In all that's been written about Jeremy Clarkson, nobody has pointed out that there's a close analogy between him and central banks.

Mr Clarkson's critics seem to believe that he should have followed the rule "don't punch people." They are wrong. If he'd obeyed this rule, he would not have twatted Piers Morgan. There would therefore have been a sub-optimal amount of twatting.

Equally, however, Mr Clarkson should not be free to hit whomsoever he wishes. This would create the danger that he would sometime hit the wrong person, and it would generate uncertainty among his acquaintances.

We have exactly the same problem with central banks. If these follow a rule* - such as "keep inflation at 2%" - there will sometimes be a suboptimal level of stimulus. For example, if commodity prices surge or if a financial crisis doesn't immediately reduce inflation, a strict inflation-targeting central bank would not loosen policy sufficiently.

Equally, though, giving the Bank full freedom to do what it wants would create uncertainty. In the classic Kydland & Prescott paper (pdf), this leads to unnecessarily high inflation.

What we have in both cases is a debate about rules versus discretion. Rules such as "don't punch people" or "target 2% inflation" can sometimes be suboptimal. But discretion also has costs.

One possible solution to this is what Ben Bernanke called "constrained discretion." This is what the Bank of England has. Its remit (pdf) says:

The actual inflation rate will on occasion depart from its target as a result of shocks and disturbances...Attempts to keep inflation at the inflation target in these circumstances may cause undesirable volatility in output due to the short-term trade-offs involved, and the Monetary Policy Committee may therefore wish to allow inflation to deviate from the target temporarily.

The hope is that this gives us the best of both worlds. The 2% target anchors expectations and so gives us certainty. But allowing the Bank to respond to shocks gives us more discretion to stimulate growth when necessary.

Again, there's an analogy with Clarkson. A better rule than "don't punch anyone" would be: "punch nobody but we'll allow some exceptions to this."

Herein, though, lies the problem. We cannot precisely specify what these exceptions might be. In the case of central banks, Daniel Thornton has explained why:

The economy is too complex to be summarized by a single rule. Economies are constantly changing in ways difficult to explain after the fact and nearly impossible to predict. Consequently, policymakers seem destined to rely on discretion rather than rules.

Much the same is true in Clarkson's case. We cannot say in advance whom he should be permitted to hit. Piers Morgan, Robbie Savage and Nigel Farage are obviously permissible targets, but there are many potential others some of which have yet to achieve public prominence.

In both cases, therefore, it seems that discretion is best.

But this too has a potentially heavy cost. As Adam Gurri says, people are "terrible" at using their judgment. Again, this is true both for central banks and Clarkson. The ECB seems to have delayed QE until the economy is recovering, just as Clarkson (allegedly) mistakenly punched an innocent man - or as innocent a one as a BBC producer can be.

I suspect one solution to this might be to have form of level targeting of the sort advocated by Scott Sumner:

If you target NGDP to grow at 5% a year, and it grows 4% one year, you shoot for 6% the next.

In effect, if (or rather when) you make an error once, you must aim for the offsetting error later. The analogy for Clarkson would be that, having hit an innocent man, he must err on the side of passivity in future. Sure, this would entail the significant cost of not hitting Piers Morgan again. Luckily, though, what's true for Clarkson should also be true for everyone, so there should be an optimal amount of twatting of Mr Morgan - by which, of course, I mean a very large amount.

* There is a useful distinction between target rules and instrument rules. I'm ignoring this.