Even using the ridiculous 400K smoothing factor favored by Basel III

Following up on my previous post:

Graph #1

Even using the ridiculous 400K smoothing factor favored by Basel III, household debt runs downhill as a percent of All Sectors debt since around 1970.

// See also: Debt grows faster than GDP.

The Great American Debt Boom, 1949-2013

The Great American Debt Boom, 1949-2013 (PDF, 36 pages) by Moritz Kuhn, Moritz Schularick, & Ulrike I. Steins.

Just from the title, you already know that the "Debt Boom" paper is about the growth of debt in America. And we didn't even get to the first sentence yet.

Here is that sentence:

The American economy experienced a dramatic increase in household debt since World War II.

Now you know that the paper is about the growth of only one part of debt in America: Household debt.

Household debt in red, All Sectors debt in blue, both as Percent of GDP:

Graph #1

Household debt is a small part of All Sectors debt.


Household debt as a percent of All Sectors debt:

Graph #2

Since 1966, Household debt has been a generally decreasing part of All Sectors debt.

Granted, it was an increasing share between 1999 and 2006, the years before the crisis. But the high point for Household debt, just before the crisis, was 28.1% of All Sectors debt. Compare that to 29.7% in 1980, and 30.5% in 1966.

In 2013, the last year studied in the Debt Boom PDF, Household debt reached a low of 23.1% of All Sectors debt. By 2017, the year the study was published, Household debt had fallen to 22.1% of all debt.

Household debt is a relatively small and generally decreasing share of All Sectors debt.


In their abstract, Kuhn, Schularick, and Steins write:

A quantitative assessment of household balance sheets demonstrates that financial vulnerabilities of different strata of the income distribution have risen substantially.

You know what? I don't doubt it. I am confident they are correct in saying that financial vulnerabilities have risen substantially across income groups.

But I am not at all confident that "a dramatic increase in household debt since World War II" is responsible for the rise in the financial vulnerability of households. I think responsibility lies with the dramatic increase in All Sectors debt, debt which the PDF fails to consider.

"Free shipping" my ass

The natural rate of interest and the financial cycle

Via Reddit: The natural rate of interest and the financial cycle by Georgi Krustev. Working Paper number 2168 from the European Central Bank.

This paper's interesting!

Well, I have to say I've been stumbling thru a lot of PDFs lately with John C. Williams's name on them, and Thomas Laubach's, and related papers on the natural rate of interest, on the decline of the natural rate, and on the cause of the decline. Given that context, this paper is mighty interesting.

Full disclosure: I'm only two pages into it. But take a look at the abstract:

I extend the model of Laubach and Williams (2003) by introducing an explicit role for the financial cycle in the joint estimation of the natural rates of interest, unemployment and output, and the sustainable growth rate of the US economy. By incorporating the financial cycle – arguably an omitted variable from the system – the model is able to deliver more plausible estimates of business cycle dynamics. The sustained decline in the natural rate of interest in recent decades is confirmed, but I estimate that strong and persistent headwinds due to financial deleveraging have lowered temporarily the natural rate on average by around 1 p.p. below its long-run trend over 2008-14. This may have impaired the effectiveness of interest rate cuts to stimulate the economy and lift inflation back to target in the immediate aftermath of the GFC.

From what I've seen, Laubach and Williams (2003) is the starting point for a lot of what's happened since, regarding the study of the natural rate of interest or "R-star". Krustev's paper takes their model and to it adds "an explicit role for the financial cycle". The paper makes finance a more central part of what's been happening in our economy, and what's been happening to it. And that's a good thing.

Krustev's change to the Laubach and Williams  model gives rise to "more plausible estimates of business cycle dynamics." In addition, the modified model confirms the sustained decline found by other models. These features are more of an advertisement for this paper than anything else. But it's a good advertisement.

The real kicker comes at the end of the abstract:

I estimate that strong and persistent headwinds due to financial deleveraging have lowered temporarily the natural rate on average by around 1 [percentage point] below its long-run trend over 2008-14. This may have impaired the effectiveness of interest rate cuts to stimulate the economy and lift inflation back to target in the immediate aftermath of the GFC.

That's interesting.

The effect of the deleveraging, pushing the natural rate down, is obvious now it has been pointed out. And, given that effect, we should have expected to find "the effectiveness of interest rate cuts" impaired. This explains both the decade of slow growth that followed the GFC, and the trouble the Fed had to bring inflation up to its two-percent target.

