Monetary Interest as a Percent of GDP

Graph #1: Monetary Interest Paid as a Percent of GDP

Now, the monetary interest shown here is not a part of GDP. Only the net interest is. And anyway you'd see it as part of GDI, not GDP. Nonetheless, there is that much interest being paid, as much as 30% of GDP being paid as interest every year.

If debt-as-liability and debt-as-assets were both equally distributed, then you could say "we pay it to ourselves". But that's not so much the case. It's more like "we pay it to the one percent." Something like that.

I always come back to this: If we spend the interest we receive, then it doesn't matter much what portion is interest. But if the interest we receive stays in savings, then it matters very much. For even if interest expense and interest income both were owned and owed equally by everybody, but we tended to save more of it than we spend, then we would eventually -- inexorably -- create the sort of financial crisis that just ruins an economy for years and years and years.

If wealth and income are not equally distributed, that only speeds the process.

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Related post: Disastrous, cumulative and far-reaching repercussions of saving

Net Interest as a Percent of Interest Paid

Graph #1: Net Interest as a Percent of Monetary Interest Paid

Interesting that the graph trends up until the mid 1970s (said to be the end of the Golden Age) and down after.

When times were good -- that is, in the golden age -- interest income grew faster than interest cost. Since then, however, in the hard times, interest cost has been growing faster than interest income.

Yeah, that makes sense. Times are good when income predominates. Times are hard when cost predominates.

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Related post: Factors (2)

Interest and Net Interest

The two higher lines represent total interest; the two lower lines represent net interest:

Graph #1: Three Measures and One Estimate of Interest

The red line is "Net interest (paid and received)". The orange line, comparable, is a component of Gross Domestic Income. The difference may be that the orange one includes "miscellaneous payments".

The blue line is "Monetary interest paid". I put that on the same graph with net interest to see whether it was substantially higher -- as it should be if it isn't also "net". I'm satisfied it's not a measure of net interest.

The green line is a shot in the dark: Total credit market debt, multiplied by an interest rate. For the interest rate I started with the Fed Funds rate plus a constant, and just kept changing the constant till the green line came close to the blue one.

I ended up at Fed Funds plus 5. Seems high to me.

"Groping"

Steve Roth's Walras and The Carpenter was really good. Sumner's The third way was really good, till I got distracted by his use of "less" for "fewer" hours. Yichuan Wang's Macroeconomics: The Illustrated Edition didn't do it for me, not before I read the other two, and not after. Even though Sumner says it was excellent, and even though Steve made it interesting.

I checked out a Walras link at Wikipedia, and things just got worse:

Yeah, that's what I do. I figure out how much I'm willing to spend, in dollars, on all of the millions of different products that are offered for sale every day. And for each of those products I calculate my demand at every possible price. Yeah.

There are of course infinitely many possible prices for each of those products.

Imagine Walmart shoppers wandering aimless and silent, awaiting the announcement of prices, then submitting via their smartphones how much they are willing to pay, and then waiting for new prices to be announced after the auctioneer receives and processes all the smartphone data. Meanwhile nobody buys anything, and no one will buy anything until everyone present has agreed upon an announced set of prices. Then, in an instant, everything in the store is sold and the customers are left to empty the store out into their cars.

Is that how the economy works? Is that the future? Is that the alternative of choice to the problem of menu costs? Give me a break!


Under what conditions will such a process terminate in equilibrium? That's what they're worried about? Don't waste my time.

I'm with Jack, who comments on Steve Roth's post:

The question that immediately comes to mind after reading your post regarding the “Walrasian view” is, Why on Earth would anyone spend even a moment of thought on such a concept?

Granted, this is a first impression.

Unscheduled stop

Hold everything. I was right.

I went thru the motions yesterday for this morning's post. As described, I got the FRED TCU data and plugged into Lars Christensen's spreadsheet in place of, actually in place of his S&P500 data. Excel picked up that data, reworked the numbers, and adjusted the lines on the graph to agree with the revision I made. All very nice, and the error that I claimed would appear on the graph did not appear. So I had my tail between my legs then, and tried to make the best of it with a funny post title.

But just now, or about 20 minutes ago really, it occurred to me: it is the NGDP series average that Lars adds in to his Market Indicator in the wrong sequence. Not the S&P500 series average. I went running upstairs, turned on the old computer, made another copy of Lar's spreadsheet with my notes (from 1 September) and plugged in the Total Capacity Utilization data in place of Lars's NGDP data. Here is the resulting graph:

Graph #1: The Red Line is Lars Christensen's Erroneous Calculation

The blue line is the original source data, in this case the TCU data. The orange line tangled up with it is my version of Lars's calculation. The red line up high is Lars's market indicator with the TCU numbers plugged in, in place of the NGDP numbers.

