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.