Saturday, April 30, 2016

Looking for weakness

Trump? Cruz? Clinton? Sanders? Whose boom will it be? No one will credit Obama, surely.

I marked up a graph of commercial loans:

Graph #1

Last time, the increase started around mid-2003. There was that awful low there just around 2006, related to the housing slump. And there were a couple feeble attempts at increase, indicated by my black arrows.

This time, the increase started in early 2010. It is a steeper climb, faster increase. There are no awful lows, and no feeble attempts at increase. No signs of trouble. I don't see recession in the cards.


Making predictions makes me nervous, so I have to say "this isn't investment advice".

Also, yeah, I'm the guy who says we have too much debt already, yeah. But as long as we base economic policy on the idea that "using credit is good for growth", increased lending is a sign growth is improving.

Increased lending doesn't solve the too-much-debt problem. To solve that problem we have to change the idea that guides economic policy.

Friday, April 29, 2016

Disorganized Writer Offers Follow-Up to 'Scatterplot Trends' Story

On the 27th I took a scatterplot -- the private-debt-to-public-debt (P2P) ratio versus inflation-adjusted GDP growth -- and tweaked the hell out of it. Ended up with the data not chronological but sorted on the P2P values, with both the x and y values expressed as moving averages of the sorted data, and with a series of short trendlines describing the path of the scatterplot trend.

That was fun to do. But the conclusion I came to, after all the fun, was

Not sure about sorting the values.

Not much of a conclusion, is it? I want to go back and get sure about sorting the values. How would it look if I put the data back in chronological order? That was my question.

Here is the last graph from the 27th:

Graph #1: 8Q subsets with 6Q Overlap, Data Sorted on X Values
You can see that the black line -- imagine the series of short black trendlines is one long line describing the pattern of dots -- the black line moves consistently rightward from lower to higher ratio values. That's because the data is sorted on those values.

When I put the data back in chronological order, the ratio values tend to get higher over time but there is some backtracking along the way. And a lot of the ratio values fall between 3½ and 5, so that we end up with a lot of dots and a lot of black trendline in that part of the graph:

Graph #2: 8Q subsets with 6Q Overlap, Data in Chronological Order
Quite a difference from the first graph. Quite a difference sorting makes.

Quite a difference, too, from my scatterplot of the unmolested data:

Graph #3: Unsorted Data, No Moving Averages, One Overall Trendline
No conclusion this time. Just pictures.

Thursday, April 28, 2016

Hamilton's find and the Phillips Curve

James Hamilton recently looked at Macrofinancial History and the New Business Cycle Facts (PDF, 55 pages). According to Hamilton,

Source: James Hamilton, from
Jorda, Schularick & Taylor
The authors find that as economies have become more leveraged, the standard deviation of output growth has become smaller, consistent with a phenomenon that has been described as the Great Moderation in the United States since 1985.

Well that's sort of a big deal. It implies that as debt grew, debt influenced GDP growth and resulted in the Great Moderation. Furthermore,

They also find that the skewness of GDP has become more negative– big movements up have become more subdued relative to downturns.

In other words, the Great Moderation wasn't really so "great". The volatility ("standard deviation") of GDP was less simply because we stopped getting the "big movements up".

Graph #1: The Great Moderation -- Output Growth No Longer Breaks the 5¼% Barrier
I think everybody knew as much. Still, it is nice to see it documented.

Remember Okun's law? When output growth doesn't go up, employment doesn't go up:

Graph #2: The Great Moderation -- Employment Growth No Longer Breaks the 3% Barrier
So Hamilton's find tells us that debt growth pushed unemployment up. Think of the effect of this on the original Phillips curve: Debt growth caused a change in the horizontal axis values. It pushed unemployment higher and farther from the origin. It shifted the curve and it raised the "natural" rate of unemployment.

To be sure, I'm the one describing a cause-and-effect relation. Hamilton quotes from the PDF that

as economies have become more leveraged, the standard deviation of output growth has become smaller

They describe correlation, not causation. And again when Hamilton quotes from the conclusion:

our core result– that higher leverage goes hand in hand with less volatility

Higher leverage only goes "hand in hand" with reduced volatility and lower growth, they say. They don't claim that excessive debt "caused" the changes.