My numbers are down near the source data, where they are supposed to be. Lars's numbers are ridiculously large and obviously in error.

This is what I expected to show earlier today. Lars's calculation adds the TCU series average to his index number first, and multiplies by the TCU standard deviation after. His sequence of operations pushes his market indicator line way up high, as expected.

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Here's the spreadsheet. It contains my VBA code for formatting my graphs. But you can disable that, as it is not used in any calculations and the graph is already done.

The donkey was me

Following up on yesterday's analysis...

I showed a series of graphs yesterday, and the only condition for my choice of data was that "the numbers [must be] up pretty high, not down near zero." The reason I imposed that condition was to make obvious the result I got in the fourth graph of the series -- to show that the incorrect sequence of operations magnifies the big number, making it ridiculously large and obviously an error.

It worked out well, for that series of graphs.

For today's post I thought I'd take Lars's spreadsheet, the one with my extra columns in it, and leave his calculations and mine untouched, but replace one of his data series with one that has the numbers up pretty high, not down near zero. I thought the result would show a similar ridiculous, obvious error. That's not what happened.

I used the same Capacity Utilization numbers as in yesterday'a graphs. But what with subtracting the average value and whatever else he does in his calc, both Lars's calc and my version put the "processed" Capacity Utilization numbers in about the same place our Market Indicator numbers were in yesterday's Graph #5. In the right place, or nearly so.

So here's the story, then: I am really pleased that I figured out the four-step sequence:
1. Subtract the series average from the Series A data.
2. Divide the resulting data by the Series A standard deviation.
3. Multiply the resulting data by the Series B standard deviation. And
4. To the resulting data add the Series B average.
I think this is a magnificently clever way to make two datasets visually comparable. And I have Lars to thank for it.

But that's all I got from his spreadsheet. Whatever else he did escapes me. Apparently it's not a mistake. It's just some complex calculation that I couldn't disentangle.

Pin the Tail on the Donkey

I came to Lars Christensen's Markets are telling us where NGDP growth is heading by way of Examining the Case for NGDP Targeting by Unlearning Economics, at Pieria

Unlearning writes:

I copied this method of estimating NGDP expectations from Lars Christensen, a market monetarist. Christensen seems to take this graph as confirmation of his views, but in fact it shows the opposite of what he wants it to show.

I see neither confirmation nor its opposite in the graphs these guys show. I think it's funny that Christensen's Market Indicator has already been used as proof and disproof, and I'm still just checking the arithmetic. Funnier yet, I think the arithmetic is bad. I had my doubts about it since I first noticed that odd fudge-factor subtraction in Lars Christensen's calculation.

But the clincher is the reverse-order thing...

Reverse engineering some grade-school arithmetic

Pick a number

10

Subtract 4

10 - 4 = 6

Divide by 3

6 / 3 = 2

Good. Now let's get the original number back. Last time we subtracted 4 and divided by 3. This time we'll add 4 and multiply by 3. Start with our final answer

2

Add 4

2 + 4 = 6

Multiply by 3

6 * 3 = 18

And there is our original number, restored. Oh, wait a minute! We started with 10 and we ended up with 18. That's not right. That's not right. What happened?

What happened is, we tried to backtrack and we reversed the steps, but we did not also reverse the sequence of those steps.

The first time we subtracted, and the second time we added. The first time we divided and the second time we multiplied. That's good.

But the first time, we subtracted first and divided second. When we backtrack we have to start with the last step and backtrack it first. The first time, we divided by 3 last. This time we have to multiply by 3 first. And then we can add 4.

2 * 3 = 6

6 + 4 = 10

And that gives us the number we started with.

Off topic, but this exercise shows how easy it is to screw up the math when you don't actually *DO* the math. That's what's wrong with those math-like models economists come up with all the time, that they never actually work out in a spreadsheet.


Here's a copy of Lars Christensen's spreadsheet with some notes I made in it.

Lars starts out by gathering his data.

Next, he "standardizes" each dataset by subtracting the dataset average and dividing the result by the standard deviation of the dataset. This is the stuff that fascinates me.

Then he takes one of his standardized datasets and subtracts it from another. He calls the result an "index". (But if you look at the spreadsheet, you may notice that the index column is NO LONGER STANDARDIZED. The column average is still zero, but the column standard deviation is now about 1.46. It is not equal to 1 because of the subtraction which in my opinion is done at the wrong time.)

