Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Thursday, October 6, 2011

Wanted: more nuanced economic hammers

A little over a year ago we were treated to this article, suggesting that the Wise, All-Knowing Bearded One would bring us to a land of low unemployment via the harsh medicine of low interest rates. Now it's true that The World Complex has already hit this particular piece of low-hanging fruit, but I thought it worth a look to review how the plan is unfolding.

Yes, yes, we've seen this before. How do we explain what went wrong?

Askari and Krichene (in the paper at top) report that the US Fed reduced interest rates in order to preserve employment. Assuming this is a correct assessment of the Fed policy, we need to consider why it does not appear to have worked.

The alarming picture above appears to be a system displaying the property of multistability. Multistability is a concept related to that of equilibrium--except that unlike simple systems with only one equilibrium point, multistable systems have more than one (some authors use the term bistable to describe systems with two equilibria, and multistable for three or more. We shall use multistable to describe any system with more than one equilibrium state).

Multistability is a property of a system, which is neither completely stable nor unstable, but shifts from one stable state to another, at regular or irregular intervals. A short search for systems that display multistability yields living systems, neural networks, some control systems, and global climate subsystems. To this list I would add the unemployment/real-interest-rate system (and stock prices--and commodity prices--and the unemployment/money-creation system--and probably numerous other economic subsystems).

When you have a system with more than one equilibria--as in the unemployment rate/real-interest-rate system illustrated above, your ability to control which equilibrium you enter is limited. For instance both equilibria in the graph at top are characterized by low real interest rates. So how do we make sure the economy evolves towards the equilibrium with low unemployment, rather than the one with high unemployment?

A characteristic of multistable systems is memory. The equilibrium occupied at any particular time is dependent on the entire past history of the system. This makes control a tricky matter.

Are economists aware of the possibility of multistability? The Fed policy described above would suggest no, but the truth may be more nuanced. From a mathematical standpoint, it is very difficult to create a system of equations to describe a system with multistability. It is more likely that the equations will describe a system with a single equilibrium. If this system is used to inform policy, then that policy will be of the simplistic "press button A, bell B rings" type.

Perhaps economists are unaware of multistability. Perhaps they are aware of multistability but are unable to account for it through systems of equations and so use 'fudge factors' to explain why the equilibrium point moves around. Or perhaps they are fully aware of it and can explain it through their equations, but these explanations are so complex that no trace of them ever appears in the public record of their activities.

In any event, their policy, as reported, does not appear to be having the desired effect. Perhaps it is time to use a tool more delicate than a hammer. If a solution isn't found, the US may become New Europe.


  1. Hey I just came across your blog today and it seems really interesting. Where does all this phase space and multistability stuff come from and where can I learn more about it?

  2. I have tried to produce a somewhat accessible approach to phase space in the How Life Imitates the Stock Market series






    But to a large extent I did this by sparing you much of the theory.

    A more formal treatment starts here:


    For myself, I learned the basics from Abarbanel's book:


    I would add that the behaviour of the systems in I have been highlighting on the blog are different from the simple chaos that is normally studied by these approaches.