## Tuesday, September 8, 2015

### Quantitative jellybeans

David Glasner ends this post discussing Scott Sumner's example of the EMH and adjusting (rational) expectations. This first paragraph is Glasner's quote of Sumner:
All citizens are told there’s a jar with lots of jellybeans locked away in a room. That’s all they know. The average citizen guesstimates there are 453 jellybeans in this mysterious jar. Now 10,000 citizens are allowed in to look at the jar. They each guess the contents, and their average guess is 761 jellybeans. This information is reported to the other citizens. They revise their estimate accordingly.
Glasner responds:
But there’s a difference between my example and Scott’s [example above]. In my example, the future course of the economy depends on whether people are optimistic or pessimistic. In Scott’s example, the number of jellybeans in the jar is what it is regardless of what people expect it to be. The problem with EMH is that it presumes that there is some criterion of efficiency that is independent of expectations, just as in Scott’s example there is objective knowledge out there of the number of jellybeans in the jar. I claim that there is no criterion of market efficiency that is independent of expectations, even though some expectations may produce better outcomes than those produced by other expectations.
I was wholly confused by Sumner's use of concrete jellybeans in this example. The point Glasner makes is precisely the point Sumner makes most of the time. Sumner's jellybean example is the view of the people of the concrete steppes. His view of QE in Japan, the US and EU was that expectations were independent of the actual number of jellybeans (dollars in the monetary base).

That expectations in market monetarism do not anchor on objective measurements is exactly the point of this post that didn't get much attention (I thought it was pretty good). To put this example in the form of that argument, Sumner is now claiming (with b = number of jellybeans) that the output of the expected value of beans E(b) from theory T is:

E(b) = T[E(b), b] ≈ T[E(b) = b] + β (b - E(b)) +  · · ·
(1)   E(b) ≈ T[E(b) ≈ b]

with β small o(1) (since b - E(b) is small) whereas Sumner's theory of QE (and market monetarism in general) -- and Glasner's point about expectations -- is:

E(b) = T[E(b), b] ≈ T[E(b)] + α b +  · · ·
(2)   E(b) ≈ T[E(b)]

with α small. The emphasis is that we are looking at a theory T that has any expectation E(b) (2) and one that has anchored expectations around some fundamental E(b) ≈ b (1).

Basically, Sumner is saying rational expectations plus the EMH sometimes is (1) and sometimes it's (2). And it seems to me it's (2) when (1) doesn't work -- e.g. QE is expected to be taken away, so the value of QE doesn't strongly matter (α is small).