So I'll say it: Excessive accumulated debt caused the changes: The lower growth. The reduced volatility. The increase in "house prices" since 1950. The "more severe tail events". And the shift in the Phillips curve.

Wednesday, April 27, 2016

Scatterplot Trends

"Learn to program" -- Bill Gates

I had some trouble determining the trends shown by scatterplots. Looked at that on 21 April ...

Graph #1: Five-Year Subsets of Annual Data

... and again on 23 April.

Graph #2: 12-Quarter Subsets of Quarterly Data
For the second of those two graphs I used Excel VBA to automate creating the trendlines.

Neither of the above graphs satisfied me. Wanting to improve the result as painlessly as possible, I decided to tweak the VBA code.

I added a couple variables, one to hold the start row, and one to hold the end row of the data. Since my habit is to put dates in Column A and data in Columns B and C, the start-row and end-row values are enough so that my code knows where to find the data on the spreadsheet.

Then I added a couple more variables, one for the number of data points to include in each trendline, and one for how much of an "overlap" I want from one set of data points to the next. I wanted these as variables because I wouldn't know what the graph looked like until it was done. And I wanted it to be easy to make the trendlines longer or shorter, and overlap them more or less, based on how the graphs looked.

I put all four variables together, near the top of the code. I have to go in and change the values, then run the code to change how the graph looks. But if I was doing it by hand I'd have to go into the Select Data Source form to subset the data, and then go into the Format Trendline form to finesse the trendline. I just put all the finessing in my code instead.

On both graphs above, some of the trendlines are long and some are short. It depends on the values, the RGDP growth values and the debt ratio values. On both graphs above, the data is in chronological order even though the dates are not shown on the graph. I thought I might get trendlines more equal in length if I sorted the data by the debt ratio values.

Graph #3: 8-Quarter Trend Lines with 6-Quarter Overlap, Sorted on X Values
Eh, lots of the lines are still short and lots of them are still quite long. Sorting didn't help.

Still, sorting the data for a scatterplot is an interesting idea. I wouldn't want to do it for a Phillips curve, say, where there is a trade-off between x-axis values and y-axis values. But on these debt-and-growth graphs, where I'm looking at the debt ratio as cause and RGDP growth as effect, I think sorting might make sense.

If I was looking at RGDP growth over time, for example, the x values -- dates -- would be in chronological order. Why shouldn't the x values be in order even when those values are not dates? Especially if you have "cause" on the x-axis and "effect" on the y-axis.

But sorting didn't make my trendlines all the same length. Oh, well. It's the leftmost lines that strike me as long -- from the early years, when the business cycle pushed RGDP values up and down without any great "moderation". (Of course, you wouldn't know it's the early years, as there are no time values on Graph #3.) I thought I might condense the data variation by using a five-quarter moving average of the RGDP values:

Graph #4: 8Q Subsets with 6Q Overlap, Sorted on X Values
Well, the lines still look long where the ratio is low, but between 5 and 6.5 on the x-axis the dots clustered nicely, and the trendlines too. Hm. I like it.

I increased the moving average from 5 to 9 quarters for the y-axis, and changed the ratio values to a 5-quarter moving average for the x-axis. Moving averages on both axes now. And now I'm starting to see a shape in those dots:

Graph #5: 8Q subsets with 6Q Overlap, Sorted on X Values
I like it!

Summary: Not sure about sorting the values. But using moving averages on both the x- and the y-axis sure did make a pattern stand out.

// The Excel file. Don't believe the Google Drive preview. Download the file & open it in Excel and the graphs will be fine.

Tuesday, April 26, 2016


Ran across this graph from December of 2013:

Graph #1: PGDP from 2005 (blue) and 2013 (red)
The graph shows the growth rates for two estimates of Potential GDP, the January 2005 estimate and the February 2013 estimate. Eight years separate the estimates.

Two years and some have passed. Time to update the graph.

Graph #2: PGDP from 2005 (blue), 2013 (red), and 2016 (green)
Red and blue as the same as above. Green is new. Potential GDP is still falling.

Graph #1 shows the older FREDGraph output, before the revision of March 2014. Graph #2 shows the newer output, from after the revision. The new default background color is faint, and the left margin label overwrites the vertical axis.

