Richard Rorty would be scratching his head
Nick Rowe is on a roll with a series of very clever posts on the EMH. In this one he draws a S&D graph with the two axes labeled:
1. Extent to which EMH is true
2. Extent to which EMH is believed true
As a good Rortian I am trying to figure out the difference between the two axes. I wonder if Nick realizes how deeply he is wading into an epistemological morass. But don’t be put off by my sarcasm, it is a really clever way of framing the issue. And like Oliver Sacks’ Anthropologist on Mars, I do know how normal humans think about truth. In fact I used to be a normal human. Really.
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24. January 2010 at 19:36
Thanks Scott! I’m glad someone picked up on the epistemological angle. The EMH is a sort of self-denying belief, the opposite of a Lewis-style convention.
Here’s another fun one for you, which is a self-confirming belief, in which the demand curve will be upward-sloping:
Horizontal axis: “extent to which people believe that people drive on the left/right side of the road”, going from “100% believe that 100% drive on the left” to “100% believe that 100% drive on the right”.
Vertical axis: “extent to which people actually drive on the left/right side”.
The demand curve should slope up, in a sort of reverse Z-shape, and will presumably cross the upward-sloping diagonal supply curve in 3 places: 100% left; 100% right; and 50/50, with the middle equilibrium being unstable.
24. January 2010 at 19:36
Here’s my response to Nick.
When arguments have such structure, it is an indication that we are asking bad questions. Its similar to the Calvanist vs. Anabaptist debate in Protestant Christianity. They debated whether or not we have free will, when that isn’t the real question. The real question is if we have responsibility for our actions or not.
In the same way EMH answers are bad question. The question shouldn’t be “are markets efficient,” the real question is “Can certain individuals given power consistently make better choices for a society than a market.”
24. January 2010 at 19:39
Thats a neat example, Nick, actually though most of the epistemology of economics, when properly formulated should be of the “upward sloping demand form” that you describe. Getting the downward form is a clue that we are asking a bad question, and belief in the answer itself is a force to expel it from the debate.
24. January 2010 at 19:53
Scott: give up on Rorty, it’s bad for you.
Do you believe that you mean something specific when you write something? Presumably so, which why you write it: because you have a wish to convey that belief to someone reading it and an expectation that you will successfully do so if you express yourself well and they are reasonably intelligent and literate in English. Then you are committed to truth statements about what you mean and what you say. But what you say is a state of the world like anything else. Therefore you are committed to truth in a straightforward sense of the word. All users of language are: the concept of truth is inherent in using language, (this word means …, that word means …) let alone the function of language.
Including Richard Rorty, which is why he wrote all that stuff explaining and defending his position. And doing so advancing a theory of truth completely undermined by his own actions. (He would have been very annoyed, for example, to have been taken to supporting certain political positions.)
Doc Merlin: nicely put, but is that not more a labeling problem? Should not the EMH be something like “the incorporates-all-information hypothesis”?
24. January 2010 at 19:58
Beautiful. Henceforth, I rely on Rowe’s foundational analysis to support my bubble definition:
“…when too many people instinctively feel something is heavily overpriced but ignore their own beliefs because of an overriding belief that the market is better at predicting than they are.
In such circumstances, a narrative or paradigm can persist indefinitely until a body of evidence (or a sufficiently vocal authority) becomes so inconsistent with the paradigm that people begin to question the value of the EMH in the particular market.”
24. January 2010 at 21:29
hahaha, thats great StatsGuy.
24. January 2010 at 21:42
@Lorenzo
Thanks. And no, the “the incorporates-all-information hypothesis” is false on its face, because if you find out something new, the price hasn’t included your information in it yet, until you buy or sell.
Also that hypothesis suffers from the same structural problem as the “markets are efficient” theory or the “there is no free will” theory.
@StatsGuy
hahaha, thats great StatsGuy.
25. January 2010 at 02:04
From the point of view of an information channel, the stock researcher has to look at the total of all trades, wholesale and retail, and view the variables of relative size of the trade and the frequency. Skip stock price in the analysis, price is a derived measure. Use as relative size the proportion of the outstanding stock traded.
