Scott Sumner wrote a post commenting on my previous post about Paul Krugman’s column in the *New York Times* last Friday. I found Krugman’s column really interesting in his ability to pack so much real economic content into an 800-word column written to help non-economists understand recent fluctuations in the stock market. Part of what I was doing in my post was to offer my own criticism of the efficient market hypothesis (EMH) of which Krugman is probably not an enthusiastic adherent either. Nevertheless, both Krugman and I recognize that EMH serves as a useful way to discipline how we think about fluctuating stock prices.

Here is a passage of Krugman’s that I commented on:

But why are long-term interest rates so low? As I argued in my last column, the answer is basically weakness in investment spending, despite low short-term interest rates, which suggests that those rates will have to stay low for a long time.

My comment was:

Again, this seems inexactly worded. Weakness in investment spending is a symptom not a cause, so we are back to where we started from. At the margin, there are no attractive investment opportunities.

Scott had this to say about my comment:

David is certainly right that Krugman’s statement is “inexactly worded”, but I’m also a bit confused by his criticism. Certainly “weakness in investment spending” is not a “symptom” of low interest rates, which is how his comment reads in context. Rather I think David meant that the shift in the investment schedule is a symptom of a low level of AD, which is a very reasonable argument, and one he develops later in the post. But that’s just a quibble about wording. More substantively, I’m persuaded by Krugman’s argument that weak investment is about more than just AD; the modern information economy (with, I would add, a slowgrowing working age population) just doesn’t generate as much investment spending as before, even at full employment.

Just to be clear, what I was trying to say was that investment spending is determined by “fundamentals,” i.e., expectations about future conditions (including what demand for firms’ output will be, what competing firms are planning to do, what cost conditions will be, and a whole range of other considerations. It is the combination of all those real and psychological factors that determines the projected returns from undertaking an investment, and those expected returns must be compared with the cost of capital to reach a final decision about which projects will be undertaken, thereby giving rise to actual investment spending. So I certainly did not mean to say that weakness in investment spending is a symptom of low interest rates. I meant that it is a symptom of the entire economic environment that, depending on the level of interest rates, makes specific investment projects seem attractive or unattractive. Actually, I don’t think that there is any real disagreement between Scott and me on this particular point; I just mention the point to avoid possible misunderstandings.

But the differences between Scott and me about the EMH seem to be substantive. Scott quotes this passage from my previous post:

The efficient market hypothesis (EMH) is at best misleading in positing that market prices are determined by solid fundamentals. What does it mean for fundamentals to be solid? It means that the fundamentals remain what they are independent of what people think they are. But if fundamentals themselves depend on opinions, the idea that values are determined by fundamentals is a snare and a delusion.

Scott responded as follows:

I don’t think it’s correct to say the EMH is based on “solid fundamentals”. Rather, AFAIK, the EMH says that asset prices are based on

rational expectations of future fundamentals,what David calls “opinions”. Thus when David tries to replace the EMH view of fundamentals with something more reasonable, he ends up with the actual EMH, as envisioned by people like Eugene Fama. Or am I missing something?In fairness, David also rejects rational expectations, so he would not accept even my version of the EMH, but I think he’s too quick to dismiss the EMH as being obviously wrong. Lots of people who are much smarter than me believe in the EMH, and if there was an obvious flaw I think it would have been discovered by now.

I accept Scott’s correction that EMH is based on the rational expectation of future fundamentals, but I don’t think that the distinction is as meaningful as Scott does. The problem is that in a typical rational-expectations model, the fundamentals are given and don’t change, so that fundamentals are actually static. The seemingly non-static property of a rational-expectations model is achieved by introducing stochastic parameters with known means and variances, so that the ultimate realizations of stochastic variables within the model are not known in advance. However, the rational expectations of all stochastic variables are unbiased, and they are – in some sense — the best expectations possible given the underlying stochastic nature of the variables. But given that stochastic structure, current asset prices reflect the actual – and unchanging — fundamentals, the stochastic elements in the model being fully reflected in asset prices today. Prices may change ex post, but, conditional on the realizations of the stochastic variables (whose probability distributions are assumed to have been known in advance), those changes are fully anticipated. Thus, in a rational-expectations equilibrium, causation still runs from fundamentals to expectations.

The problem with rational expectations is not a flaw in logic. In fact, the importance of rational expectations is that it is a very important logical test for the coherence of a model. If a model cannot be solved for a rational-expectations equilibrium, it suffers from a basic lack of coherence. Something is basically wrong with a model in which the expectation of the equilibrium values predicted by the model does not lead to their realization. But a logical property of the model is not the same as a positive theory of how expectations are formed and how they evolve. In the real world, knowledge is constantly growing, and new knowledge implies that the fundamentals underlying the economy must be changing as knowledge grows. The future fundamentals that will determine the future prices of a future economy cannot be rationally expected in the present, because we have no way of specifying probability distributions corresponding to dynamic evolving systems.