The economy's not getting any better, and the graphs ain't, either.

US. Congressional Budget Office, Real Potential Gross Domestic Product [GDPPOT], retrieved from ALFRED, Federal Reserve Bank of St. Louis, April 25, 2016.

Monday, April 25, 2016

April Update: We are at the bottom ...

From mine of 3 March 2016:
We are at the bottom now, ready to go up.

Graph #4: DPD with Trend out to 2030
We're right there right now. DPD is ready to go up right now.

Remember: When the downtrend turns and an uptrend begins the economy for a while is very, very good. This is not going to be your typical anemic recovery. This is going to be the full tilt, rapid output growth, rapid productivity growth, high performance boom.

I can't promise you it'll last long, because the level of debt is already very high. But it'll be a good one while it lasts.

Cheese, I gotta make a better graph!


There are a few people who might see things as I do...

... and a few headlines that suggest such things...

... but for the most part, projections look like this month's New York Fed Staff Forecast: RGDP growth slowing from 2½% in 2014 to 2% in 2015, holding at 2% in 2016, and slowing to 1¾% in 2017. Sluggishness on top of sluggishness.

They predict no improvement. They are assuming that the existing state of affairs will continue indefinitely. Not me. I have specific reasons to expect a change: I have my Debt-per-Dollar graph. I predict strong growth to develop over the next three years, and to last perhaps five years.

// see also: A Pictorial History: Private and Public Debt

Sunday, April 24, 2016

Population Growth as a Recession Indicator

Looking at "bottoms" in population growth: decrease, then bottom, then increase.

  •  A bottom in 1953Q2 falls just before the 1953 recession.
  •  A population-growth bottom comes just after the 1958 recession.
  •  A bottom at 1960Q3 falls just as the 1960 recession begins. Concurrent indicator.
  •  A bottom at 1969Q1 leads the 1970 recession.
  •  A bottom at 1974Q2, concurrent with the 1974 recession.
  •  No indication of the 1980 recession.
  •  A bottom at 1981Q4, concurrent.
  •  A bottom well before the 1990 recession; then very strong increase.
  •  A slowing and then speedup at 2000Q4, leading indicator.
  •  A bottom and then increase well before the 2008 recession.
  •  No present indication of recession.

Population growth changes are associated with nine of ten recessions shown on the graph. Of those nine changes, only one is a lagging indicator. Set that one aside as uninformative. Eight of ten recessions find leading or concurrent indicators in population growth. That's an 80% chance population growth gives some indication of recession. Don't ask me why.

The graph gives no indication of recession at present.

Surprise! At this writing (22 April 2016) FRED's "Total Population" series shows population growth thru the end of 2016.

I guess we're safe for a while :)

Saturday, April 23, 2016

Quarterly: Private Debt relative to Public Debt

At FRED, when you get the Real GDP series GDPC1 it defaults to Quarterly frequency. When you get the series TCMDO ("all sectors" debt) or FGTCMDODNS ("Federal government" debt) it defaults to "Quarterly, End of Period". Now, like me, you might think quarterly is quarterly. But when you try to make a scatterplot of GDP and debt, disappointment sets in:

For scatter plots, both data series in a pair must have the same frequency. The following data series pair has been skipped: data series #1 with frequency Quarterly and data series #2 with frequency Quarterly, End of Period.

Switch to Annual frequency, and you get the scatterplot.

I don't think it's a technical measurement problem. I think it's a programming glitch. Regardless, I couldn't do my scatterplots using quarterly frequency at FRED. So defying all logic, I switched to Annual, looked at the scatterplot at FRED, then exported the annual data to Excel and did all my work there anyway. I could have been using quarterly data all along since I was working in Excel. But no.

Guess what frequency I'm gonna use now.


Here's a first look. I used my graphing VBA code on it, which is for line graphs, not scatters. So it came out with lines instead of dots. Then I added some "how it looks" (HIL) lines -- trendlines by eye -- in red:

Graph #1:Scatterplot Preliminary with HIL Lines
Darned if it doesn't look like a hill! Up, gracefully, to a high point at the last quarter of 1965. Down thereafter amid a scribble of activity. It is interesting that "low" activity (below the HIL line) subsides when the debt ratio (on the horizontal axis) is between 2.5 to 3.25 or so. I thought the optimum range for the private-to-public debt ratio would be lower, around 2.25 to 2.5 as in the early 1960s. I still think that. But I'm keeping an open mind...