Doing this, then the stock market looks like a flow of arriving trades and you have set the situation up as Kelly trades:
http://en.wikipedia.org/wiki/Gambling_and_information_theory
Then, when information is maximally utilized, the amount of information learned from each of the flow of trades will be exactly equal to the equilibrium measurement uncertainty. which is the uncertainty talked about in the Stiglitz/Grossman paper:
http://go2.wordpress.com/?id=725X1342&site=modeledbehavior.wordpress.com&url=http%3A%2F%2Fwww.sendsms.cn%2Fdownload%2Fwavecom%2FAT%25D6%25B8%25C1%25EE%25BF%25E2%25A3%25A8%25B4%25F3%25C8%25AB%25A3%25A9%2Fon%2520the%2520impossibility%2520of%2520informationally%2520efficient%2520markets.pdf
Stock prices may or may no reflect properly depending on how equilibriated is the banker yield curve, which is not adequately represented in the stock market.
(Jeez what a URL!)
In the Stiglitz paper, the Y axis will be the variance of the trades, but that Y axis is incorrect because it assumes that the distribution is Normal. Money at equilibrium is a Normal variable because of the way we use money. The correct measure on the Y axis is entropy, or its complement redundancy depending on the sign.
Look at:
http://en.wikipedia.org/wiki/Information_theory
Entropy is a different norm than minimum variance. At equilibrium, each trade received contains the same quanta of information and is the uncertainty associated with the random walk.
25. January 2010 at 06:10
Nick, That is interesting. Are these graphs a familiar part of game theory research? I vaguely recall Thomas Schelling making similar arguments in other contexts.
Doc Merlin, That’s one important question, but there are many others.
Lorenzo, You said;
“Therefore you are committed to truth in a straightforward sense of the word. All users of language are: the concept of truth is inherent in using language, (this word means …, that word means …) let alone the function of language.”
I had thought language is a perfect example of Rortian pragmatism. Don’t philosophers now believe that words don’t have fixed meaning, but rather the meaning is how they are regarded by the people who use the term. The official meaning of ‘bachelor’ is “unmarried male adult.” The official meaning of ‘spinster’ is “unmarried female adult.” If you believe that is what the words actually mean, I encourage you to start using ‘spinster’ wherever appropriate.
Richard Rorty believed “truth is what our peers let us get away with.” And he devoted his life to persuading his peers.
Mankind can search from now until the end of time, but we will never discover a “truth” that is separate and superior to that which we believe is true–AT THE TIME.
Statsguy, That is cute, but so few people actually believe in the EMH that we need not worry about that “hall of mirrors” scenario.
mattyoung, It sounds like you know what you are talking about, but I’m afraid I am not familiar with the Stiglitz literature.
Everyone, Here is a general comment that may or may not relate to Mattyoung’s point, as well as the views of others. Some people argue that the EMH won’t hold if it is believed, as no one would then have an incentive to make the market efficient by searching out information. The same argument could apply to the interest parity condition. If the IPC works perfectly then the expected depreciation of country’s X’s currency should equal the gap between country X’s nominal interest rate and country Y’s nominal interest rate. However this relationship will only hold if arbitragers take advantage of any discrepancies. And if the IPC works perfectly there won’t be any discrepancies.
What happens in the real world? The IPC is a reasonable approximation of reality, at least for most purposes. And that is all that matters. It doesn’t work perfectly, but small discrepancies are enough to generate the needed arbitrage. And I’d say the same about the EMH.
25. January 2010 at 07:48
I just posted the following comment over at Nick’s site:
25. January 2010 at 13:29
“It doesn’t work perfectly, but small discrepancies are enough to generate the needed arbitrage. And I’d say the same about the EMH.”
That’s quite sensible.
Then it just becomes a debate about whether the appropriate test of EMH is invoked pre-arbitrage or post-arbitrage. Pre-arb suggests it’s always false. Post-arb suggests it’s always true. (It is impossible for information timing and arb timing to be precisely coincident.)
25. January 2010 at 13:47
Here’s ECON 101:
Knowledge is so divided / individualized, and the time structure of the market across BOTH relative prices AND production process is so massively complex that NO ONE can anticipate / “predict” systematic adjustments to that structure caused by systematic distortions produced in that structure by shifting central bank policy, massively expanding / contracting bank leverage, shifting foreign exchange policies, etc.
If these systematic across time structural changes in production process and relative prices are systematically unanticipatible in any particular instance, the EMH cannot be true.
Hence EMH is false no matter how many or how few believe it.
QED
26. January 2010 at 06:28
Jeff, A very good point, but the example with two people is too extreme, as you’d have to assume perfect information, which isn’t realistic. In practice each person sees a part of the big picture, so you need more than two.
JKH, I see your point and agree, but my only quibble is that I think terms like “true” and false” are too categorical for the social sciences. In practice our theories are almost never completely true, the question is whether they are close enough to be useful approximations of reality.
