Saturday, October 11, 2014

The Ridges on the Rocks

Maybe you need an accordion axis. Or maybe the lag amounts mean something.

There is a story I like very much, told by Lionel Ruby in "How the Scientist Thinks":
Darwin and a fellow scientist were searching for fossils in the north of England. They were not aware of the glacial theory at the time. Years later Darwin revisited the area, and he was now astonished to discover how clearly marked were the glacial ridges on the rocks. He had not noticed them on his earlier visit because he was not looking for them.... Darwin was able to appreciate the glacial markings only after he became aware of the glacial theory.

Sure: If the glacial theory was wrong, knowing about it and looking for it would still have led some people to see it in the rocks. But that's the trade-off, isn't it. If the glacial theory is right, and you don't know about it, you may not see it even if it is clearly marked in the rocks. Even if you are Darwin.

Me? I'm just lookin at the economy.

From the interactive experiment I captured some images with different lag values. On each image I highlighted in yellow the the part where I think the two graphs match. Some are obvious. Some may be a stretch. It's all by eye anyway; this is conceptual economics. But hey, it can't be any worse than the stuff that passes for "mainstream".

Slide your mouse back and forth across the Animation Bar below the graph:

Lagged Effects of Base Money: an Animation

Zero Year  Lag Two Year  Lag Four Year  Lag Five Year  Lag Seven Year  Lag Six
Year  Lag 
Five Year  Lag 

Now I want to show you the ridges in the rocks. I want to show you what I see.

First, notice that the red line does not move when you drag the mouse across the Animation Bar. The red line is the same in every frame because inflation is a resultant and because the history of inflation is what it is. As your eyes pass over the red line from left to right, you are simulating the passage of time.

Second, notice that the yellow highlight moves from left to right as you drag your mouse from left to right across the Animation Bar. The yellow highlight directs your focus to "similarities" between the red and black plot lines on the graph. The similarities are highlighted left to right because I tend to read graphs from left to right, again simulating the passage of time.

To my mind, the similarities offer a way to measure lag: Slide the Base Money graph over the Inflation graph until you find similarity. Then observe the distance you moved the graph. On our horizontal axis, that distance is a measure of time. It is the time it takes for the pattern of the one graph to show up on the other. We are measuring lag.

Third, notice that the black plot line, the Base Money plot, moves as you drag your mouse from left to right across the Animation Bar. At each step, the black line is offset a number of years from chronological time; this offset is the lag.

Granted it's all done by eye, and the annual steps are large and ungainly. Still, we are only attempting to observe similarities between two data sets -- and this is no more than common practice. What's odd is that the similarities show themselves separated by "large and variable" lags.

In order to see the similarities we need to develop an "accordion axis". For if you observe the movement of the black line as you move the mouse across the Animation Bar, you will notice that the black line moves first from left to right and then from right to left. The "similarities" depend at the start on an increasing lag, and, by the end, on a decreasing lag.

I am arguing that an increasing lag is associated with a slowing economy and that a decreasing lag is associated with a recovering economy. I am preparing to argue that the size of the lag is proportional to the severity of the economic slowdown.

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