With the dots shown and the connecting lines removed and an overall trendline added (by Excel) now it looks like a scatterplot:

Graph #2: Excel's Trendline (red) shows Growth is Better when the P2P Ratio is Low

I duded up some VBA code to subset the data series into consecutive 12-quarter periods and display the period trendline for each:

Graph #3: Many Trends to Look At

If you feel the need to identify the trendlines, download the Excel file. Hover over a trendline in Excel and a little label pops up to identify the start-date of that 12-quarter period.

This is crude as hell, but hey: If you want good GDP growth, keep private debt to no more than 3.25 times the size of the Federal debt.

Policy guidance.

Friday, April 22, 2016

The ratio of what to what?

Thursday, April 21, 2016


I don't know why I didn't look at it before. Started with this

Graph #1: Selecting the central cluster, and calling the rest "outliers"
and only looked at the central group:
Graph #2: The Central Cluster
Here are all three groups:

Graph #3: Three Subsets
Two of the three trendlines go the wrong way. Or, no: I was wrong, two out of three. I shoulda showed it before. Can't think of everything though, not all at once.


Okay. I decided to look at this "Three Subsets" thing because I sort of expect to see the trendline show increase in the early years -- the 1950s when private debt was particularly low. Once it gets to its optimum level, though, any further increase in debt should drive economic performance -- and the trendline -- down. That's my thinking, anyway.

Well, maybe I was right, two out of three.


This is just quick. Took the same annual data in the scatterplot we looked at for a week and more, got rid of the one overall trendline, and added trendlines for a series of 5-year periods:

Graph #4: Many Subsets
It is close to half-and-half. About half the trendlines are up-sloping, and half down-sloping. I guess, with scatterplot points all over the place, and an arbitrary chopping-up of the series, that is to be expected.

Still, the bigger, steeper up-trends occur at low levels of the P2P ratio, and none occur at high levels. There is only one down-trend for ratio values below 3.5, and it is all downtrend at high ratio values. These observations suggest, once again, that the low P2P is better for GDP growth than the high P2P.

Overall, taking all the trendlines as one general movement, that movement is down to the right: less growth of real GDP as the ratio of private to public debt increases.

I stand by my story.

Wednesday, April 20, 2016

Thank God for them billionaires, huh?

Figure me completely ignorant. That way if I know anything at all it's a plus.

I spend almost as much time watching Hinterland as I spend on graphs. The show is set in Wales in the midst of poverty, desolation, and faces full of character. So now I like Wales. Oh, plus the show is filmed twice: in Welsh, and in English. Because in Wales, preserving the native tongue is a big deal. I like that.

At we read:

In 1536, English became an official language in Wales. So Welsh was prohibited to speak in the school and everywhere. And teachers were prohibited to teach Welsh by the Education Act of 1870. However, the preservation movement of Welsh became active when becoming the 20th century. Therefore, the number of people who can speak Welsh has increased. Now Welsh became an official language as well as English and became a bilingual country. And every signs and the official document are written in two languages.

In two languages: signs, official documents, and Hinterland.

Poverty, desolation, and strength of character. In our time, that's a model of the economy. That's one reason I like the show so much.

So I started looking for economics blogs by Welshmen. Didn't find any yet. I did find Wales Online, a site doing its very best to look rich, promising, and giddy. I much prefer poverty, desolation, and character. Even on a good day.

They link to Forget all the doom and gloom the global economy is in good shape says leading economist Kevin Gardiner. The title is longer than some of my posts! But ... yeah ... I like hearing that the economy is in good shape, especially since my recent prediction of an imminent US boom. So I bit.

First six words of the article? "While another financial crisis is inevitable..."

Second paragraph? "... the global investment strategist for the wealth management division of Rothschild said the world has never been in a better place in terms of the average wealth of its population."

Ah, the average wealth of the population, yeah. Seven billionaires, seven billion people in poverty: On average the world has never been in a better place.