Greg, The fact that people cannot predict something doesn’t make the EMH false. What would make it false is if a subset of people (Austrians?) could tell us that too much housing is being built because of low interest rates, but the rest of the market could not predict this.
26. January 2010 at 07:51
Scott: “Are these graphs a familiar part of game theory research? I vaguely recall Thomas Schelling making similar arguments in other contexts.”
In a two person game, you usually draw two reaction functions A(B) and B(A). In a multi-person symmetric game, you normally draw the reaction function for a representative agent as a function of the actual outcome, and then draw in a 45 degree line. (So desired y is on the vertical axis, and actual y is on the horizontal. The Keynesian Cross, C+I+G and AE=Y, can be interpreted this way). Or you could put “expected y”, or “what people believe y is” on the horizontal axis, which is what I have done.
If the reaction function of the representative agent slopes down you have negative feedback (standard micro), and if it slopes up you have positive feedback (the Keynesian multiplier, for example). With strong positive feedback you can get multiple equilibria.
Yes, this is very much what Schelling was doing. David(?) Lewis on Conventions had more impact on philosophers, especially philosophy of language, I think. There is a second stable equilibrium in which “dog” means cat, and vice versa.
IIRC, from 35 years ago, the main philosophical problem is distinguishing differences in belief from differences in meaning. How far can you push Quine’s “Principle of Charity”? (wherein you translate from another’s language by assuming he has the same beliefs as you, roughly speaking). The problem is compounded in social science, where beliefs about the world change the actual world.
Here’s another one, that’s both fun, and deadly serious in current contexts:
Horizontal axis: belief that monetary policy is interest rate policy.
Vertical axis: truth that monetary policy is interest rate policy.
Here we have a positive feedback system. There are probably two (stable) equilibria: one in which monetary policy *is* interest rates, and we can get stuck in liquidity traps; and a second in which it isn’t, and we don’t get stuck. Social construction of reality, again, which is just an extreme form of a convention, which not only affects how we behave, but how we see the world. It defines the “social facts” of what central banks “do”.
Question: if this (above) view is correct, what exactly is it that Scott Sumner is *doing* (on this blog)? What *is* he? Not a policy advocate, in the standard sense.
And, if this view is correct, forget about trivia like cutting the overnight rate by 0.25%. Banning all public mention of the overnight rate would be a more effective policy!
I think I may have jumped the shark. Never mind.
26. January 2010 at 09:29
[…] interesting feedback. This is the tail end of a much longer comment he left at the end of my Richard Rorty post from a few days back: Here’s another one, that’s both fun, and deadly serious in current […]
26. January 2010 at 12:16
Scott, I think you missed my point. I think the question “is EMH true” is malformed. Because of the nature of social constructs, ones that are self-de-reinforcing (is that even a word) tend to be unstable. A better way to handle it, is to reform the belief/question in such a way that the answer is self-reinforcing so it is a meaningful institution.
27. January 2010 at 18:57
Nick, I did a post on your comment.
Doc, I have no idea what the last sentence means. What do you mean by “it”? What do you mean by “meaningful institution?”
28. January 2010 at 14:26
I guess I wasn’t clear. And I used a bit of jargon I shouldn’t have.
Institution = “Institutions are structures and mechanisms of social order and cooperation governing the behavior of a set of individuals within a given human collectivity”
A meaningful one would be one that had an actual effect on how people behaved.
By “it”, I meant the epistemological problem we were talking about.
To clarify, in a free market of ideas. Belief in ideas that when believed become true are self-sustaining once it reach a critical point in the amount of acceptance. Thus they become an important part of how society functions. (This is what I meant by “meaningful institution”)
The belief of ideas that are less true when believed, becomes less likely as acceptance in the ideas grow. Thus widespread belief in them are much less likely to be accepted and have an impact on society. So, if we want the parts of EMH that are useful to be accepted we have to reformulate it in a way that allows belief in the reformulated EMH to be self-sustaining.
29. January 2010 at 06:48
Doc, I think is is fine for little guys and academics and government regulators to believe in the EMH. It is still self-sustaining as long as Wall Street pros don’t believe it.
29. January 2010 at 09:24
“Some people argue that the EMH won’t hold if it is believed, as no one would then have an incentive to make the market efficient by searching out information. The same argument could apply to the interest parity condition. If the IPC works perfectly then the expected depreciation of country’s X’s currency should equal the gap between country X’s nominal interest rate and country Y’s nominal interest rate. However this relationship will only hold if arbitragers take advantage of any discrepancies. And if the IPC works perfectly there won’t be any discrepancies.