The one-paragraph abstract is followed by a one-page "non-technical summary". The summary expands on what we've seen in the abstract. There is another advertisement for Krustev's paper. He points out an apparent flaw in the Laubach and Williams model, which is rectified by extending the model to include the financial cycle:

... updated estimates of output gaps from the LW model since the Global Financial Crisis (GFC) have shown substantial deviation from results derived on the basis of production-function approaches; consequently, their plausibility has been questioned ...

This kind of advertising I could read all day.

In addition, the summary points out again that

strong and persistent headwinds due to financial deleveraging have lowered the natural rate of interest on average by around 1 p.p. below its long-run trend over 2008-14. This might have impaired the effectiveness of interest rate cuts to stimulate the economy and lift inflation back to target immediately after the GFC.

But the deleveraging worked itself out. People apparently began to feel that they had deleveraged enough. The focus on deleveraging gave way to other things. Krustev's story includes this change:

The dissipation of these headwinds implies that monetary policy should have regained traction since 2015 as the natural rate of interest rebounded, aligning itself to its long-run component.

I can only imagine that less deleveraging means less downward pressure on the natural rate, so that the rate may have been tending to rise since 2015. I guess that's what "regained traction" means. I'm looking for as much as a "1 p.p." increase in the natural rate since that time. And again I have to say: That's interesting.

By way of comparison, let me share part of what I hoped would become part of a long blog post about my thoughts on the natural rate of interest:

In 2015, in Measuring the Natural Rate of Interest Redux, Thomas Laubach and John C. Williams observed that:

Persistently low real interest rates have prompted the question whether low interest rates are here to stay.

Their answer? Here to stay, yes:

Since the start of the Great Recession, the estimated natural rate of interest fell sharply and shows no sign of recovering.

Shows no sign of recovering.

In 2016, in Measuring the Natural Rate of Interest: International Trends and Determinants, Holston, Laubach and Williams pointed out that

Sustained extraordinarily low interest rates in most advanced economies since the global financial crisis have heightened interest in the question of whether the natural rate of interest has permanently declined and why.

On the question of a permanent decline, they answer:

We find no evidence that the natural rates are moving back up recently.

More recently, in May of 2018, in The Future Fortunes of R-star: Are They Really Rising?, Williams wrote

Recently some economists and central bankers have pointed to signs that the fortunes of r-star are set to rise. I wish I could join in this optimism, but I don’t yet see convincing evidence of such a shift. The longer-run drivers still point to a “new normal” of a low r-star and relatively low interest rates.

And by the way, Williams is talking about where interest rates will be, "not just over the next few months, but over the next several years".

Low, for the next several years.

John C. Williams has held for some time that the decline in the natural rate of interest is "permanent" and that there are no indications of any rise in the rate. This has been bothering me for a while now, because when I look at the Laubach and Williams data I see a definite bottom around 2013 (blue) or now (red) and a very likely increase thereafter:

Graph #1: The Natural Rate of Interest, from Laubach & Williams Data

Krustev's evaluation is more like my own. So naturally I prefer it :)

This paper is interesting. I gotta go read more now.

Federal and non-Federal debt should be roughly equal

Last time, I looked at the use of "control" variables in regression, and tried to express something that's been bothering me about them for a couple months now:

• "it seems pretty strange to me, this idea that if you make something a control variable, it suddenly has no effect on the outcome."
• "the idea that you can just "control" some variables to find out how your one "independent" variable affects economic growth is ... absurd"

My objection was that the outcome doesn't change. The economic growth we got over the past 70 years is what it is. It doesn't change, for example, when you control for everything except Federal debt, and then you change to controlling for everything except corporate debt. The outcome doesn't change, period. The growth we got is the growth we got.

Maybe that's a little silly, I dunno. There would be different measures of correlation, comparing economic growth to Federal debt versus comparing economic growth to corporate debt. Sure. And maybe you can turn that into a story about the effect of Federal versus corporate debt, on economic growth. Something like we find in The Real Effects of Debt. Maybe you can. But I let it sit in the back of my mind for a couple months, and I still couldn't see it.

Jerry responded in comments on my previous post. He said okay, lets say X is the Federal debt, and Y is the private debt -- corporate and household -- that I was looking at. And he set up two examples, a linear one and a non-linear one.

In the linear example, economic growth is Z, and Z = X + 2Y is how the economy works.

Jerry says we can hold Y constant, and change X, and calculate the effect of that change on Z.