Better for the billionaires, for sure. For global investment strategists at the wealth management division of Rothschild, and people like that. And if they can sucker the rest of us into spending more money, they'll be more than glad to take it.

I guess you caught me on a bad day.

From the article:
Mr Gardiner said: “It is important to keep in mind though that at end of the day economies are driven by underlying things like spare capacity, education, labour and technological process.

“And the economy most of the time grows and the global economy is already larger than it was before the financial crisis.

“And whenever the next crisis does hit, it is important to remember that we will muddle through it somehow.

"Whenever the next crisis does hit" -- ?? When ever? This guy is giddy. Probably why the article ended up at Wales Online.

And another thing. The guy's strongest argument is that "the economy most of the time grows". Yeah yeah, between dark ages. But it's not "most of the time" I'm worried about.

If history repeats itself then the world is cyclical, and if the world is cyclical it is because the economy is cyclical, and if the economy is cyclical, then what goes up must come down. Not today, not in a week, not "whenever", but it must come down. Or at least it certainly will come down unless we know it is likely to come down and we are vigilant in our efforts to prevent it.

You know all those vigilant people worried about the size of government, who want to drown it in a bathtub? Well, people like that are trying to bring it down. And they don't even know it, most of them, I think. (If you want a smaller government, that's fine. But if you think the size and scope of government is the problem, you're an idiot.)

From the article:
And he believes many of the fears that people have, like around debt levels, demographic pressures, deflation and depletion of scarce resources, were overstated.

But he's not talking about demographic pressures, deflation and depletion of resources. He's only talking about debt:

Mr Gardiner said: “If you take debt then for every borrower there is a lender and it does all net off. And in most of the analysis of debt, when applied to larger economies, people tend to forget that.

The man's an idiot. By definition, when one person borrows money from another and promises to pay it back later, both an asset and a liability are created. The fact that the asset and the liability "net off" does not mean there is no problem. Economic problems are not solved by accounting definitions.

The asset side of debt is not usually a problem. Maybe that's what the guy was thinking. But the liability side is obviously a problem when you have a financial crisis, especially when another financial crisis is said to be "inevitable". Besides, when we had the last financial crisis with all those toxic assets even the assets were a problem.

“They tend to think, for example, that the US consumer is horribly indebted and the reality is that the average US consumer is one of the wealthiest people on the planet.

Ah, the average again. The "average consumer" is doing great. Thank God for them billionaires, huh? They bring up the curve for everybody.

Tuesday, April 19, 2016

Reaching a conclusion

The series starts here

I was looking at this graph again ...

Graph #1:
... and I noticed the big clump of dots in the middle. Pretty obvious, really. Most of the dots fall between 3.0 and 5.0 (give or take) on the horizontal axis. You could think of the dots to the left of 3.0 as outliers. I think you'd be stretching it, because there's a lot of dots there, but you might argue it. Same for dots to the right of 5.0. Or 5.3 maybe, somewhere in there.

If all those leftmost outliers by some odd coincidence happened to favor the high side of RGDP growth, well, that would bring up the left end of the trendline.

And if all those rightmost outliers happened to favor the low side of RGDP growth, that would push the right end of the trendline down.

To be sure, to my eye, the leftmost dots favoring high RGDP growth and the rightmost dots favoring low RGDP growth, that's the whole point. That's what I'm trying to get you to see. I don't think they are outliers at all. I think they are evidence.

But let's say there is some unknown force or invisible hand that pulls the leftmost dots up and pushes the rightmost dots down. I don't know, maybe there is such a force. If it's unknown, you don't know it. So let's just assume (for the moment) that there is such a force affecting those outlier dots on the left and the right.

Let's add some red lines to separate the central cluster from the outliers:

Graph #2: Selecting the central cluster, and calling the rest "outliers"
In Excel, if you hover over one of the dots, a little window pops up to identify the point and tell you the values. A nice little window, not like that big clunky thing you get at FRED. I used that little window to determine the outlier values I would ignore. I'm ignoring everything to the left of 3.25 on the horizontal axis, and everything to the right of 5.25.

The line at 3.25 was a tight fit!