What happens in the real world? The IPC is a reasonable approximation of reality, at least for most purposes. And that is all that matters. It doesn’t work perfectly, but small discrepancies are enough to generate the needed arbitrage. And I’d say the same about the EMH.”
Maybe the currency market is more efficient than stockmarket, as it is easier to short currencies than stocks. In stockmarkets there are plenty of examples where the same stock trades at wildly different prices on two different exchanges.
31. January 2010 at 07:16
123, I’m confused here. I thought people like Fama only claimed that the EMH held where arbitrage was allowed. If you have exchange controls in a place like China, i would expect stock prices there to be different from the US, because all the fundamentals of their economy are different. If there is a wall between the two markets, doesn’t the EMH allow for different prices?
Nevertheless, I agree with your broader point. My argument wasn’t meant to prove the EMH. It obviously could be false even if the IPC is true as you need a lot more for it to work. Rather I merely intended that as an analogy to help people understand that there was no logical internal contradiction within the EMH, as is often alleged. Or more accurately, the logical internal contradiction might not produce statistically signficant problems for the EMH.
31. January 2010 at 10:59
I was thinking about the cases where there are no capital controls, such as Shell double listing in London and Amsterdam, and more recently Thomson in Canada and London:
“Tuesday, June 23, 2009 12:26 PM
Thomson Reuters (TRI-T35.710.340.96%), the global electronic information company, announced Monday that it would drop its listing on the London Stock Exchange, ending a 144-year-old presence on the British exchange. The Toronto-based company is also traded on New York and Toronto exchanges, and maintained the London listing after the 2008 takeover of Reuters.
this stock consistently traded at a lower price in London than it did in North America. At one point last summer, the British paper traded at a 20 per cent discount to its North American cousin, despite the fact that the two shares enjoyed identical ownership rights in the same company. ”
I agree that the logical internal contradiction is not really important. But for me it is very important to measure the effect of unrealistic assumptions behind the EMH (such as unlimited leverage etc.). And even such obvious cases like Thomson Reurters show that these assumptions are very important.
1. February 2010 at 06:42
123, That is really weird. Investors should have definitely bought shares in the London exchange, why would anyone buy in NY? As soon as they were delisted from London investors got an immediate pop in the price as it was moved to NY, perhaps as much as 20% free money. That is weird. i have no explanation.
1. February 2010 at 13:22
I haven’t seen any academic studies about this very recent Thomson case, but Andrei Shleifer has previously discussed a very similiar Royal Dutch Shell case here:
http://www.cb.wsu.edu/~nwalcott/finance325/template/readings/Are%20Markets%20Efficient%20–%20No.pdf
Shleifer blames noise trader risk.
3. February 2010 at 12:34
123, But that doesn’t answer my question. Why wouldn’t mutual funds choose to buy the less expensive version, if they really were identical?
Here is an anlogy. Two auto dealers are side by side. Both sell identical Camrys. One charges 27,000 and the other charges 25,000. How can that be? Your answer is that it is costly to buy and sell, or arbitrage, the cars. That’s true, you lose more than $2000 the minute you buy a new car. But that doens’t answer the question of why doesn’t every single consumer (mutual fund in my example) buy the cheaper car. Why didn’t every single mutual fund buy the cheaper shell stock?
My hunch is that they weren’t identical. Alternatively, what if both had had the same name, and both sold on American exchanges (NY and Chicago) would the price still have differed?
BTW, You got to love it when someone tries to get rich by beating the market, by assuming the EMH is wrong. Then they fail and go bankrupt, and the anti-EMH people say “see, that proves that the EMH is wrong.”
10. February 2010 at 07:11
British mutual fund prefers Shell listed in London because it is more correlated to FTSE and because it is lazy, dutch mutual fund prefers Shell listed in Amsterdam for similar reasons.
11. February 2010 at 10:38
123, I thought investors prefered investments uncorrelated wit the FTSE.
14. February 2010 at 16:48
Theoretically they should, but in practice majority of investors have a home bias.
15. February 2010 at 09:22
123, But even if they have a home bias, don’t they prefer investments with negative betas? (if that’s the right term–I mean investments with negative correlations with their home index, like products that people buy more of in recessions.)
18. February 2010 at 07:15
But this is just a definition of a home bias. Home bias is avoidance of foreign assets that enhance risk/return profile of your portfolio. Home bias goes contrary to the assumptions and consequences of CAPM.
18. February 2010 at 11:13
123, There is a difference between assets in the FTSE, and assets correlated with the FTSE.