

I'm looking at compound annual growth rates for ten-year periods. Looks like CM&Z have it wrong way round. Debt growth shows increase since the 1950s. It was fast since the 1970s, faster than it's been since the mid-1990s! But since 1986, debt growth has been slowing:

Graph #1
Slowing since 1986. That's why GDP growth sucks.

However, because of the growth of debt since the beginning, the level of debt is now very high. This is the reason that the relatively small growth increase of 2001-2008, on my graph, appears as a massive increase in debt in billions and in the debt-to-GDP ratio on everybody else's graphs.

Nonetheless, the trend of debt growth is downward since 1986, and this explains the slowing of economic growth.

Each dot on the graph represents the compound annual growth rate for the 10-year period ending at the date of the dot. The first dot, for example, shows the growth rate for the 1947-1957 period.

The plot peaks at over 12% in 1986 (that is, the 1976-1986 period). It falls to a low of about 5.5% in 2001. It peaks in 2008 at about 7.5%. The graph ends in 2017 with debt growth at about 4% for the last ten years.

The 2008 peak value was exceeded back in 1973.


Check/duplicate my work:
The value for 1947 is in cell C12, with the following years' data on the rows below. In Column D on row 22 (the row for 1957) is this formula:
with that formula copied to the rows below. Values from Column D are displayed on the graph.

Saturday, August 11, 2018

An outright contradiction

As I tell the circling buzzards while I'm mowing the lawn, I'm not dead yet. I'm working on something that's taking forever. So I interrupt my silence to present some related material.

In an upcoming post I quote Stephen G Cecchetti, Madhusudan Mohanty and Fabrizio Zampolli (CM&Z) from BIS Working Paper No 352: The real effects of debt:
Overall, real debt of the non-financial sector in advanced economies has been growing steadily at a rate of slightly less than 4½% for the past 30 years.
That's not for the US. Their growth number is an average for 16 advanced economies.

I have easy access to US data, at FRED, and I'm comfortable working with US data -- call me a patriot! -- so I want to compare CM&Z's growth number to US data. I'll be using "Domestic Nonfinancial Sectors; Credit Market Instruments; Liability, Level", which is similar to CM&Z's debt measure except mine includes the debt of nonfinancial noncorporate business. Should be good enough. I just want to get a rough idea.


Following CM&Z, for real debt I'm dividing by the Consumer Price Index. (They describe their first graph as showing debt "deflated by consumer prices". Seems odd to me, but okay.)

Here's the graph for US data:

Graph #1: Real US Non-Financial Debt (see text)
I get a growth rate of 3.79% 4.05% (see The big picture is wrong). A little less than their number.

It looks like real debt goes up a lot faster after 1980 than before. This agrees with CM&Z, whose "past 30 years" is the 1980-2010 period. (Their paper is from 2011.) Still...

Exponential growth is growth that doubles at a constant rate.  I wonder how long it takes for this debt to double. Here is the same graph again, with some numbers on it:

Graph #2: Doublings
Starting in 1950 at 1709.6, the debt reaches twice that level in 1967, 17 years later.
Starting in 1967 at 3431.2, the debt reaches twice that level in 1986, 19 years later.
Starting in 1986 at 7136.4, the debt reaches twice that level in 2006, 20 years later.

The debt growth looks roughly exponential to me. If anything, debt growth was faster early and slower late.

Here's the same data again, this time showing logged values:

Graph #3: Logged
Definitely slower late. This is an outright contradiction of what CM&Z said.


Let me review what CM&Z said, exactly. They said:
The past three decades have witnessed a remarkable rise in advanced country indebtedness.
Graph 1 shows the aggregate non-financial sector debt of advanced economies and its composition since 1980.
What these panels show is that the surge in non-financial debt preceding the recent crisis is not a new phenomenon. It is merely the continuation of a trend that was ongoing over the entire period for which we have been able to assemble comprehensive data...

One clear limitation of our dataset is that it starts in 1980. It is sufficient, however, to look back at the history of the United States (for which long back data are easily available) to understand how extraordinary the developments over the last 30 years have been. As Graph 2 shows, the US non-financial debt-to-GDP ratio was steady at around 150% from the early 1950s until the mid-1980s.
I'm not showing their graph. As I read it, they are saying:
Debt has been growing rapidly since around 1980: since long before the housing bubble. This rapid growth since 1980 is extraordinary: much different than what came before. For evidence that debt growth was slow before 1980, look at the US data.
I don't see slow debt growth before 1980 in the US.

I don't see an extraordinary change around 1980.

I see rapid debt growth from the start.