Okay, so I sorted the data in Excel. Sorted on the P2P ratio. That brought all the ratio values that are less than 3.25 to the top of the list. I deleted them. And from the bottom of the list I deleted all the rows with a ratio value over 5.25. So now the list includes only the dots that are between the red lines on Graph #2.

Here is the graph showing the subset:

Graph #3: The Central Cluster
See the trendline? It is still higher on the left and lower on the right.
Even if we make the outrageous assumption that two thirds of the dots on the original graph are outliers, when we eliminate them and look at what's left, the graph shows that the economy performs better when the ratio of private debt to public debt is low.

There is no odd coincidence pulling the leftmost dots up. There is no invisible hand pushing the rightmost dots down. There is no such force affecting the outlier dots. The dots are not outliers. It is a low P2P ratio that pulls dots up, and a high P2P ratio that pushes dots down. The ratio of private debt to public debt affects economic growth.

// The Excel file

Monday, April 18, 2016

Plain as the nose on your face

The series starts here

Sunday, April 17, 2016

And you thought the similarity showed insignificance

The series starts here

Annual RGDP looks like this:

Graph #1: Annual RGDP, 1947-2015

Percent change from year ago for annual RGDP looks like this:

Graph #2: Percent Change in Annual RGDP

Switching to Excel and adding a linear trendline and dots at the data points:

Graph #3: Percent Change in Annual RGDP, with Linear Trendline
Trendline Values Run about 4.5 to 2.0

Sorting the data by 'percent change' value:

Graph #4: Same Data, Sorted by Growth Rate
Trendline Values Run about 7.0 to -1.0
Oddly symmetrical.

I sorted the values from high to low to get a downsloping trend like the one we've been looking at all week. Funny thing: After I sorted the values, the graph didn't change. I had to go in and take the dates off the horizontal axis; when I did that, it took the shape you see here. (Excel added the "1900" numbers.)

Each point on the blue line represents one year's growth number.

The most common growth rates are between 2% and 4% or, say, between 1% and 5%. Growth rates of less than one or two percent are less common, as are rates of more than four or five percent. Where the numbers are more common, they take up more space in the "x" (horizontal) direction. That makes the blue line more flat than the trendline where the numbers are more common.

Growth rates above 4.7% or so are less common; at rates above that number the blue line moves back toward the black, and then above it. Similar story for values of less than one or two percent.

A histogram would show it.

Yesterday I said

In a scatterplot focused on some detail (like the P2P debt ratio) there is no reason to assume you'll get the same range of trend values you get when you look at the data chronologically.

Graph #4, above, is such a graph. It is focused on growth rate values without regard for chronology. There is no reason to assume that we'll get the same range of trend values we got on Graph #3. And we don't get the same range of trend values.

The point I was making yesterday was about the scatterplot of P2P versus RGDP growth. The trendline on that graph runs from about 4.5 to about 1.8. With yesterday's graph we do get almost the same range of trend values.

There is no reason to assume that you'll get the same range of trend values on two related graphs. The fact that we do get similar ranges suggests to me that yesterday's graph is significant in regard to economic growth. As I said yesterday, those are the numbers.

// The Excel file.

Saturday, April 16, 2016

Those are the numbers!

The series starts here

You mighta seen this graph before:

Graph #1: Economic Growth is better when the Private/Public Debt Ratio is Low
The trendline runs from 4% annual inflation-adjusted-GDP growth down to 2% annual. Four percent or a little more. Two percent or a little less. Those are the numbers.

Those are the same numbers people use when talking about good and bad economic growth in general in the U.S.

Okay, it stands to reason that they are the same numbers, because the vertical axis shows real growth. The numbers are not made up.

But it's not like the dots only occur in the 2% to 4% window. The dots are all over the place, from more than 8% annual to near 3% below zero. 40% of 'em are above the 4% line. Yet the trend line is right there, in the range we expect growth to be.

It's not simply that this is the range we expect for economic growth. There's more to it than that. In a scatterplot focused on some detail (like the P2P debt ratio) there is no reason to assume you'll get the same range of trend values you get when you look at the data chronologically. The dots could have ended up grouped so that the scatterplot trend goes from 6% to zero, for example. But that didn't happen. Or the trendline could have been flat. But that didn't happen, either.

