Central Banks as Control Systems or Can We Replace Ben Bernanke with a Computer?

Being in a technical field I encounter control systems all the time.  But that is because everyone encounters control systems all the time.  They make elevators stop at the right floor in a comfortable fashion, your car humming along efficiently and presumably keeps your oven at the specified temperature, though they never seem to actually be correct.  You are a control system when you adjust your shower water knob for maximum pleasure.  In short, modern life would suck without control systems.

For those unfamiliar with control systems, the basic principle is you measure a variable and apply some sort of forcing to the system based on what you want the variable to be.  It is really that simple.  The standard is a PID controller or proportional-integral-derivative controller.  You have a process variable which you measure and you compare that to your desired setpoint to create an error value.  The proportional part of the controller applies a force, wait for it, proportional to the error value.  Next up the integral part integrates the error over a period of time and applies a force proportional to that.  Lastly, the derivative part looks at how quickly the error changes and forces according to that.  By far the most important is the P part, but I is also important since with just P you will only asymptotically reach the setpoint (the dreaded droop).  D is great for increasing the speed of you control system, but is also sensitive to noise and is a pain to set.

Now as the title implied I was going to tie this into central banks.  Central banks look at some set of economic variables and then nudge the economy with various tools, most importantly the open market operation.  The process variable is in most places inflation and in the U.S. its setpoint is 2%.  In fact economics has a simple rule called the Taylor rule that provides guidelines on how to adjust interest rates to maintain desired inflation.  In fact if you look at it is basically a P controller where a_pi is the proportional gain on an error signal generated by the difference in desired and current inflation.

Great, so central banks have a P controller and all is well, right?  Well, no.  As I said earlier without an I term you will always undershoot your setpoint.  Evidence of that is quite explicit in our current predicament.  We still have a weak economy six years after the financial crisis and the Fed is currently beginning to taper its bond purchases.  This is a clear sign of a P-only droop.  For maximum speed in arriving at the setpoint you actually want to overshoot.  In contrast, central banks seem to regard their inflation targets as ceilings, yet there is no argument for being afraid of breaching the inflation target.  On the other hand, there is an argument for returning the economy to normal as quickly as possible.  Every year of high unemployment is another year of millions of people suffering.

The other problem is that the Taylor Rule targets two variables: inflation and the output gap.  Now these have a “divine coincidence” in some economic models, but in the real world it is likely that you cannot hit an inflation target and close the output gap simultaneously.  Thus, one should switch to targeting nominal GDP growth which is something of a combination of the two.  This has worked quite well under Stanley Fischer at the Israeli central bank and there are some detailed theoretical arguments for why it is better than an inflation target.  In my mind, it just makes sense to target the growth of the economy than some ancillary variable like inflation.  Anyways this makes designing a control system a bit easier.

If I were designing a rule then I would make an error signal that is the difference in nominal GDP and the target nominal GDP (lets say 6%).  Then we would determine the amount of our open market operations by an amount proportional to that error signal and proportional to the error signal added up over lets say the last two years.  All you need to do is set the gain coefficients for the two terms and then you don’t even need a board to determine monetary policy, it’s just an algorithm.  Ben Bernanke is obsolete.

The nice thing about a PID controller is that you don’t need to know anything about the system you are controlling.  You just need to look at how it reacts to your forcing.  However, we have an entire discipline called macroeconomics that attempts to model the economy and with that knowledge we could make our control system more sophisticated.  Now feedforward is possible.  Or we could just add a differential term that responds to the severity of the shock.  It makes relying on the simple P controller of the Taylor Rule look monumentally stupid when easy modifications abound.

Ideally, the people in charge of the central bank are already a control system.  Yet an analysis showed that most central bank operations are described fairly well by just the Taylor Rule.  Also, history shows that humans are really bad at the job.  They either don’t do enough (Great Depression, Great Recession) or don’t put on the brakes (70s inflation in the U.S.).  Some of this is political pressure, some of this is that most central bankers are drawn from a culture that is deathly afraid of any bit of inflation for reasons they can never articulate cogently.  Therefore I propose that we just automate it.  Publish the coefficients so everyone knows what will happen.  This actually implements something the Krugman/DeLong axis of economists have been shouting about.  Namely, that in a liquidity trap we need to credibly commit to higher inflation.  The integral term basically does that.  It follows the engineering maxim of “if it doesn’t work, apply more force.”  That is, if the economy is consistently underperforming it just keeps shoveling more and more money at the problem.  However, I suspect like Switzerland when it fixed its exchange rate briefly, the credible commitment to a policy anchors expectations such that you don’t actually need to do much.  I am not saying we wont have recessions (or bubbles) but I suspect they will be much shallower just because people know that our control system central bank will do whatever it takes to bring the economy back.

As far as I can tell, nobody has made this analogy between central banks and control systems.  Furthermore, I don’t think anyone has proposed removing human agency from how they operate.  Well I just did and I think it is the future of central banking.

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One Response to Central Banks as Control Systems or Can We Replace Ben Bernanke with a Computer?

  1. Anon says:

    If you can figure out an optimal method create a cryptocurrency that does this. Also I believe both Alan Greenspan and Zhou Xiaochuan (PBoC chair) have proposed algorithmic central banking.

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