## 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