The trendline we actually got shows that we get the kind of good growth we expect when private debt is only a little more than public debt. It shows we get the kind of bad growth we expect when private debt is a lot more than public debt.

It shows something that gives us the growth we expect.

We're not just looking at economic growth. We're looking at growth as influenced by the level of P2P (the private-to-public debt ratio) and we come up with growth in the range we expect. This tells me that the P2P ratio plays a major role in determining economic growth.

Friday, April 15, 2016

Three samples

The series starts here

Over the last few days we looked at FRED data for the period 1948-2014. And we looked at Historical Statistics data (along with RGDP from MeasuringWorth) for the period 1916-1970. Overall, 1916-2014. Almost a century.

I want to drop the first two years, 1916 and 1917, wartime years that throw off my trendline. So suppose we do that. And then, suppose we take what's left and divide it up into equal parts. Near equal: 1918-1949, 1950-1981, and 1982-2014.

Now I've got three non-overlapping time periods that span near a century in total. For each period, I want to do what I've been doing lately: figure the P2P (Private-to-Public debt) ratio. Make a scatterplot with P2P on the horizontal and RGDP growth on the vertical. And add a trendline, but this time a curved trendline for each period.

I want to put all the data and all the trendlines together on one graph. And I want to compare trendlines.

I expect each period will show higher RGDP growth associated with a lower P2P ratio. // yup, it does.

I expect the scatterplot trend will always show an increase in RGDP growth when P2P is below optimum, a peak at optimum P2P, and decrease when P2P is above optimum. // nope, it doesn't.

What I would like to see is whether the peaks occur together or not. My inclination is to expect that as private debt increases and as financial innovation develops ways to support that debt, we will see the peak shift rightward toward a higher P2P ratio. But that's just a gut feel. // the peaks came out all over the place, with no apparent relation even to the previous graph.

This is why we do graphs. // yup.

I'll go with the same data sources as in the earlier posts -- Historical Statistics and MeasuringWorth for the 1918-1949 period, FRED for the later years.

Graph #1
A little disappointing: It lacks clarity. The blue line peaks early -- at a low P2P, I mean -- but the red line hits bottom at that point. And the red is low again around 4.0 P2P where both blue and green are peaking. So there will be no jumping to conclusions today.

Still, growth does appear to be better at lower levels of P2P. The blue line has an obvious high at around 1.5 P2P, with a weaker high later. The red has a peak above 5% RGDP growth near 3.0 P2P, with a weaker high later. And the green has a peak near 4.0 P2P, with a weaker high later. In each sample there are two highs in RGDP growth, and in each sample the better growth occurs at the lower P2P.

Policy guidance.

// The Excel file.

Thursday, April 14, 2016

"This again?"

Yup, this one again:

The big one
When I first put the trend line on it, I was imitating what I've seen many times. Straight line thru scatterplot. But then I got thinking about it. I wonder what a curved trend line would look like. I was thinking: Maybe it shows a high that suggests the P2P value we'd need to maximize economic growth.

I don't really have a reason for picking a "linear" trendline over one of the curved ones. I picked linear because that's the one I always see. Don't remember many curved trendlines on scatterplots. The only one I can remember is the Phillips curve, and things didn't work out so well for that one.

I've long felt there must be an optimum range for the P2P ratio, one that best promotes economic growth. And a curved trendline might show such a range, where the linear cannot. So I decided to look at some trendlines. Note: I can't tell you anything technical about trendlines. (Maybe you can tell me?)

All these "little" graphs are the same except for the type of trend line they show. Click them to see them bigger, should the need arise.

This first one is the linear, same as I've been using since Monday. It shows a general trend -- the "gist" of the numbers, as I said the other day. Of course, I don't believe for a moment that all those dots in all those spots could ever meld together to produce a perfectly straight trend, except in the world of numbers.
The "exponential" trendline option was not available  for this particular graph.

This little graph shows the "logarithmic" line. Looks similar to the linear line and sits in about the same position --high on the left, low on the right. But this line has a slight sag to it.