After that comes his Market Indicator calculation. He takes the index and adds to it the average of the NGDP dataset, to center the index on the NGDP dataset.

Oddly, then, from that sum he subtracts the arbitrary value 1.5. This subtraction will move the Market Indicator off-center and make it a bit low relative to the NGDP data.

The resulting value he then multiplies by the standard deviation of the NGDP data, and divides by the standard deviation of his index data. It gets a little gummy and confusing here in this final bit of the Market Indicator calculation. Lars is dividing the standard deviation (of the index) out of the index and out of the NGDP average and out of the arbitrary -1.5. That seems wrong to me, to divide the SD of the index out of anything other than the index just doesn't seem right. (But hey, it's Lars's Market Indicator.)

Then he multiplies by the standard deviation of the NGDP data. (As I pointed out before, it is really NGNP data.) Multiplies it into the index value, and into the NGDP average (now, this has to be wrong!) and into the constant that he is subtracting. Awfully gummy stuff.

This is Lars Christensen's Market Indicator we're looking at here. Lars can figure it any way he wants. I don't mean to say he has anything "wrong". But there are some things that don't make sense to me, things that look like mistakes to me. Things that Unlearning Economics apparently didn't pick up when he used Lars's market indicator.

The thing that seals the deal for me is the "order of operations" problem. The Market Indicator calculation must be in error. I'm sure of it.

He begins beautifully, subtracting the average value first, and dividing by the standard deviation second.

He ends terribly, adding the average value first, and multiplying by standard deviation second. He has reversed the operations, but he has not reversed the order of operations. He adds the average value (and a fudge factor) first, and multiplies by the standard deviation value afterwards. This is one gummy mess.


Suppose I take a time series graph from FRED, one that has the numbers up pretty high, not down near zero. I'll go with Capacity Utilization:

Graph #1: Total Capacity Utilization

Suppose we want to take the blue line and move it down so that what's 80 now becomes zero, and what's 85 becomes 5, and like that. It's easy to do: All we have to do is subtract 80 from the original numbers. The formula in the upper border of the graph below shows this subtraction:

Graph #2: Total Capacity Utilization Moved Down from 80 to Zero

The graph still looks the same. But the numbers on the vertical scale are different. Everything is 80 less than it was before.

Now suppose we notice that the blue line is almost entirely contained between the values 10 and -10 and lets say we want to change that. If we divide everything by 10, the line will be almost entirely contained between the values 1 and -1:

Graph #3: Total Capacity Utilization Moved Down 80, then Divided by 10

But the blue line still  looks the same.

That's the important thing. We didn't change the pattern of Total Capacity Utilization. We just moved it, and scaled it down some. There are reasons for doing such things, as Lars Christensen has shown.

The trouble with what I did here is that it's entirely arbitrary. I picked the value 80, basically because on Graph #1 there was a line at that level. I thought it would be neat to make that the zero level. And then after that, conveniently, the numbers 10 and -10 showed up on the vertical axis, so I just divided by 10.

Lars does something a little more sophisticated. Instead of subtracting 80, he figures the average value of the data points, and subtracts that value from the data. And instead of dividing by 10 because 10 is a nice round number, he figures the standard deviation of the data points and divides by that. Now you might say it's still arbitrary to do what Lars does, but if it is, it's arbitrary with principles.

And I don't think it's arbitrary. The average value tells us where the activity is taking place, and the standard deviation tells us how wide-ranging the activity is, but the pattern itself is completely independent of both those things -- as you noticed in the graphs above.


Now consider what happens when we reverse the operations but fail to reverse the order of operations. Adding 80 and then multiplying by 10 pushes the Total Capacity Utilization number up to around 800. That's a lot of utilization:

Graph #4: Reversal of the Graph #3 Calcs in the Wrong Order (blue)
Reversal of the Graph #3 Calcs in the Correct Order (green)
Original Data for Comparison(red)

The red line down near 100 on the graph is the original data. The green line, hanging low with the red one, shows the result of correctly reversing the order of operations. The calculation for the green line is in the third line of the upper border. The first and fourth steps raise and lower the value by 80; the second and third change it by a factor of ten.

Reversed correctly, the numbers return to their original values, so the green and red lines overlap. (I made the red line a little wider than the green line so you can see both of them.) Here's the link to the FRED page for this graph, size large.


After figuring out what was bothering me, I went through Christensen's spreadsheet carefully. I ended up inserting a few columns into it and showing the calcs that make sense to me right there alongside the existing calculations. I recreated Lars's graph with an extra line that displays the result of my version of Lars's calculation.

