The question I would like to address herein and in posts going forward pertains to the nature of the world. This interest is not purely academic, for in our increasingly authoritarian world, policies are set in accordance with a picture of the world as imagined by TPTB. If that picture is incorrect, the policies will not have the desired effect.

The principal paradigm of the ages up to now has been that life is linear. We have come to recognize that this is not the case, however the means to study the nonlinearities of natural and human systems are poorly developed. This blog is about understanding data from nonlinear systems.

The major technique used herein is the state space projection. This is just a graph in which one variable is plotted against another, and instead of drawing the best-fit line through all the points, we trace a trajectory through the points in sequence. Thus the graph may be understood as a representation of the evolution through time of the system.

In particular we will use two-dimensional state space diagrams (also known as phase space diagrams), not because they are the best to work with, but because they are the easiest to display on your screen and I am presently very limited in my choice of 3d plotting software.

Let us consider U.S. unemployment. We will even use the official figures.

Unemployment comes from the BLS site. CPI also comes from BLS (but a different page) and interest rates from the Fed.

We can plot any of these variables in isolation, but things get very interesting when we plot unemployment vs. our calculated real interest rate (the difference between the 3-month treasury interest rate and the 3-month average of the annualized monthly rate of change of CPI). I used a 3-month moving average for CPI to smooth it a little.

Unemployment rate vs real interest rate

We interpret these sort of figures by trying to develop a simple picture of the dynamics. Common behaviour of such systems includes linear growth (which might be a straight line starting at one area of the graph and moving away in any direction), simple chaos (something like a Lorenz “butterfly” diagram), or the system may show some form of multistability, and have more than one equilibrium state (although only one equilibrium is in effect at any particular time).

A multistable system will be characterized by the data clustered in regions of the graph, with rapid evolution from one such region to another. In our graph above, there appear to be two such regions. We may call these attractors, but a better formal name might be “Lyapunov-stable areas” or LSA for short.

In the diagram above, we see that from 2001 to about mid-2008, the unemployment rate was generally below 6%. The burst of deflation we experienced in late 2008 popped the real interest rate, but since they have been slammed back down, we find ourselves in a new LSA with unemployment rates generally >9% (and those are the official numbers–the real numbers are worse!).

What does multistability imply? It means that the rules governing the system are time-dependent. When the system is in one equilibrium state, it is governed by one set of rules. When the system state changes, and the system evolves rapidly until it settles down in a new state (a different LSA), where it is governed by different rules.

Monetary policy appears to be designed for a world in which such systems do not exist. For instance, it is commonly believed that lowering interest rates will result in a lower unemployment rate. Our inspection of the graph above suggests that this has not been the case for nearly four years. In 2008 the unemployment rate-real interest rate system suddenly changed states, and is now in one where apparently low real interest rates foster high unemployment rates.

Note that we cannot be sure why the system changed states. I have a hypothesis I would like to propose. Under the “ordinary” condition, when interest rates are close to what the market would demand, borrowed money tends to be used for largely productive purposes, as only productive ventures will allow the interest to be carried until the loan in repaid. If, on the other hand, interest rates fall far below the normal market rate, some participants may elect to gamble their loans on our increasingly casino-like markets until they win big. If they lose, they can borrow more. Eventually they win, and can repay the loans. This is much less risky than building a factory that makes refrigerators. The entire market changes its preference to unproductive activities. Getting that back will be tough.

This explanation is not interpreted from the above graph. It is merely consistent with it. We have no way of knowing if it is correct.

Future postings will include more exposition on the topic of dynamic systems.

 

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