Earlier this week, I had a vision of how analog circuit design theory could have provided some useful insights into how to avoid bubble markets. I haven't found too much on this from googling, although this paper looks pretty close from the abstract (I don't have a subscription so can't verify whether they're actually thinking the same way).

The field that physicists and applied mathematicians call Control and Dynamical Systems has basically developed to aid engineers in building systems that use feedback to stabilize the state of any system that goes through cycles. There are lots of things that machines (like the stealth fighter) do that humans would not be able to do because of the magic of feedback-stabilized oscillation.

The implications that this has for business cycles in public and private markets is so obvious that I'm quite certain that somebody already knows how to do this. Alas, they're probably making boat loads of money on it as we speak. Another problem worth solving is how to give incentives to such people to share their insights through something other than bidding or asking price. (Actually, granting patents on financial engineering innovations isn't a bad way to do this. But a two-decade term would be overkill in most cases.)

In the interest of aiding translation between physicists and economists (and hopefully help avoid yet another major bubble in our financial markets), I'm going to identify the simplifying assumptions that I think are most useful in modeling markets with control theory, and then offer a few extremely crude observations about the potential benefits of applying this theory. I'll use electrical engineering terminology to show the relationship between the variables.

* Price can be modeled as a two-dimensional current signal in time and demand P = P(t, d)

* Price changes will be amplified by bundling supply and demand (e.g., through securitisation) so that P = A*P where A is either less than 1 (supply bundling) or greater than 1 (demand bundling) depending on whether buyers or sellers are being aggregated by a particular security.

* Transactions cost can be modeled as resistance (and Price * Transactions Cost will approximate Demand)

* External money supply can be modeled as capacitance (which will introduce a phase lag into price)

* Liquidity can be modeled as inductance (which also introduces a phase lag into the price)

* Demand can be modeled as voltage

For purposes of this model, I'm assuming that the external money supply obeys some predictable rules (like Taylor's Rules). The system is going to be extremely indeterminate if the external money supply doesn't behave in predictable ways. (There's a useful result right there! Let's implement Taylor's Rules.)

From my very crude understanding of theory, this kind of model would permit the following predictions to be worked out from the nonlinear differential equations that govern such a system:

* Systems that include both inductance and capacitance (i.e., external money supplies and liquidity) are going to oscillate at a characteristic frequency. That frequency is the "resonance peak," and it's amplitude will vary depending on the amplifiers. If they're too strong, the circuit blows up.

* Systems that include large inductance but low capacitance (i.e., liquidity but no external money supply) are going to decay exponentially to zero price

* Systems that include mostly positive feedback (i.e., amplify demand without inverting or phase shifting the input signal) are going to increase exponentially (until they blow up). (This was Monday's insight.)

* Systems that are tuned to include just the right amount of positive and negative feedback are going to oscillate stably within a limit cycle for long-periods of time. In fact, such systems will "magically" self-correct price to demand. Actually, this is most markets, most of the time. We just haven't been paying enough attention to the bigger picture.

Somebody out there must have done some graduate school research on this topic. We should send them to Bernanke and hope for the best.

UPDATE: Thanks Google. Here's Steve Fairfax of MTechnology making a similar point. And here's Donald D. Hester and D.L. Brito making a similar point... in 1974! Do we ever learn? (Don't answer that.)

UPDATE2: Here's a book on "Economic Dynamics" with a whole section working out a version of control theory applied to a more complicated model.

UPDATE3: I've worked out a numerical example with estimates for the subprime mortgage market here.

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