Thursday, February 26, 2015

Market monetarism and the Keynesian beauty contest

Attention: conservation notice. Over 1500 word essay about universality classes and kittens.
In my recent post on expectations, I wrote this:
Overall, I'd sum up my problem with the centrality of expectations with a question to Scott Sumner: what happens to your theory if markets don't believe market monetarism? In a sense, this question cannot be addressed by market monetarism. The "market" piece presumes markets believe the theory (i.e. market expectations are consistent with market monetarism, i.e. assuming rational expectations in market monetarism ... I called this circular reasoning before, but charitably, this could be taken that market monetarism is the only self-consistent theory of expectations as I mention in a comment at that link).
One thing I forgot about until I was doing some searching on Sumner's blog was that Sumner had basically assumed it explicitly:

Markets are market monetarists (23 Mar 2012)
It’s not surprising that the markets are market monetarist, as my views of macro were largely developed by watching how markets responded to the massive and hence easily identifiable monetary shocks of the interwar period.  That’s why I never lose any sleep at night worrying about whether market monetarism will ever be discredited; I know the stock market agrees with me.
I'd like to expand on what I meant by market monetarism claiming to be the only self-consistent theory of expectations. I borrowed the phrase self-consistent from physics; let me elaborate on what I mean by that [1]. I'd also like to better explain why I think market monetarism is more an ideological movement than an economic theory.

Let's call market monetarism M, which is a functional of expectations E, i.e. M = M[E]. But additionally, the ouptut of "market monetarism" as an economic theory defines the expectations one should have given a set of economic variables n, m, ... (say, NGDP, base money, ...). That is to say, M[E] gives us E as one of the outputs. This is rational expectations, aka model consistent expectations. So what we have is this:

(1) E(n, m, ...) =  M[E = E(n, m, ...)]

There are many paths of variables (n, m, ...) that can lead to the same expectations E (it's called indeterminacy), but that's not important right now [2]. Basically, expectations held by the market represent a fixed point of M ... like a Nash equilibrium of some expectations game. This is all well and good, and is really just a straightforward application of rational expectations. You could say the same of a New Keynesian theory ... E = NK[E]. In fact, a wide class of theories can have fixed points like this (any RBC or DSGE model, for example).

The thing is that market monetarism doesn't think there is that kind of freedom, and the reason is that market monetarism is almost entirely expectations. This is an uncontroversial categorization of market monetarism. For example, Scott Sumner wrote a post to that effect:

Money and Inflation, part 5: It’s (almost) all about expectations (1 Apr 2013)

And here is a quote from a Nick Rowe comment at Tony Yates' blog that's even more concise:
Monetary policy is 99% expectations, so how monetary policy is communicated is 99% of how it works.
Why does market monetarism's insistence that the theory is 99% expectations lead inexorably to the conclusion that market monetarism makes the (erroneous) claim to be the only theory of expectations and therefore indisputable? Let me tell you.

In general, the other theories have explicit dependencies on observable quantities x like the monetary base (i.e. not only do expectations have something to do with whether x is well above or below trend but that expectations can be anchored by real observable quantities):

E(x) = NK[E(x), x]

but in the market monetarist model we have, expanding around x = 0:

E(x) = M[E(x), x]

E(x) ≈ M[E(x)] + α x  ... with α << 1

Concrete steppes (like QE) have little to do with expectations and as Nick Rowe said above, the theory is 99% expectations (i.e. α ~ 0.01). Scott Sumner would have to lump what I call α x into a error term or "systematic error" term SE in his post here. It represents the difference between pure expectations (an NGDP futures market or credible central bank target) and reality. I'd call it the influence of the actual value of NGDP on the expected value of NGDP.

So what's wrong with that, you say? Well, the explicit dependence on x above is what makes these theories with expectations different from each other since they're all based on people making decisions. It's what forms the basis of the model dependence of the expectations. In Keynesian models, x includes things like interest rates and unemployment. In RBC models, x includes "technology". The lack of an explicit dependence on x in M is what I mean by model independent expectations in this post. It also couples the theory to the empirical data. Without it the only dependence on x is via E(x) -- that is to say the value of x doesn't matter, it's what people think x is (like what Allan Meltzer thinks inflation is, or what Republicans think Obamacare is).

Here's the kicker, though. Since all of these theories are based on economic agents (people) with human expectations, market monetarism is making the claim to be the only expectation-based theory. If we expand around x in a generic theory T ...

E(x) = T[E(x), x] ≈ T[E(x)] + τ x + ...