Told ya the line shouldn't be perfectly straight!
This one is a second order polynomial trend. Like the logarithmic line, it looks similar to the linear, again higher on the left than on the right. But this line instead of being straight or sagging has a bit of an arch to it.
Third order polynomial. Finally, a trend line with some shape to it! Something of an S-curve. Higher on the left and lower on the right. But this time the ends of the line are not the high and low points. Now that is something I can believe!

The high point of the curve looks to be somewhere between 2.0 and 3.0 on the horizontal axis. So, a private-to-public ratio somewhere around 2.5. Sounds right to me.
Fourth order polynomial. An S-curve, like the previous trendline. A little less curve on the left, a little more on the right. I think these trendlines are overly influenced by the absence of data beyond the endpoints -- as people say of the Hodrick-Prescott calc, and as I suggested recently about starting a dataset in the midst of wartime conditions.

Anyway, the high point of the curve again appears to be between 2 and 3. A policy target?
Fifth order polynomial. The shape is a little more complex now. A little too complex, I think. I don't think you're going to get a high-low-high-low-high-low response from growth by repeatedly increasing the level of private debt relative to public debt. It just doesn't seem reasonable.

The sixth order polynomial looks very much like this one.

I wonder what curve calculation old Bill Phillips used...

Wednesday, April 13, 2016

Reinforcing the P2P:RGDP growth connection

Last couple days we looked at the FRED data for private debt and public debt (the ratio of one t'other) and RGDP growth. When I say "FRED data" you should know it means the numbers only go back to some time around 1950.

With one page from an old edition of the Historical Statistics and a quick download from MeasuringWorth you can take the story back to the 1916-1970 period. So, I did. Here's the ratio of private debt to public debt:

Graph #1: The P2P Ratio (Private Debt per Dollar of Public Debt)
When I saw it I said: Oh yeah, I did look at that before.

I put dots on the line to show the data points that define the line's shape. Notice, right at the start, the data point for 1916 is way high. It's a good inch (on my screen) down to the next data point, the 1917 point. Big drop. Another big drop, not quite so big, between 1917 and 1918. After that, it's soon back to normal.

Those first data points come right in the middle of World War One (1914-1918). It's the winding down of that war that let things get back to normal.

I'm a little uncomfortable using data that starts in the midst of a big change like that. A couple years before 1916, and I don't know where we'd be. So I can't say anything about the first few data points. I'm only comfortable evaluating the years since about 1920, where a new pattern establishes itself.

Anyway, we can take the vertical axis values -- the debt ratio values -- and stretch them out on the horizontal axis of a new graph. On the vertical axis of this new graph we can show the growth rate of inflation-adjusted GDP. Plot the data as a "scatter" and add a trend line to get the gist of it, and this is what you get:

Graph #2: Real Growth and the P2P Ratio, 1916-1970
Well look at that: We got the same exact values on the horizontal axis here -- from zero to sixteen -- that we got on the vertical axis of Graph #1. That's Excel's finesse, not mine. And see that one blue dot way over by itself on the right? That's the data from 1916 on Graph #1, the high point.

Ignore the outlier from 1916 and do the graph again, and it comes out like this:

Graph #3: Real Growth and the P2P Ratio, 1917-1970
With that one dot gone, the others spread out across the plot area. Also the black line -- the linear trend line that Excel calculates for me -- the black line is downward-sloping and not almost perfectly flat, the way it is on Graph #2. Removing that one dot had a big effect on the trend line.

The downward slope of the trend line here is reminiscent of the downward slope on Monday's graph. As on Monday, the trend line tells us that high rates of real GDP growth are associated with low levels of private debt relative to public debt, and low rates of real GDP growth are associated with high levels of private debt relative to public.

Graph #3 runs from 1917 to 1970. Monday's graph runs from 1948 to the most recent annual data, 2014. There is some overlap. Actually, it is the "golden age" that shows up on both graphs. Maybe that influences the result? Maybe it's the golden age that makes the trend line downward sloping? So let me eliminate the overlap. This next graph runs from 1917 to 1948 and leaves off where Monday's graph picks up.

Graph #4: Real Growth and the P2P Ratio, 1917-1948
Still downsloping. Once again, the trend line shows high RGDP growth when private debt is relatively low, and low RGDP growth when private debt is relatively high.

Two graphs. Two separate time periods, covering almost 100 years. And both graphs show the same thing.