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Alpha Beta and the Libra Twist

Summary:
Suppose I promise to be in the same place as you; but you make no promise to be in the same place as me. Then I am Beta follower and you are Alpha leader; because you go where you want to go and I must go to the same place to keep my promise. We get the same Alpha-Beta relationship with asymmetrical fixed exchange rates. If the US Fed decided (for some unknown reason) to peg the exchange rate of the US dollar to the Canadian dollar, but the Bank of Canada makes no such promise the other way, then the US Fed becomes the Beta follower and the Bank of Canada becomes the Alpha leader. US monetary policy is now decided in Ottawa. It's the same Alpha-Beta relationship between central bank and commercial banks. The Bank of Montreal pegs the exchange rate of the BMO dollar to the Bank of

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Suppose I promise to be in the same place as you; but you make no promise to be in the same place as me. Then I am Beta follower and you are Alpha leader; because you go where you want to go and I must go to the same place to keep my promise.

We get the same Alpha-Beta relationship with asymmetrical fixed exchange rates. If the US Fed decided (for some unknown reason) to peg the exchange rate of the US dollar to the Canadian dollar, but the Bank of Canada makes no such promise the other way, then the US Fed becomes the Beta follower and the Bank of Canada becomes the Alpha leader. US monetary policy is now decided in Ottawa.

It's the same Alpha-Beta relationship between central bank and commercial banks. The Bank of Montreal pegs the exchange rate of the BMO dollar to the Bank of Canada dollar; but not vice versa. So the Bank of Montreal is Beta follower to the Bank of Canada's Alpha leader. The Bank of Canada decides Canadian monetary policy, not the Bank of Montreal.

Now let's add the Libra twist to this simple story.

Suppose I promise to be at a point midway between you and Alice; but you and Alice make no promises about where you will be relative to me. I am Beta follower. But Alpha leadership is now shared 50-50 between you and Alice.

If I understand it correctly (I quite possibly don't) Facebook's new Libra currency is supposed to be pegged to a basket of international currencies. Libra is then a Beta follower, just like a normal commercial bank. But unlike a normal commercial bank, which follows only one Alpha leader central bank, Libra will be following a basket of several central banks. So Alpha leadership is now shared (in proportion to those basket weights) between those central banks.

Which is an interesting twist.

My guess is that Libra will not take off into wide usage (JP Koning's good post explains why). But suppose it does take off, and replaces the money created by normal commercial banks which follow only one central bank each. What happens if the US Fed wants to loosen world monetary policy and the ECB wants to tighten? It's like you and Alice both running off in opposite directions, each trying to run faster than the other, to get me to follow in your direction rather than her direction and vice versa.

Update: it's like Libra creates the incentive for a Tug-of-War between the Fed and the ECB, with Libra tied to the middle of the rope. Except that it's not a rope but a very elastic rubber band.

This doesn't look like a stable equilibrium to me.

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