Wednesday, September 16, 2015

The Blob

Source: Wikipedia, of course

On mine of 13 September Jim said "I agree that the cost of debt to households (and to business?) appears to be correlated with economic expansion/contraction (but not to the quantity of debt). And it is worth exploring why that correlation exists."

Jazzbumpa quoted Jim, and replied:
Well, here is the correlation.

It looks like a correlation, but I think that is a mirage. Eliminate the 5 extreme points at the top left and the 8 at bottom right - that's 13 out of 141 - and you're left with an amorphous blob in the middle.
An amorphous blob? At first glance, perhaps.

I replied:
Jazz, connect the dots by turning on the line that connects them. Your amorphous blob begins to take on definition. I see mostly downsloping (left-to-right) lines, suggesting that higher cost-of-debt is associated with lower GDP growth, and lower cost-of-debt with higher growth.

These downsloping lines appear to be flatter when the cost of debt is lower, and more sloping when the cost of debt is higher.

Some of the lines are upsloping (left-to-right). I suggest that these show phase changes, times when people are learning to deal with a permanently higher level of debt cost, for example. We saw something comparable in Noah Smith's Phillips Curve graph a few years back.

Jim replied to Jazzbumpa as well:
If you were following the discussion: It started with the ratio of private debt to all debt. That ratio drops on every single recession since 1950 for a few years and then slowly climbs upward till it hits the next recession and then repeats. The debt service graph has similar characteristics - particularly since 1990.

Jim sees a clear relation between the debt ratio and economic performance, and a similar relation between debt service and economic performance. Jazzbumpa shows an amorphous blob, and sees an amorphous blob. Maybe he is challenging us to make a better argument.

I'll take that challenge.


I downloaded the FRED data for Jazz's graph, along with quarterly recession indicators in case I need that. Loaded up the data into Excel and made a scatterplot comparable to the one Jazz did at FRED:

Graph #2: "mostly downsloping (left-to-right) lines"
I connected the dots, of course.

I suppose you could find a high-density region of blue dots around 5% NGDP growth, like this:

Graph #3
Or perhaps like this:

Graph #4
Okay. But if you don't add lines to the graph, if you just look at the lines that are on the graph, you don't see a lot of lines showing a steep slope up and to the right:

Graph #5
The lines that connect the dots show the year-by-year pattern. Most of those lines seem to run either flat or high on the left and low on the right. Yes, there are a large number of dots clustered around the 5% annual growth number. But that just means the most common NGDP growth rate is in the neighborhood of five percent annual.

The thin red lines on Graph #5 do not show a lot of activity in the steep upward direction indicated by the thick red line on Graph #4. That tells me that even though most of the annual numbers end up somewhere near 5%, we cannot say that the trend is upward and to the right.

The apparent clustering of dots in the neighborhood of 5% annual GDP growth allows us to imagine a trend that is upward and to the right. But that clustering is unrelated to household debt service payments as a percent of disposable personal income. There are other factors -- factors, real or expectational, but not shown on the chart -- that favor NGDP growth in the neighborhood of 5%. These factors are the source of the clustering. The clustering and the fat red lines on Graphs #3 and #4 are not relevant to the analysis of Graph #5.


These thoughts may have implications for the time-shifting Phillips Curve.


The Arthurian said...

Looking at Jazzbumpa's graph with lines, and without dots, the lines are, again, either downsloping (high on the left, low on the right) or horizontal (flat). There is no great preponderance of upsloping (low left, high right) lines from which to generate a true upsloping trend.

In order to get from a low downsloping line to a high downsloping line, you hop on a horizontal and go right, then make a left onto the higher line.

In other words: first, GDP growth increases while debt service payments are stable (i.e. a horizontal line), and then GDP growth decreases while debt service payments rise.

The false (fat, red) trend lines shown on graphs #3 and #4 -- lines that show GDP growth increasing as household debt service increases -- those lines are the mirage.

I say again, this analysis has implications for the time-shifting Phillips curve.

Jazzbumpa said...

I can't find the way in FRED to toggle the lines and dots on and off.

How do you do that?


The Arthurian said...

Hey Jazz. In the EDIT DATA SERIES 1 window, the LINE WIDTH is set to zero. Increase the line width value, and the line shows up right away.

I sent you an email just as you were sending me this note!