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.