Arrow’s Economics 1

The annual Summer School in Economics at HU was directed until last year by Kenneth Arrow, along with Eyal Winter. Arrow decided this year to step down as a director and Eric Maskin is replacing him. The 2008 Summer School was devoted to Arrow’s economics. The list of speakers was quite impressive, with six lecturers who are Nobel Laureates. (Our local Institute for Advanced Study runs five schools every year, in Physics, Economics, Life Sciences, Jewish Studies, and Mathematics.)

Economic puzzles told by Arrow

Let me tell you about three economics puzzles mentioned by Arrow in an earlier summer school. I doublechecked some details with Arrow himself; still, if my description contains errors I will be happy to be corrected. (Arrow spent a considerable amount of time talking with the workshop students. Another remarkable thing about him: he takes lecture notes! Is it a good idea to take detailed lecture notes at lectures? Let’s return to this question sometime.)

Puzzle 1: Why is there unemployment?

Why is this even a puzzle? Because the economics teaching that “the market will clear” means that all people who can work will. A person who can work and is not working represents inefficiency, which is not supposed to exist in a competitive economy. Part of the issue is referred to as “friction” and accounts for economics processes being slow rather than instantaneous. But it appears to be true that there is more to unemployment than that. What can explain the 30% unemployment that was witnessed in the US in the 1930s?

Is this puzzle a scientific problem? You bet it is! And it is a fairly clear-cut scientific problem. I suppose there are several answers to this puzzle in the literature but we are far from a definite understanding of the issue.

Puzzle 2: What is the reason for high volatility of prices in markets, say in stock markets?

The price of a stock, according to economics theory, represents the long-term value of the company. What accounts for the fact that the overall value of the entire stock market may fluctuate by more than 1% on a typical day? What accounts for fluctuations (more often drops) of 3-5% in one day? (Such fluctuations are not rare.) A famous question is to explain the one-day drop of 20% in October 1987.

Arrow mentioned in this context the Milgrom-Stokey “no trade theorem” which asserts that under certain assumptions markets in equilibrium will exhibit no trade (even if traders have private information).

Private companies conduct a lot of research on stock market behavior, probably much much more so than universities. I asked Arrow whether we should expect some progress toward understanding the fundamental issues regarding stock-market behavior to be achieved there. Arrow was quite skeptical about it.

In my opinion, stock market behavior is an example where scholarly research is important even in areas where much research is taking place outside academia. (It is also an important and delicate matter to ensure that the external research and activity not vitiate academic goals and integrity.)

A relevant blog post concerning financial mathematics is Tao’s recent description of the Black-Scholes formula. Explaining the systematic difference between the Black-Scholes formula and the actual behavior of options prices is another interesting question.

Puzzle 3: What accounts for the huge futures trading in foreign currencies?

Another puzzle that Arrow mentioned is this: futures trading in foreign currencies can be explained by agents involved in international trade wanting to reduce their risk. This suggests that the volume of currency futures trading  will be below the volume of international trade. Yet currency futures trading is 300 times larger. What can explain this phenomenon?

Following are a few lectures that I would like to tell you about, in some detail, in a later post. Maskin’s lectures on social choice and “the robustness of majority rule” were perhaps the lectures closest to my own research interests (and related to Arrow’s theorem about voting). Roger Myerson in his lecture asked: “Is capitalism better than socialism?” He was referring to the Soviet Union-type of socialism and the way firms operate under such a system. John Geanakoplos talked about models of general equilibrium theory with collateral and gave a hilarious account of Shakespeare as economist. His model provides some insight into the current subprime crisis in the US.  And Herb Scarf returned to cooperative game theory and proved his theorem on the nonemptyness of the core for balanced games. A link to all lectures is here

Apropos of the comparison between capitalism and socialism, Myerson’s work does not deal with a comparison between the US system and the slightly more socialist West European version. (The difference does not lie in the way firms operate but in governmental redistribution of resources.) Personally, I like the West European economic free-market system and even the most “socialist,” Scandinavian version of  it, and this once almost got me in trouble. When I visited Stockholm, in the late 80s, I was sitting next to a local Swedish person in a Chinese restaurant on Nybrogatan Street, and I was telling him at some length how highly I thought of the Swedish system. The guy listened carefully to what I said and at the end he was so angered by it that I thought he would kill me. (In Sweden, at that time, the punishment for murder was 10 years in prison, of which only five had to be served; yet murder rates were low.) It appears that one should be careful about giving compliments almost as much as about criticism.

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12 Responses to Arrow’s Economics 1

1. elad verbin says:

Very interesting puzzles. About puzzle 2: the obvious guess would be that it’s an issue related to what Sociologists call Common Knowledge versus other kinds of knowledge. Once someone sells a stock, the other people assume that he has a good reason for selling, so they sell, and then others sell, and so on. The process stops when the price is low enough to make people be willing to take the risk of staying with the stock, even though there’s a bad feeling in the air about it.