He says we can hold X constant, and change Y, and calculate the effect of that change on Z.

He says we can take the two effects and add them together, to calculate the total effect on Z.

So in other words, there is nothing wrong with the method: holding private debt constant while evaluating the effect of Federal debt; and holding the Federal debt constant while evaluating the effect of private debt; and then using or comparing the effects; there is nothing wrong with this method.

But Jerry did say that the total effect we calculate may or may not be close to accurate, depending on whether debt actually has a "linear" effect on economic growth. This is probably a much stronger objection than the one I made.

I think Jerry is right. His explanation is overwhelmingly good.

Still, in Jerry's example and (I presume also) in the Real Effects of Debt PDF, you can calculate how economic growth would have changed if Federal debt was constant while private debt was growing. And you can calculate how it would have changed if private debt was constant while the Federal debt was growing.

But I suspect you cannot know if either of these alternate realities are correct. Because, as Jerry says, regression is only "a 'mostly valid' way to examine a nonlinear system", and that's only if "you're studying small movements in the system. As the movements get larger, the regression gets less valid".

And if there is one thing we know about debt, it is that its effect is not linear.

Now let me throw something else into the mix. You can have a straight line, or a line that isn't straight. Linear, or non-linear. But the line that isn't straight may be almost straight, or it may be extremely curvy. Maybe Jerry's "mostly valid" case holds true more for curves that are almost linear than for those that are extremely non-linear. I want to suggest that it is not only whether you're "studying small movements" that affects the validity of your results; but also the degree of non-linearity of your source data.

Jerry would probably say that for extremely small movements, the line is very close to linear no matter what. Okay. But he also says that determining whether a movement is large or small is "a little subtle". In other words, the accuracy of the regression is a difficult thing to determine with confidence.

I suspect that a small, "mostly valid" movement can be much larger for a curve that is almost linear than for an extremely non-linear curve. Or, in other words, a small movement of any given size will be less accurate for data with a high degree of non-linearity than for data with a low degree of non-linearity.

Just throwing that into the mix.

I also want to suggest that debt might have had linear effects, the very first time somebody borrowed money. When the first payment was made against that debt, however, the effects immediately became much more complicated. Since the very first time a loan was repaid over a period of time, the effects of debt would have been non-linear. And the greater the "financialization" of the economy, the greater the degree of non-linearity in the effect of debt.

Put that in your pipe and smoke it.


I want to go back to my concern with seeing the results change when debt changes. I don't want to focus on calculating differences that may not even be valid. I want to see the differences in actual economic growth that are due to differences in debt growth. That, I think, would be useful.

Suppose we take debt other than Federal debt, and look at it relative to the Federal debt:

Graph #1: The Non-Federal Debt relative to the Federal Debt

Here we have a picture of the relation between debt other than Federal, and the Federal debt.

We do not attempt to calculate how it would look if Federal debt was constant while private debt was growing. We do not attempt to calculate how it would look if private debt was constant while the Federal debt was growing. We simply look at the actual relation between the private ("Non-Federal") and the Federal debt.

Note that the accuracy of this picture does not depend on anything being linear or non-linear. Nor does it depend on the degree of non-linearity of the source data. It is simply a picture of the historical record.

I want to compare this ratio to economic growth, and look for the effect of changing debt on growth. So I add to the graph a series showing the growth rate of real GDP:

Graph #2: Non-Federal to Federal Debt (blue), and RGDP Growth (red)

Next, to see the relation between the two, I convert the graph to a scatter plot:

Graph #3: The Non-Federal to Federal Debt Ratio (horizontal) and RGDP Growth (vertical)

And then bring the data into Excel and put a trend line on it:

Graph #4: Showing a Linear Trend Line

We get a downsloping trend: Economic growth is in the neighborhood of 4% annual when the Non-Federal debt is roughly equal to the Federal debt. Economic growth is half as much when Non-Federal debt is around five times greater than Federal.

The trend remains generally downsloping when we make the trend line non-linear:

Graph #5: Showing a Non-Linear Trend Line

Again, trend growth runs in the neighborhood of 4% when the debt ratio is low (near 1.0) and in the neighborhood of 2% when the debt ratio is high (near 5.0).


These graphs do not answer the question How much debt should we have. But they do offer a perspective on how debt is best distributed between Federal and non-Federal entities. The graphs suggest that the Federal and non-Federal debts should be roughly equal. Thus, if we are concerned that the Federal debt is too big, when the non-Federal debt is three to five times bigger, we would do well to concentrate on reducing the non-Federal debt first, and put off our concern with Federal debt until later.

