A monetary policy Pascal's Wager

In the 1600s, French philosopher-mathematician Blaise Pascal made the following argument for believing in God: "If I believe in God, and I'm right, I'll go to Heaven, which is infinitely awesome. But if I don't believe in God, and I'm wrong, I'll go to Hell, which is infinitely bad. Therefore, it makes sense to believe in God." Any economist will recognize this as being an expected utility calculation - even if there is only a tiny chance that God is real, the expected utility of believing in God is still infinitely higher than the expected utility of not believing in God. So believe in God, ye rational agents!

The problem is, as you probably figured out before you even finished reading that paragraph, is that it assumes that you only have two choices - Christianity and atheism. Suppose we also introduce Islam. Suppose the Christians say "If you believe in Jesus you'll go to Heaven; if not, Hell." And suppose the Muslims say "If you believe in Allah you'll go to Heaven; if not, Hell." Call this the Two-Sided Pascal's Wager. Well, in this case, your expected utility is undefined no matter which religion you choose. And you can't choose both! You are basically screwed. Maybe you end up choosing one or the other, but you always reserve the right to switch.

So what does this have to do with monetary policy, you ask?

Via David Glasner, I see that John Taylor is now pushing the idea that the Great Recession of 2009-whenever was caused by too-high interest rates in 2008 (which were in turn necessitated by too-low interest rates earlier in the decade). Taylor has repeatedly stated that "too high" and "too low" are to be measured relative to his Taylor Rule. 

This is interesting, because it means that Taylor believes that the Fed's decisions have absolutely enormous power over the macroeconomy. I know Suppose, hypothetically, that I know someone else who believes the same thing: Scott Sumner just for fun let's call him "Scott Sumner" (Update: This does not seem to characterize Scott Sumner's actual position. See bottom of post. For now, go with the hypothetical.). Also, Suppose both Taylor and Sumner appear to believe that Fed commitment to an optimal monetary policy rule is essential to prevent large recessions. And each economist has a very specific idea of what that optimal rule should be.

Here's the weird thing, though: Their rules are different rules.

Taylor basically says: "If the Fed does not credibly commit to a Taylor rule with coefficients of 1.5 and 0.5, the economy will experience big recessions and/or big inflations."

Sumner basically hypothetically says: "If the Fed does not credibly commit to NGDP level targeting to keep NGDP on a 2% 5% growth path, the economy will experience big recessions and/or big inflations."

So suppose you are a central banker, and you are very very risk-averse. You absolutely dread big recessions and big inflations. If you pick the wrong monetary policy rule, you're absolutely screwed. But you also have model uncertainty; you don't know for sure whether Taylor's story or Sumner's story perfectly describes the world.

Well, since you're risk-averse, you'd ideally like to choose a mix of the two rules. You'd like to buy insurance. But you can't buy insurance, because there is no way to mix the two rules! Both Taylor's and Sumner's models each insist that for the policy to work, there can be no wavering from firm commitment to the rule. Your choice set is convex.

In this case, Taylor's and Sumner's dueling propositions look very much like a Two-Sided Pascal's Wager between Christianity and Islam. You are a risk averse agent faced with a convex choice set over two high-risk alternatives, with no low-risk alternative available. In other words, you are screwed.

This is why I think that economists who advocate models in which A) small monetary policy mistakes have severe negative consequences, and B) commitment is crucial are, ironically, doomed to failure by the extreme nature of their own arguments. The central bank operates under a great deal of model uncertainty, and is highly risk-averse. Unless it is extremely confident of one single model of the macroeconomy, the Fed will choose discretion (or a model like Woodford's, in which deviating from the rule does not come at a huge cost) rather than the kind of rigid commitment advocated by economists like Taylor. Which is to say, even if the Fed picks a rule, it will reserve the right to modify or drop that rule if conditions seem to warrant, just like a person reserves the right to change their religion. And since people know that the Fed reserves that right, they will never believe that the Fed will ever fully commit to any rule. Which means that no rule that requires absolute commitment can work.

This leaves discretion as the only feasible policy. The Two-Sided Pascal's Wager is a wager you just can't win.

Update: Commenters, including Scott Sumner, have suggested that the position I initially attributed to Sumner is more characteristc of economists other than Sumner. If so, I apologize for mischaracterizing Sumner's opinion, but really I was just trying to use any example in order to demonstrate the general principle.

Update 2: In a Twitter discussion, Andy Harless raises the possibility that Fed commitment to any rule might dominate pure discretion. Scott Sumner (I think) puts forth the same idea in the comments. Fair enough. That could be true! But, given that John Taylor disagrees - that he thinks that any non-Taylor rule will spell disaster - and given that the Fed gives Taylor's ideas nontrivial levels of credence, my point still holds!

Update 3: In the aforementioned Twitter discussion, I said:

My point is that if the Fed gives Taylor ANY credence, no one else will persuade the Fed to commit firmly to a non-Taylor rule...Let me put my point more informally: Taylor probably scares the Fed away from credibly committing to ANY non-Taylor rule...just by invoking Hell, Taylor is FORCING a Pascal's Wager on the Fed, regardless of what [any other economist] does or who is right.

That should clear things up, for those who found the above discussion a bit dense.