Sunday, August 5, 2018

With one eye closed

I've been looking at an old PDF lately: The real effects of debt, the 2011 paper by Cecchetti, Mohanty and Zampolli (CMZ). They show this graph:

They write:
As Graph 2 shows, the US non-financial debt-to-GDP ratio was steady at around 150% from the early 1950s until the mid-1980s. In some periods, public debt was high, but then private debt was low; while in others it was the reverse.
Their remarks are footnoted:
See Friedman (1981 and 1986) for a discussion.
I wondered if they meant Milton Friedman because, far as I know, debt wasn't really his thing. So I checked their list of references, and found this item:
Friedman, M (1981): “Debt and economic activity in the United States”, in M Friedman (ed), The changing roles of debt and equity in financing US capital formation, University of Chicago Press.
Friedman, M, they say. But I think they mean Benjamin M. Friedman, whose 1981 paper Debt and Economic Activity in the United States is available from NBER. The paper "documents a long-standing stability in the relationship between outstanding debt and economic activity in the United States". Must be it.

So now I'm looking at an even older PDF.

From a page dated March, 1981, here are the opening sentences of Friedman's paper:
Businesses and individuals, in an economy like that of the United States, can finance their activities in a rich variety of ways. Businesses investing in new plant and equipment can rely on internally generated funds, or they can raise external funds from the financial markets. When they do turn to external sources of funds, they can issue either debt obligations or new equity shares in the enterprise. Individuals can likewise use their own or borrowed funds to make major purchases like automobiles, and many individuals can also borrow to finance ordinary consumer spending apart from major hardgoods. Even in arranging home purchases, transactions that are almost always partly debt financed, individuals usually can choose what fraction of the purchase price initially represents their own equity. In principle, businesses and individuals are continually making these and other financing choices on the basis of yield comparisons, credit availability, and other considerations, so that the total amount of debt financing does not necessarily have to bear any close relationship to the underlying economic activity.

In fact, however, the relationship between outstanding debt and economic activity in the United States is remarkably steady — indeed, just as steady as the more widely recognized and better understood relationship between economic activity and money. The aggregate outstanding indebtedness of all nonfinancial borrowers in the United States has been approximately $1.40 for each $1.00 of the economy's gross national product, ever since World War II. Throughout the postwar period the overall debt—to—income ratio has displayed neither trend nor cyclical variation.

And again, the sentence on which I focus:
The aggregate outstanding indebtedness of all nonfinancial borrowers in the United States has been approximately $1.40 for each $1.00 of the economy's gross national product
Friedman in 1981 considers nonfinancial debt only. His paragraphs are engorged with detail, but he offers no justification for the exclusion of financial debt.

Cecchetti, Mohanty and Zampolli, like Benjamin Friedman, consider only non-financial debt. The funding of borrowers is the focus. The funding of lenders merits no consideration.

As if our problems with debt can be reduced by failing to count the half of it.

Friday, August 3, 2018

A look at the growth of debt using "Kruger Industrial" smoothing

Household debt, for starters. Quarterly data. Change in billions, relative to Disposable Personal Income in billions. Flow relative to flow.

The numbers are small: 1%, 2%, 3%. That's because it's quarterly data. Multiply by 4 to approximate annual values, and we're talking 8-to-12% annual increase here.

That ain't nothin.

Graph #1
The blue is the FRED data. The red is the super-smooth trend, the Hodrick-Prescott with a smoothing factor of 400,000.

The trend line shows household credit use rising already in the 1960s and, if you look, already even in the 1950s.

Inflation may have caused an increase in borrowing in the 1960s and '70s, as prices went up on things purchased on credit. But prices went up also on things purchased not on credit; and inflation caused an increase in incomes, in the "nominal" numbers. So inflation cancels itself out of the "change in debt relative to income" calculation.

The same is not true for "accumulated debt relative to income" of course. Because last year's debt is increased by the addition of this year's credit use, but last year's debt is not increased by this year's inflation. That's why inflation is said to be good for borrowers and bad for lenders, at least as long as wages are going up along with prices.

Come to think of it, the "bad for lenders" thing could be the main reason wages no longer go up along with prices. That would be just one more piece of evidence saying there's too much finance in our economy these days, and that we go out of our way too much for finance, and that this creates problems for people, and it changes the economy.

Well this post sure didn't end up where I thought it might.

Wednesday, August 1, 2018

Yeah, Bill, but

Bill Mitchell writes:
Unsustainable growth processes are those that rely on households accumulating ever increasing debt levels.
That's true. But don't get your undies in a bunch. The last time we relied on households accumulating ever-increasing debt levels it worked for 60 years, from 1947 to 2007.

After 2007 the US economy went into ever-decreasing debt levels mode, which lasted about four years. Then it took another four years or so with household debt on the increase, before it finally went above the pre-crisis peak. Then we started to hear the knee-jerk warnings about debt causing another crisis.

I'm empathetic. I agree that debt is the problem. But it is not necessarily a problem if debt today is more than it was yesterday. That happens all the time. There is too much baseless fear in our gut these days, left over from the problems of 2007-2009.

It is true that household debt is now (and has been since 2016) higher than it was at the previous peak:

Graph #1

But that is not true for debt relative to income:

Graph #2
Not even close. Actually it looks like it's still going down. (When it starts going up, that's when we get the vigor I've been predicting since 2016.)

Likewise, debt service costs remain low:

Graph #3
It's too soon to panic over debt. First comes the vigor.

Stop and smell the roses.