The "control" variables

Where I want to start trying to understand "regression".

Pondering The Real Effects of Debt by Cecchetti et al

I've never done regression. So maybe I don't know what I'm talking about. It wouldn't be the first time that happened. If I have something wrong, please do point it out.


I googled controlling for variables in regression. Got a bunch of quotables. Here are the first three:

What does it mean when you control for a variable?
Importantly, regression automatically controls for every variable that you include in the model. What does it mean to control for the variables in the model? It means that when you look at the effect of one variable in the model, you are holding constant all of the other predictors in the model.
A Tribute to Regression Analysis - Minitab Blog
blog.minitab.com/blog/adventures-in-statistics-2/a-tribute-to-regression-analysis

Control variables are variables that you "are holding constant".

Why do you control for variables?
The number of dependent variables in an experiment varies, but there can be more than one. Experiments also have controlled variables. Controlled variables are quantities that a scientist wants to remain constant, and she must observe them as carefully as the dependent variables.
Variables in Your Science Fair Project - Science Buddies
https://www.sciencebuddies.org/science-fair-projects/science-fair/variables

Control variables are variables you want "to remain constant".

Why do we need to control variables?
The control variable strongly influences experimental results, and it is held constant during the experiment in order to test the relative relationship of the dependent and independent variables. The control variable itself is not of primary interest to the experimenter.
Control variable - Wikipedia
https://en.wikipedia.org/wiki/Control_variable

Control variables are variables that are "held constant".

That's interesting because, normally, a value is is either a constant or a variable.


The same Google search turned up this bit:

What are control variables in regression?
A control variable enters a regression in the same way as an independent variable - the method is the same. But the interpretation is different. Control variables are usually variables that you are not particularly interested in, but that are related to the dependent variable.
What are control variables and how do I use them in regression ...
https://www.quora.com/What-are-control-variables-and-how-do-I-use-them-in-regressio...

This, okay, I like it; this makes some sense to me.

The dependent variable is, say, economic growth. We want to know what it depends on.

Or actually, we think we know it depends on some "independent" variables and we think we know what they are. So we use them in our regression, to see if we are correct. For example we think economic growth depends on debt: on government debt and household debt and corporate debt. So we have three independent variables, all changing, and having or not having an impact on economic growth.

So then we decide to look at these independent variables one at a time. So we pick one and call it the "independent" variable, and we make the other two "control" variables. We hold them constant, so that we can see the effect that the independent variable has on economic growth.

The crude version of this might be simply to ignore the control variables and pretend that the independent variable is the only thing that influences economic growth. In the more sophisticated version you run the test repeatedly, giving each control variable a chance to be the independent variable.


Maybe I'm misinterpreting what it means to hold something "constant". But it seems pretty strange to me, this idea that if you make something a control variable, it suddenly has no effect on the outcome.

I mean, suppose we take Federal debt as our independent variable. And we make household debt and corporate debt our control variables, holding them constant. So then we can see how the Federal debt affects economic growth.

But this is some kind of nonsense, because economic growth is influenced by household debt and by corporate debt as well as by the Federal debt. If we hold household and corporate constant, what the regression tells us is that all the effects of debt on economic growth are due to the Federal debt and the Federal debt alone.

Suppose for example that increases in household and corporate debt always boost economic growth. Well, in the real world those increases really happened. Therefore, economic growth was boosted up by those increases. But our regression tells us that all of that boost was due to the Federal debt. Pretty ridiculous, no?

Suppose instead that increases in household and corporate debt always harm economic growth. Again, in the real world those increases actually happened. Therefore, in the real world, economic growth was held down by those increases. But our regression says the Federal debt is responsible for that poor growth. This is pretty ridiculous, too.

Yet until 2008 or so, that's how economics was done. Some economists still do it that way, asserting that all our economic troubles are due to the Federal debt and none to any other debt. To my mind, that's obviously wrong.

I don't know anything about regression, so I probably shouldn't talk. But it seems to me the idea that you can just "control" some variables to find out how your one "independent" variable affects economic growth is more grotesquely absurd than anything that was done before 2008.

The outcome we got is the outcome we got. You can see it on a graph of GDP growth. Even if it is true that growth is affected by all the components of debt, we're not going to see the GDP growth of the last 70 years change when we hold most of those components constant.

