Wednesday, July 14, 2010

Out Of Control

Analog Designer and control engineer Bob Pease and I have had a discussion or two via e-mail about control theory and control engineering. So when I came across a bit by him in a back issue of Electronic Design on how control control theory relates to how the Federal Reserve ought to control the money supply, I was interested. Here is what Bob had to say about the Fed:

FINANCIAL FLOOBYDUST * Switching gears, Alan Greenspan has admitted that he screwed up and had a bad model for the economy. He claims he misunderstood what was going to happen. What did Spice suggest for him to do? I coulda told you that Greenspan was not doing a good job on his PID controller.

He waited too long to start decreasing the interest rates, and then he decreased them too slowly. I noticed that at the time! Then, by leaving the interest rate at 1% for too long, he got the ARMs to start out too low. And then when the rates went up, the subprime mortgage holders got whip-sawed.

This is exactly how you make a limit-cycle oscillator! In other words, Mr. Greenspan did not have enough D (derivative) term in his controller, and he failed to anticipate new problems. And he had too much gain in the I (integral) path. I can do this any day, on my bench, but I don’t destroy a nation’s economy.

No, I don’t want to take over Greenspan’s job. I don’t want that job. But I could still do it less badly.
Notes: SPICE is an electronic circuit simulator. And you might like a general overview of PID controllers. For reasons I'm not going to go into here this is my favorite mathematical model of a PID controller.

In private conversations with friends who are interested in economics I have maintained for years that economists are ignorant of control theory, treat all economics problems as if they are a calculus problem that can be solved in the limit, and ignore the short term dynamics of our economic plant. Which is to say they are looking for equilibriums rather than dynamisms. I read an economics paper once that said that if you follow the right path - not too much of this or too little of that - you will get optimum results. Assuming of course that the right path can be known in advance. But what if you don't know the right path in advance? Well then you are in need of a control system tuned to the economy that will tell you when and how much to correct your inputs to give a close enough approximation to the ideal path. And if your control system is not properly tuned? Well it will wreck the economy.

We do have a control system and it is not properly tuned. Welcome to the current wreck.

You can read more of my thoughts about control theory and economics at this posts: Economics Made Simple

Here are a few pages of books on Control Theory and Economics.So it is not as if there has been no thought about the problem before. The problem in my estimation is that these books have not influenced practicing economists much. Pity. For all of us.

Cross Posted at Classical Values


Neil said...

Sadly, control theory breaks down pretty bad when you've got multiple cross-coupled loops. Which the economy certainly is. You've got to decouple things before you can really guarantee stability in the presence of parameter variations.

However, getting economists to think seriously about path dependency rather than equilibria would be a good start.

M. Simon said...

Even control theory breaks down when the rate of adjustment required exceeds the capacity of the plant. You get "wind up" or in economic terms latent demand.

And to a certain extent if there are enough cross coupled loops you can put in a "black box" they can be treated to a certain extent as an entity.

To get a "better" plant you have to shorten the cycle time - the time from an "error" (demand change) input until the plant starts to respond.

Of course as you point out deciding what the controlled parameters ought to be is critical. Then you have to constantly monitor the plant for changes in input to output coupling. i.e. changing response function.

Neil said...

Yes, it's probably true that "controlling" the economy is a case of trying to control a massive plant with a tiny actuator. Integrator gains must be small, and the overall controller gain can't be very big anyway.

But even if you could use an actuator that can dominate one or two inputs, it's a multiple-input, multiple-output system. And all the inputs and outputs are cross-coupled. If you try to control each input independently, you wind up with an n-integrator oscillator. In other words, because each input affects multiple outputs (each of which affects the error term of a controller), you have multiple paths through the plant to each individual controller, and each of those paths contains at least one integrator.

Draw it out in a block diagram with a two-input, two-output cross-coupled system, with a controller on each input, and you'll see what I mean. Input A summed with output B goes to an integrator goes to output A, Input B summed with output A goes to an integrator, and a feedback controller on output A and output B. Each controller ends up trying to control a 4-integrator system in addition to the direct feedback path!

M. Simon said...

Yes. But we could not do economic analysis at all if there were no general trends.

We could not control a chemical plant if we had to take into account the behavior of every molecule. So we take advantage of the statistical properties of the system. Of course those have to be monitored to detect changes in the I/O function. And of course you detune to some extent so that small shifts in the I/O function do not dive the plant into instability.

RavingDave said...

Bob Pease is awesome! I read his "Pease Porridge" column every month.

Apart from that, It has long been my observation that a lot of badly performing human dynamics could be corrected with negative feedback. One of my favorite examples is excluding non-taxpayers from the voting franchise, the way it worked in practice for most of this nation's existence.

RavingDave said...

When troubleshooting a defective control system, you need to break the feedback loop, or force it to some specific value so you can see what stage is malfunctioning.

Since that is hardly practical in terms of Society and it's finances, I think the only available option is to increase the negative feedback.

I have long believed that one of the major problems in this nation's society and finances is the removal of feedback mechanisms that would have prevented much of the mess we are now dealing with.

Some negative feedback ideas:
Term Limits for congressmen. Make people pay their Federal taxes out of their Paychecks instead of automatically deducting it so that they aren't even aware of it. Make voting day April 15th. Get the Unions out of Government. Make it HARD to register to vote. Etc.

LarryD said...

Eliminate the special pension plans for Congress, etc.

Make them use the 457 (or whatever the government equiv of a 401(k) is), so they have skin in the game.

In the same vein, prohibit Congress from investing overseas, make them invest their money in this country.

Going back to economists, I think it would be salutary if early economy courses had mass labs where students played different roles in a mock economy. It might help students realize that behind the abstractions of Market and Economy are large numbers of people, pursuing their own goals. Who will be trying to adapt to, if not out smart, the system and any managers.