If future fundamentals are logically unknowable — even in a probabilistic sense — in the present, because we can’t predict what our future knowledge will be, because if we could, future knowledge would already be known, making it present knowledge, then expectations of the future can’t possibly be rational because we never have the knowledge that would be necessary to form rational expectations. And so I can’t accept Scott’s assertion that asset prices are based on rational expectations of future fundamentals. It seems to me that the causation goes in the other direction as well: future fundamentals will be based, at least in part, on current expectations.

David,

You said:

“The future fundamentals that will determine the future prices of a future economy cannot be rationally expected in the present, because we have no way of specifying probability distributions corresponding to dynamic evolving systems.”

I think this hits on a fundamental problem with rational expectations. Because of the central limit theorem, the mean and variance of a future distribution can imply a mean and variance of a present distribution. However, a mean and variance do not completely specify a probability distribution (so information is lost). Therefore the “rational expectations operator” that translates this future information into the present is a lossy process.

There are two ways of getting around this: one plausible, the other less so. The implausible one is to only consider the mean and variance in the above (the choices of millions of agents in the present can be reduced to a single distribution with two parameters). The plausible one is that the expected value of, say, inflation in the future has no requirement to be the actual value of inflation — and in fact the expected value becomes just another (possibly dynamic) parameter in the theory.

I wrote about this a couple months ago in the context of the “neo-Fisher” model:

http://informationtransfereconomics.blogspot.com/2016/04/neo-fisherism-and-causality.html

Yes, although it is probably even worse, as those lab experiments show, that even knowing fundamentals and pinning one point of certainty cannot fix the path to it.

I’m a little bit puzzled by the way people link low rates in long maturity forwards and low current rates. Fama&Bliss (1988) [[ http://marshallinside.usc.edu/dietrich/aer-1987-fama-bliss-infofwdrates.pdf ]] show us that what current forwards predict is mainly about risk-premia, not future expected rates. So what we should infer from current low rates is that people are not really ready to bear additional risk, or at least not as ready as they were before. The way Krugman interprets it is that rates are going to be low for a while, but this is not we have statistically observed in the past.

What about the fact that animal spirits are often irrational? E.g. Dan Ariely etc.

Could it be that, as GDP per capita and mean household income diverge, aggregate demand declines causing expectations to diminish causing interest rates to decline?

“… then expectations of the future can’t possibly be rational because we never have the knowledge that would be necessary to form rational expectations. ”

So does that mean rational expectations by necessity reduce to adaptive expectations?

Really brilliant David, very insightful for me, definitely.

David,

How would you account for the powerful ability of prediction markets to predict the future (in terms of probability) so accurately? For example, here is Hypermind’s accuracy:

https://blog.hypermind.com/2015/12/17/hypermind-accuracy-over-its-first-18-months/

Ilya — That graph hypermind shows does not imply accuracy and is in fact consistent with random (“irrational”) market exchanges given a budget constraint and a large number of dimensions:

http://informationtransfereconomics.blogspot.com/2015/10/corporate-prediction-markets-aggregate.html

This essentially follows from Gary Becker’s 1962 paper “Irrational Behavior and Economic Theory”.

Jason, What you say seems really interesting, but I think that I need you to unpack it a bit more for me, before I can really understand it. The post you link to is helpful, but I am afraid that it would take a long time to work through it.

Lord, Which lab experiments are you referring to?

franic, Current forwards predict both future expected rates and risk premia. The general model includes both effects; there is no inconsistency. In a given situation, one or the other effect may be more or less important depending on the circumstances.

Andrew, Expectations are sometimes rational and sometimes not.

wayne, I don’t know what it means to say that GDP per capita and mean household income diverge.

Henry, Adaptive expectations refers to some sort of mechanical procedure for forming expectations. It may be useful to model expectations as adaptive under some circumstances, but I don’t believe expectations are formed adaptively as a general rule, because expectations are formed based on many sources of information not just past observations.

Miguel, Thanks so much.

Ilya, Prediction markets that I am familiar with are generally focused on predictions of specific outcomes of known future events, that’s only a very small sliver of the future outcomes which people are forecasting.

Jason, Good point.

“…because expectations are formed based on many sources of information….

So where do these sources of information come from? They can only come from the past.

Henry, Adaptive expectations refers to a particular mechanical way of extracting inflation expectations as a distributed lag of past observations of inflation. Obviously we can’t form expectations of the future without background knowledge of the past; the issue is whether it makes sense to assume that expectations are formed by simply drawing a trend line through past observations and assuming that the future inflation rate will lie along the trend line of past observations.

David,

Having consigned rational expectations to the fires of hell does it then not follow that the whole of neoclassical theory deserves similar imolatory treatment?

Henry, I think we have very different conceptions of what the term “neoclassical theory” encompasses.

David,

Have your blogged on these matters?

Could you refer me to a paper which explains your conception of neoclassical theory?