Let's say that the Federal debt is always bad for economic growth; and that household and corporate debt is always good for economic growth. (Until 2008, this is more or less what economists thought.) Well, if we control for household and corporate debt, we should see only the bad effects of the Federal debt. Economic growth should be less. The growth numbers should go down. But that doesn't happen. The growth numbers don't change.

If we suddenly switch variables then, controlling for household and Federal debt, we should see only the good effects from corporate debt. Economic growth should be higher. But obviously, it isn't. The growth numbers don't change. The outcome doesn't change retroactively when you control for different variables.


I was a math major in school. But I've never done regression. So maybe I don't know what the hell I'm talking about. If I have something wrong, or if I seem to have something wrong, please do point it out.

causation, correlation, canary

The canary dies.

Is the coal mine dangerous because the canary dies? No. And yet we know the coal mine is dangerous, because the canary dies.

Le Mot Un-Juste

Subtract the rate of inflation from GDP growth, and you get what economists call the rate of "real" GDP growth.

Subtract the rate of inflation from the rate of interest, and you get what they call the "real" interest rate.

Subtract the inflation rate from a "nominal" rate, and you get a "real" rate. That's the arithmetic of it.

You may have questions about GDP and interest rates, and the economy, and even about this calculation, but you cannot challenge the arithmetic. It works.


Our topic is the interest rate. The arithmetic allows economists to say things like this:

Since the global financial crisis, short-term nominal interest rates in many developed economies have hovered around zero. Similarly, inflation rates have been quite low by historical standards, although they have remained positive and roughly stable on average in most countries. As a consequence, real interest rates—defined as nominal rates minus expected inflation—have also been very low, even falling negative for some countries.

Now I have a problem. I don't have a problem with the first two sentences, which provide facts. My problem is in the third sentence. But the problem is not about how to calculate real interest rates, which is comparable to what I started with, above. Nor is the problem with their observation that real interest rates have been very low; this is simply the result you get from the calculation. My problem is with the first three words of the third sentence; in particular, the third word:

CONSEQUENCE

It is simply the wrong word. It implies that real rates are low because interest rates and inflation are low.

Nay, not "implies". It says as much.

Consequence is defined as a result or effect of an action or condition. To say that interest rates and inflation are low and, as a consequence, real rates are low, is to say that real rates are a result of interest rates and inflation. The result, that is, of the subtraction. This is absurd.

The whole discussion that economists have been having, about the real rate of interest, is an important discussion. If the economists are right, if the real rate is low and stays low, our economy will not be the same. Economic growth will be slower, for one thing.

What's that you say? Growth has been slow for a decade, you say? Yes, indeed; and this is intimately related (if those economists are right) to the fall of the real interest rate to a low level. (I keep interrupting myself to say "if those economists are right" not because I'm challenging them, but to make it clear that I am presenting their view. Not my view. I don't have a "view" on this. I don't yet know what my thoughts are.)

So when you say "Growth has been slow for a decade", what you are saying is that it's a good thing economists are looking into this "low real rate" thing.


I mean to create the impression that the real rate is a factor of great importance for the economy. The "real" interest rate is a key real-world factor. Obviously it is not simply the "consequence" of the subtraction. It exists, if these economists are right, and it is powerful enough to make economic growth go from bad to worse.

We know the value of the real interest rate because of the subtraction. Actually, the real interest rate is not "observable". It cannot be measured; it can only be calculated by working backwards from observable things. That's what the subtraction does: it gives us a number for the real interest rate by working backwards from inflation and the nominal rate.

But the fact that we can work backwards to get the number tells us that the real rate exists, if those economists are right. They see it as a driving force, a force that causes the value of the nominal rate to be what it is, given inflation.

But if this is true, if the real interest rate is a driving force, then surely it is wrong to say the value of the real interest rate is a "consequence" of inflation and the nominal rate. The real rate is cause, not consequence. We know the value of the real rate as a result of the subtraction; this is certainly true (if those economists are right). But the value of the real rate is not a "consequence" of the subtraction, nor of the nominal rate and inflation.

Let me take their third sentence and shorten it:

As a consequence, real interest rates have been very low.

In that form, I find the sentence unacceptable. But in this form it is completely acceptable:

As a consequence, we know that real interest rates have been very low.

We know, because of the subtraction. We know, because of the values of inflation and the nominal rate. Our knowledge is a consequence of these things. But the real rate is not.

If those economists are right.