Graph #5: Lars's Graph Recreated, with my Version Added

Blue is the NGDP (or really, NGNP) data. Red is Christensen's calculation. Orange is his calculation with my modifications. Orange and red run close for the most part except briefly around 2003 and -- interestingly -- in the latter 1990s.

However, Christensen's calculation makes use of a fudge factor. As noted above, he subtracts the arbitrary value 1.5 before the multiplication. (And oh, yeah, he has the order of operations wrong.) Removing that arbitrary value from his calculation gave me this graph:

Graph #6: Graph 5 Repeated, with Lars's Fudge Factor Eliminated

Now Lars's Market Indicator (the red line) is significantly higher than both my version and the NGNP data.

FPI and Christensen-Fitted Debt

Couple weeks back I looked at the calculations behind Lars Christensen's Market Expectations Index. He did some nifty stuff with averages and standard deviations, to "fit" one line to another on a graph, to make visual comparison easier.

I saw an opportunity to practice that calculation, to compare the movements of TCMDO debt to Fixed Private Investment.

But first I took the easy way out, and in Graph #3 of the 25th I "fitted" TCMDO to FPI by eye. After looking at the unfitted graph, I wanted to scale the debt numbers up by a factor of 3. Then after seeing the result of scaling, I decided to subtract 20 from the debt numbers to shift the debt line down and get it close to the FPI line.

But it was all just ballpark.

So I downloaded the numbers from FRED for Graph#2 of the 25th, sat down to work, and applied Christensen's calculations to the debt numbers.

Graph #1: TCMDO Debt (red) Christensen-Fitted to Fixed Private Investment (blue)

For comparison, here's the "no finesse" graph I showed on the 25th:

Graph #2: TCMDO Debt (red) Fitted by Eye to Fixed Private Investment (blue)

Pretty good, for no finesse.

Funny thing. When I was doing the "no finesse" graph and writing that post, I was careful not to talk about the one line being "higher" than the other. It's okay to talk about something happening first in the one line and later in the other. And it's okay to observe the one line changing more rapidly than the other. But you can't say one is "higher" or "lower" or even that it changes from higher to lower (or the reverse) because the relative positions, higher and lower, depend on how much you subtract as part of the "Christensen Fit" calculation.

Actually I was disappointed when I sat down to do the calculation Lars's way. I had forgotten that Christensen's calculation includes an arbitrary up-and-down adjustment term. That term puts the same ambiguity into his calc that I had in my finesse-free version: It makes the relative positioning of the two lines completely arbitrary.

That may be necessary when the calc combines two datasets for comparison to one, as Christensen's does. I don't know. But intuition tells me that if I take just one dataset (like TCMDO) and tweak it by the average and the standard deviation values for that dataset, then I shouldn't also need an arbitrary up-and-down adjustment.

I'm not linking to my spreadsheet this time, because the calc isn't clear in my head. Maybe I've got a mistake in it, that looks okay because of the up-and-down adjustment I made. I have to work through this calc and get more familiar with it.

Meanwhile, I still think it's an interesting technique.

Which one is not like the others?

Earlier this week I showed the shocking decline of Fixed Private Investment relative to total accumulated debt:

Graph #1: Fixed Private Investment relative to Total Debt
It shows significant changes before the 1980 recession, after the 1990 recession,
before the 2001 recession, and toward the end of the 2007-2009 recession.

Today, we look at Fixed Private Investment relative to components of the total debt:

Graph #2: Fixed Private Investment relative to Nonfinancial Debt
It shows significant changes before the 1980 recession, after the 1990 recession,
before the 2001 recession, and toward the end of the 2007-2009 recession.

Graph #3: Fixed Private Investment relative to the Publicly Held part of Federal Debt
It shows significant changes before the 1980 recession, after the 1990 recession,
before the 2001 recession, and toward the end of the 2007-2009 recession.

Graph #4: Fixed Private Investment relative to Non-Federal Non-Financial Debt
It shows significant changes before the 1980 recession, after the 1990 recession,
before the 2001 recession, and toward the end of the 2007-2009 recession.

Graph #5: Fixed Private Investment relative to Household Debt
It shows significant changes before the 1980 recession, after the 1990 recession,
before the 2001 recession, and toward the end of the 2007-2009 recession.

Graph #6: Fixed Private Investment relative to Financial Debt
It seems to show a trend change toward the end of the 2007-2009 recession.

Which one is not like the others?