Can this kind of intuition be theoretically formalized in a reasonable way? It seems like an interdisciplinary study might be necessary, since we’re dealing with an effect which is no less sociological than mathematical. Do game theorists do these kind of things successfully? I know the notion of common knowledge is developed and used in the game-theory literature (Aumann, Milgrom,…), but does the formalization describe reality in a satisfactory manner? My intuition is that in order to understand the behavior of the stock market, sociological tools must be applied.

About issues related to common knowledge, one reference I particularly like is Steven Pinker’s paper, The Logic of Indirect Speech. (Also see the blog (in Hebrew) מדע בזיוני).

For completeness, here’s an excerpt from the Pinker paper mentioned above, where he gives a brief description of what common knowledge means (page 5; references are available in Pinker’s paper):

[…] a concept that linguists, logicians, and economists have called common knowledge, mutual knowledge, and common ground (2,9,
25–30). In common knowledge, not only does A know x and B knows x, but A knows that B knows x,and B knows that A knows x, and A knows that B knows that A knows x, ad infinitum. As with other phenomena in linguistics in which a person is said to ‘‘know’’ an infinite number of things, the knowledge is not enumerated as an infinite list, of course, but is implicit in a finite recursive formula. In this case, it could be the formula y:
‘‘Everyone knows x, and everyone knows y’’(2). Moreover, common knowledge can be ascertained perceptually, by observing that x is perceptible or broadcasted in public circumstances.

The paradigm illustration of common knowledge is the story of the Emperor’s New Clothes. When the boy called out,
‘‘The emperor is naked!’’ he was not telling the onlookers anything they didn’t already know. Yet he was conveying knowledge nonetheless: Now everyone knew that everyone else knew, and that everyone else knew that they knew, and soon, and that common knowledge licensed the people to challenge the dominance relationship commanded by the emperor. The moral for the present theory is that language is an efficient way of generating common knowledge.

2. Gil says:

Dear Elad, there is a paper by Hart and Tauman oferring an explanation to Stock market’s bubbles and sudden collapses which is close in spirit to issues of common knowledge. You can find it here: http://www.ma.huji.ac.il/~hart/abs/crash.html

3. unemployment is easily solved by framing effects and by the discreet nature of real life.

Someone employed before 1929 for 1,000 finds it humilating/irrational to work for 500. (he may be rational in a way, but that’s another story).

Minimum wage, can also explain unemployment by the low paid, and if it diffuses upward increasing wages upward, it may explain some upper unemployment, too.

Rational unemployment also exist where people do not want to work.

Robert Frank, argues that there is a strong effect to relative consideration in accepting a job. It feels worse to work for 5,000 in a hi-tech company than to work for 4,000 in a restaurant. I guess it complicates the unemployment picture.

Bottom line, the question remains empirical, what are the parameters affecting unemployment in reality. One can check how these data correspond to various models. Remember, that epidemiological studies like these are very vulnerable to biases. In medicine, 80% of epidemiological findings are refuted by controlled experiments, demonstating how far is the hidden space of possibilities.

4. Gil says:

Dear Yechezkel, Maybe I should try to explain what I regard as a definite answer to a puzzle. It is an answer where after examining it we say “wow, we got it” (or something like this). The criteria for a definite answer when it comes to mathematics are themselves clear and definite. In other sciences this is harder.

5. Gil Kalai says:

The question “Is it a good idea to take detailed lecture notes at lectures?” is discussed over math overflow: http://mathoverflow.net/questions/12638/taking-lecture-notes-in-lectures

6. Well I like to browse around when i’m not so busy at work. So are you using any Discreet products? If so what do you use?

7. Véro says:

Je viens de découvrir votre blog, je l’ajoute de suite à mon mon Google reader !

8. Excellent article !

9. Hanoch says:

The big question is why a famous economist is amazed when reality is not following his funny models with ridiculous assumptions. Calling mistakes “puzzles” would lead your search to a wrong direction.

Here are the answers:
1. “…the economics teaching that “the market will clear” means that all people who can work will. A person who can work and is not working represents inefficiency, which is not supposed to exist in a competitive economy.”

>>your theory is not good (the economy is not competitive, people are not rational, etc) – every economist is aware of this fact. This is why economic theory cannot describe reality.

2. “Puzzle 2: What is the reason for high volatility of prices in markets, say in stock markets? The price of a stock, according to economics theory, represents…”

>>Why do you use the word “high”? What is the “right” volatility which the theory predicts? What volatility would be considered too low, according to the theory? (none)

3. “What accounts for the huge futures trading in foreign currencies?”

>>International trade is only a small fraction of the fx market, because there is a lot of speculation going on. What’s the puzzle? Why you say that the fx trade is “huge”, instead of saying that the error result from your calculations is “huge”?

10. Gil Kalai says:

Dear Hanoch, I am not sure that you really offer solutions to Arrow’s puzzle rather than rephrasing them in your own word.