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**Update:**Consider this the first open thread in comments for book discussion and initial thoughts ...

I read your book!

ReplyDeleteIt's a nice introduction to some deep issues, but there are some problems. Specifically, the exposition of the SMD theorem is off course, not quite wrong but off course. The SMD theorem does not just state that there may be multiple equilibria but it also tells us *why* - because of wealth effects.

Have you ever seen the Kurosawa movie High & Low? It's about a shoe executive whose takeover of his firm is interrupted when his driver's son is kidnapped. Imagine it was an Ozu movie and instead of a dramatic kidnapping, housing prices just went down. Then he might not be able to afford to buy out the company. Price and spending, somewhat paradoxically, go down together.

SMD was not an unexpected result. Edgeworth had explained it to Marshall and Marshall knew sufficient conditions to get around it. Any good textbook on economics from Marshall's time to this will explain how wealth effects are a boundary condition for Supply & Demand. The name "wealth effects" and the precise form of decomposition come from Value & Capital by Hicks, but SMD is not as an independent theorem (only mentioned in passing). I'm not as good at drawing as Edgeworth & Hicks, so I had to learn how to draw the SMD Theorem from Mas-Collel's textbook. If you want an accurate statement of modern theory, that's *the* book to read.

I thought your analogy to blueberries that can be made into pie or milkshakes was pleasant but misleading. There's no production in the SMD theorem, because the SMD theorem is about how *pure consumer choice* can mess up the simplistic supply & demand story. There are analogous theorems in production theory, of course.

I could write a more positive review about the excellent section on Becker's evolutionary approach. This was the best part of the book! But I figured you'd find the above more useful.

Thanks for reading and taking the time to make a detailed criticism.

DeleteOne thing I realize now is that in an Econ book, people are going to see the blueberry pie analogy as production instead of the intended *aggregation*. Blueberries are the rational agents, and the blueberry pie is the aggregate economy made from rational agents.

That said, the SMD theorem is much more general than the wealth effect explanation -- the wealth effect is used to obtain the boundary condition on demand which is the assumption in the theorem. Since there are other ways to obtain the boundary condition (notably, Becker's irrational agents or Information equilibrium) that don't require the behavioral implications of the wealth effects you can see that the boundary condition is more general.

I hope I didn't make it seem like the most important consequence was multiple equilibria -- my intent was to make the simplification (or at least the change of the effective description) of agents at the macro scale the most important consequence. I will re-read that section given your critique and see if I need to add a post to this site regarding this point.

But again, thanks so much for reading!

The book was interesting and I've reviewed your blog again, but still am not understanding the first point you make against using expectations the way market monetarists do. First, is it only from a perspective like information equlibrium that your claim holds, or is it a more general point?

ReplyDeleteIt is much more general. I'll talk about inflation though just to be more concrete.

DeleteAny version of expectations wherein E(t)[π(t+1)] = f(π(t+1)) where π(t+1) is the *observed* inflation rate at t+1 cannot involve any non-trivial dynamics of the agents (it must be a property of the system). A hot bowl of soup can cool to room temperature so that E(t)[T(t+1)] = T(t+1), but that is because the soup has no choice in the matter. Similarly, a group of agents can't make a particular π(t+1) happen unless they have no choice in the matter.

The underlying problem is that the actual future (t+1) being accessed in the present E(t)[f(t+1)], which involves essentially inverting the operator that propagates the dynamical system that is the economy into the future. Since information about the past is generally lost, the operator that takes the system into the future isn't invertible. If it existed, then we could undo the central limit theorem (each normal distribution would have a particular flavor that would tell us something about the process that generated it).

I am familar with the central limit theorem, but am not following your argument. Are you putting it in physics terms?

DeleteTo give you an idea of where I'm coming from, I earned a BS degree 20 years ago. I took stats I and II, and basic calculus, but nothing formal beyond that.

Actually, I was trying to put it in more economics terms!

DeleteIf I roll a bunch of dice, as I add dice the result looks more and more like a normal distribution even though the original distribution is uniform. That's the central limit theorem.

However given a normal distribution, I can't determine if it was the result of rolling 6-sided dice or even a more complex non-uniform distribution. Most of the information in the original distribution (6-sided dice, 20-sided dice) is lost.

