Saturday, 9 May 2009

Control theory and capital

The beginnings of control theory can be summarised as 'nail it in the right place'. Suppose there's a plank over a barrel. You can keep the plank level by putting a weight in just the right place, so that it balances.

The problem with this is that any perturbation will cause the plank to swing away from the level. A gust of wind might even do it: the equilibrium is unstable. Therefore control theory 101 would suggest that you move the weight dynamically to keep the plank balanced. If one end swings up, move the weight slightly that way until it swings back.

Over the years, a lot has been discovered about how to control unstable objects moving in unpredictable environments. Modern fighter aircrafts are in some ways a triumph of control theory: without the computers which control their flight surfaces, they would fall out of the sky. And what the computers do is determined by control theory.

One of the many reasons that the current regulatory capital regime is pants (not to put too fine a point on it) is that it is stuck with static control. That is, think of a number, and that's the amount of capital that you need. In reality, the regime needs to be dynamic: the anticyclical capital of earlier discussions is one piece of this puzzle. What struck me as I walking home from a lecture last night (one which touched in passing on control theory) is that we do not even have the right inputs to develop a control theory of bank capital. That is, we don't really know what the equivalent of the angle of the plank (or the speed, pitch, yaw and so on of the fighter) is. One can think of some things that it might make sense to monitor, like credit spreads or the availability of interbank liquidity, but so far as I am aware, there has been no systematic study which discusses the indicators of health of the banking system, let alone identifies how they respond to changes in regulation. That would be the basis of a serious control theory of banking.

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Blogger Dave said...

It's great to see an economist who understands control engineering (or are you a control engineer who understands economics?).

Maybe with this background you could turn your mind to a question that has long bothered me. Given the lags and uncertainty involved, is it actually possible to control an economy using monetary policy?

1:21 am  
Blogger David Murphy said...

It depends what you mean by control. Sorry to be Delphic - let me try to explain.

In the standard quadratic control problem, lags introduce errors. If the system is subject to random influences, and you can only correct some time later, the error distribution is Gaussian with width proportional to the lag. The monetary policy problem is at least as bad as this, which is one reason why we have an inflation band 1-3% rather than a target.

Much worse is the fact that the impulse function is variable and unknown - we don't know what a given tightening or loosening will do exactly. This makes thing worse too, especially as loosening is bounded at zero (a problem at the moment - hence QE, which really is new territory for central banks).

I like to think about monetary policy as a control problem where the relaxation time is longer than the time between random external influences. You never reach equilibrium. That doesn't mean control is useless: just that you have to settle for moderating the envelope of behaviours, not precise control, and you might get it horribly wrong sometmes.

7:19 am  

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