(2) E(x) ≈ T[E(x)]

T is completely unspecified right now. Now there are two possibilities here. First, is that equation (2) doesn't specify T. In that case, whether T = NK or T = M depends on what humans believe and there is no specific theory of pure expectations (or you just have to convince the market that T = X and it is entirely political ... X could be communism or mercantilism or the Flying Spaghetti Monster). 

Obviously market monetarists don't believe that. Therefore they must believe that equation (2) specifies T. In that case, market monetarists are claiming T = M. Basically, the first term in any expansion of any theory in x is M (i.e. the first term is unique) ...

T[E(x), x] ≈ M[E(x)] + τ x + ...
NK[E(x), x] ≈ M[E(x)] + k x + ...
M[E(x), x] ≈ M[E(x)] + α x + ...

But also, α = τ = k is small (according to market monetarism), so the first term is all that matters! If you expanded a theory and didn't end up with M[E(x)] as a first term, then whatever that expansion was would be a theory equally valid to market monetarism.

Physicists out there probably recognize this idea: market monetarism is making the claim (without proof or comparison to empirical data) to be the universality class of macroeconomic systems. Universality classes are why the same kinds of processes happen in totally different systems, or things like the normal distribution show up everywhere.

This is a lot different from e.g. Scott Sumner just saying "my theory is right". It is Scott Sumner saying "every theory reduces to my theory" [3]. He is not explicitly saying this; it is implicit in his argument that the theory is primarily expectations and somehow unique (or at least has a reason to be advocated besides pure opinion).

Now that I've gone off the deep end of abstraction, let me close with something concrete to show how preposterous this is.

Kittens.

Yes, kittens. NPR's Planet Money did an experiment to illustrate Keynes' "beauty contest" in markets, but it gives us an excellent illustration of expectations and theories of expectations. Planet Money put up three pictures of animals (a kitten, a slow loris -- my personal favorite, and a polar bear cub) and asked people not only which one they thought was the cutest, but which one they thought everyone else would think is the cutest ... i.e. the expected winner of the poll.

Here are the images and results:

Picture from NPR's Planet Money.



I have a couple of theories for the result. The first one is that the most commonly experienced critter will be expected to win the poll. Call this theory MC, and it depends on the actual data of which critter is most common. Call that c. The second theory is that the one with the biggest eyes (relative to body size) will be expected to be the winner. Call this BE and it depends on eye size e. Both of these theories will expect the kitten to win. In our notation above, we have the self-consistent (e.g. Nash) equilibria: 

E(c) = MC[E(c), c]

E(e) = BE[E(e), e]

(If you repeat the "game" with the same pictures, the result would rapidly converge to nearly 100% for the kitten for the expected result.)

Now if we make the market monetarist assumption that the empirical values (c and e) have little influence on the result we can say:

MC[E(c), c] ≈ MC[E(c)] + α c
BE[E(e), e] ≈ BE[E(e)] + α e

With α being small. The alpha terms measure how much the fact that kittens are actually the most common critter of the three influences what people think the most common critter is (or how big the critters' eyes are measured to be in the pictures influences how big people think they are). Now take α → 0 and look at our self-consistent theories above:

E(c) ≈ MC[E(c)]
E(e) ≈ BE[E(e)]

These are not the same theory! However, the market monetarist claim is effectively saying that the "Most Common" theory and the "Big Eyes" theory must be equivalent -- or else they're effectively advocating something that is pure opinion (taking α → 0 has decoupled our theory from the 'concrete steppes' of empirical data).

Update 27 Feb 2015:

The Keynesian beauty contest above also illustrates Noah Smith's contention of uninformative data being the reason we can't select between different theories in macro. We'd need to see a lot more critters to determine which of the "big eyes" or the "most common" theories were correct (or maybe neither of them).

Footnotes:

[1] What I write here is actually borrowed a lot from physics; E(x) is a quantum field, M[...] is essentially a path integral given a Lagrangian ('the theory') in an abuse of notation. So one would view E(x) = M[E(x)] as a matrix element/expectation value, in a self-consistent field approach.

[2] Sumner:
Unfortunately the role of expectations makes monetary economics much more complex, potentially introducing an “indeterminacy problem,” or what might better be called “solution multiplicity.”  A number of different future paths for the money supply can be associated with any given price level.  Alternatively, there are many different price levels (including infinity) that are consistent with any current money supply.
[3] I should add "as you decouple it from empirical data" to that quote. As α → 0 (or k or τ) the theory decouples from direct contact with empirical data. It is no longer about empirical data, but what you interpret markets (or important economic actors like the central bank) to think about empirical data.


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