This means the "operator" A(t) (whatever it is that moves the system from the present t = 0 into the future t > 0; in physics an example is a Hamiltonian, but in economics we don't really know what the operator is) is non-invertible. Information is irrevocably lost in the same way the original distribution of cream in my coffee is lost as it diffuses throughout it.

That means there is no inverse operator 1/A(t) that can undo the operation of moving the dynamical system into the future with A(t) to get to the future state S(t). We can move the system from the present S(0) into the future S(t):

A(t) S(0) = S(t)

but we can't do

(1/A(t)) A(t) = S(0)

because 1/A(t) doesn't exist. If it did, we could use it to undo the central limit theorem (by setting up experiments where people roll different kinds of dice to determine how much money to spend at different grocery stores).

The issue for economics is that the expectations operator is precisely this inverse operator:

E(t) = 1/A(t)

in the case where E(t) acting on an observable (like inflation) depends on the actual value of that observable in the future.

There are two ways around this argument. One is that agents are random and the future really is "universal" in the sense that the normal distribution is universal (you can obtain it from rolling different kinds of dice or a variety of other random processes). Basically: people are random and don't think about the future.

The other way is if the system is completely deterministic: if the Fed sets future PCE inflation expectations at 2%, then every agent knows exactly how to adjust their personal consumption expenditures to obtain that result (like programming a computer or the Borg).

But it is impossible to reconcile

1. Agents make decisions that have impact

2. There is at least some degree of noise or probabilistic nature

3. Expectations depend on the actual observed value at t+1

Pick two.

Thanks for the expansion. What's confusing me is pretty fundamental, but I believe I see the system as being completely deterministic. I even refuse to do statistical modeling, even within my very modest ability, because I think it's a distraction.

DeleteI picture frequently changing expectations vis-a-vis news, including that coming from central banks. I assume that central banks have 100% ability to control NGDP, within the limits of their credibility. Problems with long-term credibility are caused by FOMC turnover, in the case of the Fed, for example, and cannot necessarily be entirely overcome. Even a computer, like Friedman wanted to used, could always be reprogrammed.

But, basically I don't see the daily wiggles in liquid asset prices as noise, for the most part. Not all are related to implicit NGDP forecast, but most are, and I think much in the way of down ticks involves implicit tightening of monetary policy.

For example, aside from modest real effects on trade, many signals of slowing NGDP in the EU, China, or Japan, for example, lead to an increased demand for dollars, with US liquid asset prices falling to primarily represent uncertainty as to whether the money supply will be expanded sufficiently to avoid a related US NGDP slowdown.

I may be missing something obvious, but I operate on the assumption that if the expected demand for dollars rises with respect to the expected supply, the value of the dollar will increase proportionately versus consumption and investment.

I think the current problem with central banks around the world primarily involves what central bankers seem to see as an asymmetric risk with regard to overshooting their inflation targets, hence they tend to undershoot. Due to a lack of long-term policy credibility, due to central bank turnover, it is difficult to promise very gradual monetary tightening should central banks overshoot. No central bank wants to be responsible for causing a recession, after initially being too looose.

I've been working on simple deterministic models for relating changes in liquid asset prices to changes in expected NGDP. For many US recessions, the gap between the NGDP growth trendline and recession troughs seem to relate very predictably to changes in representative stock indexes, like the S&P 500(80% of the US stock market cap), for example.

ReplyDeleteTake the roughly 6.2% gap during the Great Recession, multiply it by the pre-recession P/E ratio of ~18, and you get a drop in the S$P 500 of about 53%, which is pretty close to the data.

1 - [1/(1+.062*18)] = ~.53

I make the value of .062*18 hyperbolically glide toward 0, to account for the fact that stock prices can't be negative.

I do something similar with unemployment rates.

1 - [1/(1+.05+.062)] = ~10%

.05 was roughly the rate when the Great recession began.

May seem silly, but this works really well for the 2001 recession, 1982 recession, and Great Depression. The prediction for the S&P change during the 1991 recession is off considerably, but much more in-line when looking more directly at expectations, such as long-term treasury rates.