Sunday, August 10, 2014

Here We Go Loopty Loo

The following post was mostly written back in April, but not finished till now.

A look at loops. This will be another of those continuing investigations, like my recurring look at the Hodrick-Prescott calculation and my recurring look at the "Christensen fit" calculation.

This time we begin with Interpreting Deviations from Okun’s Law by Mary C. Daly, John Fernald, Òscar Jordà, and Fernanda Nechio. I looked at it briefly last April. Let me open by presenting the significance of the loops that appear on their graph, as Daly, Fernald, Jordà, and Nechio see it:
Figure 1 shows the relation between GDP growth per person and the change in the unemployment rate. The gray squares show all of the points, using current data as of December 2013. The solid black line reflects the average...

 Figure 1: Real-time and revised loops in Okun’s relationship
Using current data, the solid blue line traces the path of per capita output growth and changes in the unemployment rate from the fourth quarter of 2007 through the third quarter of 2013. As the arrows show, over time these changes result in a clear counterclockwise loop. That is, when the unemployment rate was rising, GDP growth was lower than the average relationship would have predicted. When the unemployment rate was falling, GDP growth was above the average. This path for Okun’s law is an enduring feature of the U.S. business cycle.

Whether we analyze Okun’s law with real-time or revised data, countercyclical loops tracing the relationship over time are a common feature. These loops reveal an underlying characteristic of the U.S. business cycle. Changes in employment—and likewise unemployment—lag behind changes in GDP.

Changes in employment lag behind changes in GDP; this is an enduring feature of the U.S. business cycle.

That just strikes me as massively important. Best of all, their analysis arises directly from the data. From their graph. Their solid blue line makes "a clear counterclockwise loop." It shows GDP growth less than Okun's law predicts in the recession phase of the cycle, and more than Okun's law predicts in the growth phase.

This pattern of offsets from the average also shows up in other business cycles. It is an enduring feature of the business cycle, the authors write.

The article is an examination of the validity of Okun's law. But for me it is an example that clarifies the significance of the loops that appear on many graphs, not just graphs of Okun's law. In the article they do something I never did -- they put little arrows on the graph to indicate the path of the loop over time. Without the arrows, the loop could be clockwise. Turns out, it's counterclockwise. Knowing that, they can say things like "When the unemployment rate was falling, GDP growth was above the average." That's useful information.

The article provides a pretty good description of the data they used for their graph. I want to see if I can duplicate their graph -- not today, but pretty soon. And if I can duplicate it, then I want to see if I can duplicate their results. I want to go through the motions and see if it all makes sense to me.

After it makes good sense, after I'm comfortable thinking in terms of these loops, I want to use their method to examine things other than GDP and employment. Those are both outcome goals: We want growing GDP and rising employment. I want to compare outputs to inputs. Specifically, I want to compare the output goal GDP to input like debt levels. It would be interesting to confirm that GDP grows above average when debt is relatively low but increasing rapidly, and that GDP growth is below average otherwise.

I might also be able to use this tool to evaluate economic performance over time, as debt levels gradually rise.

In the meanwhile, fiddle with Graph #2. Below the graph, the hover-bar contains the values 00, 01, 02, ... up to 22, representing 23 images that highlight 23 different subsets of the full data set. Move your mouse over the hover-bar to highlight different subsets. Note how often Real GDP responds to changes in debt by forming a loop similar to the one described for Okun's law.

The start- and end-date of the highlighted subset appear on the graph, and also the slope value of the black line. Adjust your screen display, if you have to, so you can see the whole graph image plus the hover-bar.
 Graph #2: RGDP Growth versus the Change in "Total Debt relative to NGDP
 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2

The steeper the slope of the black line, the more growth we got.

// Graph #2 originally appeared in Too Much?

Jazzbumpa said...

I've done a lot of data slicing and dicing to try to understand what is happening in different time periods.

Here is an example.

http://angrybearblog.com/2014/03/equity-extraction-and-personal-consumption-expenditures.html

I try to have some set of reasons for the choices of intervals.

What protocol did you use?

Cheers!
JzB

The Arthurian said...

Hey Jazz.
For Graph #2 there I used minimums in the debt-to-gdp ratio as start & stop points. Re-displaying it for this post, I got thinking about using "official" recession-start dates as break points. Or official recession-end dates maybe...

I think the tool is most definitely useful but it could be improved. I like the idea of indicating loop direction.

Actually, regarding start-and-stop points: I have one or two columns in the Excel sheet that if I put an X in a cell, that row's data becomes a start or stop point. But I have not looked at it for a while.
The link is in my old April post, and the XLS file contains VBA code.

Jazzbumpa said...

Several of those subsets look loopish. New way of thinking about things.

By output do you mean GDP or some other measure? I want to be sure I understand this.

You might also esplore picking output minima as your end points.

Cheers!
JzB

The Arthurian said...

Jazz: "... loopish. New way of thinking about things."

Yes, exactly.

By 'output' I usually mean GDP or maybe inflation-adjusted GDP.

But in the post I wrote: "I want to compare outputs to inputs. Specifically, I want to compare the output goal GDP to input like debt levels."

My uses of the word "output" there was to mean "resultant" as when you wrote
Beckworth and Sumner are smart guys, but their reasoning is flawed. They define monetary policy not in terms of either money or policy, but as GDP growth, which is a resultant...

The Arthurian said...

I should have said it this way:

"I want to compare outcomes to inputs. Specifically, I want to compare the outcome GDP to input like debt levels."